Reinhard Oehme
Encyclopedia
Reinhard Oehme was a German-American physicist
known for the discovery of C (charge conjugation
) non-conservation in the presence of P (parity
) violation, the formulation and proof of hadron
dispersion relations, the "Edge of the Wedge Theorem" in the function theory of several complex variables
, the Goldberger-Miyazawa-Oehme sum rule
, reduction of quantum field theories, Oehme-Zimmermann superconvergence
relations for gauge field
correlation functions, and many other contributions.
Oehme was born in Wiesbaden
, Germany as the son of Dr. Reinhold Oehme and Katharina Kraus. In 1952, in São Paulo
,Brazil, he married Mafalda Pisani, who was born in Berlin as the daughter of Giacopo Pisani and Wanda d'Alfonso. Mafalda died in Chicago in August of the year 2004.
near Wiesbaden, Oehme started to study physics and mathematics at the Johann Wolfgang Goethe University Frankfurt am Main, receiving the Diploma in 1948 as student of Erwin Madelung
.
Then he moved to Göttingen
, joining the Max Planck Institute for Physics
as a doctoral student of Werner Heisenberg
, who was also a professor at the University of Göttingen. Early in 1951, Oehme completed the requirements for his Dr.rer.nat at Göttingen Universität. The translation of the title of his thesis is: „Creation of Photon
s in Collisions of Nucleon
s” Later this year, Heisenberg asked him to join Carl Friedrich von Weizsäcker
on a trip to Brazil for the start-up of the Instituto de Física Teórica in São Paulo, considered also as a possible escape in view of the tense situation in Europe. In 1953, he returned to his assistant position at the Max Planck Institute in Göttingen. During the early fifties, the Institute was a most interesting place. Oehme was there among an exceptional group of people around Heisenberg, including Vladimir Glaser, Rolf Hagedorn
, Fritz Houtermans
, Gerhard Lüders, Walter Thirring
, Kurt Symanzik
, Carl Friedrich von Weizsaecker, Wolfhart Zimmermann
, Bruno Zumino
, who all have made important contributions to physics at some time.
A year later, with Heisenberg's recommendation to his friend Enrico Fermi
, Oehme was offered a research associate position at the University of Chicago
, where he worked at the Institute for Nuclear Studies. Publications associated with this
period are described below under Work. In the fall of 1956, he moved to Princeton as a member of the Institute for Advanced Study
, returning in 1958 to the University of Chicago as a professor in the Department of Physics and at the Enrico Fermi Institute
for Nuclear Studies. Since 1998, he is professor emeritus.
Visiting Professor Positions*:
University of Maryland, College Park
, 1957; Universität Wien, Austria 1961; Imperial College, London1963-64;
Universität Karlsruhe, Germany, 1974, 1975, 1977; University of Tokyo
, Japan, 1976, 1988;
Research Institute of Fundamental Physics, University of Kyoto, Japan, 1976.
Visiting Positions*:
Instituto de Física Teórica, São Paulo, Brasil; Brookhaven National Laboratory
; Lawrence Berkeley National Laboratory
; CERN
, Geneva, Switzerland; International Centre for Theoretical Physics
, Miramare-Trieste, Italy; Max Planck Institute for Physics
, München, Germany.
Awards*:
Guggenheim Fellow, 1963-64: Humboldt Price, 1974; Japan Society (JSPS) Award, 1976.
Fellow: American Physical Society
.
(*For citations see corresponding publications and acknowledgements in publications.
)
properties of forward
Scattering amplitude
s in quantum field theories. He found that particle-particle and
antiparticle
-particle amplitudes are connected by analytic continuation
in the
complex energy plane. These results led to the paper by him with Marvin L. Goldberger
and Hironari Miyazawa on the dispersion relations for pion
-nucleon
scattering, which
also contains the Goldberger-Miyazawa-Oehme Sum Rule.
There is good agreement with the experimental results of the Fermi Group
at Chicago, the Lindenbaum
Group at Brookhaven and others.
The GMO Sum Rule is often used in the analysis of the pion-nucleon system.
Oehme published a proper derivation of hadronic forward dispersion relations on the basis of
local quantum field theory
in an article published in Il Nuovo Cimento. His proof remains
valid in gauge theories with confinement
.
The analytic
connection Oehme found between particle and antiparticle
amplitudes is the first example of a fundamental feature of local quantum field theory
: the crossing property. It is proven here, in a non-perturbative setting, on the basis of the analytic properties of amplitudes which are a consequence of locality
and spectrum
, like the dispersion relations. For generalizations, one still relies mostly on perturbation theory
.
For the purpose of using the powerful methods of the theory of functions
of several complex variables
for the proof of non-forward dispersion relations,
and for analytic
properties of other Greens functions, Oehme formulated and proved a fundamental theorem which he called the “Edge of the Wedge Theorem” (“Keilkanten Theorem”). This work was done mainly in the Fall of 1956 at the Institute for Advanced Study
in collaboration with Hans-Joachim Bremermann
and John G. Taylor
.
Using microscopic causality
and spectral properties, the BOT theorem provides
an initial region of analyticity, which can be enlarged by "Analytic Completion".
Oehme first presented these results at the Princeton University Colloquium
during the winter semester 1956/57. Independently, a different and elaborate proof of
non-forward dispersion relations has been published by Nikolay Bogoliubov and collaborators.
The Edge of the Wedge Theorem of BOT has many other applications.
For example, it can be used to show that, in the presence of (spontaneous) violations of Lorentz invariance, micro-causality (locality), together
with positivity of the energy, implies Lorentz invariance of the energy-
momentum spectrum.
Together with Marvin L. Goldberger and Yoichiro Nambu
, Oehme also has formulated dispersion relations
for nucleon-nucleon scattering.
shown that weak interactions must violate charge conjugation conservation in the event
of a positive outcome of the polarization experiment in beta-decay. Since parity
conservation leads to the same restrictions, he points out that C and P must BOTH
be violated in order to get an asymmetry. Hence, at the level of ordinary weak
interactions, CP is the relevant symmetry, and not C and P individually.
Violation of C is one of the fundamental conditions for the matter-antimatter
asymmetry of the Universe.
The results of Oehme form the basis for the
later experimental effort to study CP Symmetry, and the fundamental discovery of non-conservation at a lower level of interaction strength.
As indicated above, the letter is reprinted
in the book on Selected Papers by C.N. Yang.
Prompted by the letter, T D Lee, R Oehme and C N Yang provided a detailed discussion of
the interplay of non-invariance under P, C and T, and of applications to
the Kaon
- anti-Kaon complex. Their results are of importance for the description of the CP violation
discovered later. In their paper the authors already consider non-invariance under T (time reversal
)
and hence, given the assumption of CPT symmetry
, also under CP.
propagator
s,
undertaken by Oehme in collaboration with Wolfhart Zimmermann
,
he obtained "Superconvergence
Relations" for theories where the number of matter
fields (flavors) is below a given limit. These "Oehme-Zimmernann Relations" provide a link between long- and short-distance properties of the theory. They are of importance for gluon
confinement.
These results about propagators depend essentially only upon general principles.
several parameters, Oehme and Zimmermann have introduced a theory of reduction
of coupling constants.
This method is based upon the renormalization group
, and is more general than the
imposition of symmetries.
There are solutions of the reduction equations which do not correspond to additional symmetries, but may be related to other characteristic aspects of the theory. On the other hand, supersymmetric theories do come out as possible solutions. This is an important example for the appearance of supersymmetry
without imposing it explicitly. The reduction theory is finding many applications, theoretical
and phenomenological.
,
Rising Cross section
s, Broken Symmetries, Current algebra
s and Weak Interactions, as well as chapters in books, may be found in:
(http://home.uchicago.edu/~roehme/).
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
known for the discovery of C (charge conjugation
C-symmetry
In physics, C-symmetry means the symmetry of physical laws under a charge-conjugation transformation. Electromagnetism, gravity and the strong interaction all obey C-symmetry, but weak interactions violate C-symmetry.-Charge reversal in electromagnetism:...
) non-conservation in the presence of P (parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
) violation, the formulation and proof of hadron
Hadron
In particle physics, a hadron is a composite particle made of quarks held together by the strong force...
dispersion relations, the "Edge of the Wedge Theorem" in the function theory of several complex variables
Several complex variables
The theory of functions of several complex variables is the branch of mathematics dealing with functionson the space Cn of n-tuples of complex numbers...
, the Goldberger-Miyazawa-Oehme sum rule
Sum rule
Sum rule may refer to:*Sum rule in differentiation*Sum rule in integration*Rule of sum, a counting principle in combinatorics*Sum rule in quantum mechanics...
, reduction of quantum field theories, Oehme-Zimmermann superconvergence
Superconvergence
In numerical analysis, a superconvergent method is one which converges faster than generally expected. For example in the Finite Element Method approximation to Poisson's equation in two dimensions, using piecewise linear elements, the average error in the gradient is first order...
relations for gauge field
Gauge theory
In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
correlation functions, and many other contributions.
Oehme was born in Wiesbaden
Wiesbaden
Wiesbaden is a city in southwest Germany and the capital of the federal state of Hesse. It has about 275,400 inhabitants, plus approximately 10,000 United States citizens...
, Germany as the son of Dr. Reinhold Oehme and Katharina Kraus. In 1952, in São Paulo
São Paulo
São Paulo is the largest city in Brazil, the largest city in the southern hemisphere and South America, and the world's seventh largest city by population. The metropolis is anchor to the São Paulo metropolitan area, ranked as the second-most populous metropolitan area in the Americas and among...
,Brazil, he married Mafalda Pisani, who was born in Berlin as the daughter of Giacopo Pisani and Wanda d'Alfonso. Mafalda died in Chicago in August of the year 2004.
Education and career
Completing the `Abitur´ at the Rheingau Gymnasium in GeisenheimGeisenheim
Geisenheim is a town in the Rheingau-Taunus-Kreis in the Regierungsbezirk of Darmstadt in Hessen, Germany, and is known as Weinstadt , Schulstadt , Domstadt and Lindenstadt ....
near Wiesbaden, Oehme started to study physics and mathematics at the Johann Wolfgang Goethe University Frankfurt am Main, receiving the Diploma in 1948 as student of Erwin Madelung
Erwin Madelung
Erwin Madelung was a German physicist.He was born in 1881 in Bonn. His father was the surgeon Otto Wilhelm Madelung. He earned a doctorate in 1905 from the University of Göttingen, specializing in crystal structure, and eventually became a professor...
.
Then he moved to Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
, joining the Max Planck Institute for Physics
Max Planck Institute for Physics
Max Planck Institute for Physics is a physics institute in Munich, Germany that specializes in High Energy Physics and Astroparticle physics. It is part of the Max-Planck-Gesellschaft and is also known as the Werner Heisenberg Institute, after its first director.It was founded as the Kaiser Wilhelm...
as a doctoral student of Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
, who was also a professor at the University of Göttingen. Early in 1951, Oehme completed the requirements for his Dr.rer.nat at Göttingen Universität. The translation of the title of his thesis is: „Creation of Photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s in Collisions of Nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
s” Later this year, Heisenberg asked him to join Carl Friedrich von Weizsäcker
Carl Friedrich von Weizsäcker
Carl Friedrich Freiherr von Weizsäcker was a German physicist and philosopher. He was the longest-living member of the research team which performed nuclear research in Germany during the Second World War, under Werner Heisenberg's leadership...
on a trip to Brazil for the start-up of the Instituto de Física Teórica in São Paulo, considered also as a possible escape in view of the tense situation in Europe. In 1953, he returned to his assistant position at the Max Planck Institute in Göttingen. During the early fifties, the Institute was a most interesting place. Oehme was there among an exceptional group of people around Heisenberg, including Vladimir Glaser, Rolf Hagedorn
Rolf Hagedorn
Rolf Hagedorn was a German theoretical physicists working at CERN. He is known for the idea that hadronic matter has a "melting point". The Hagedorn temperature is named in his honor.-Early life:...
, Fritz Houtermans
Fritz Houtermans
Friedrich Georg "Fritz" Houtermans was a Dutch-Austrian-German atomic and nuclear physicist born in Zoppot near Danzig, West Prussia...
, Gerhard Lüders, Walter Thirring
Walter Thirring
Walter Thirring is an Austrian physicist after whom the Thirring model in quantum field theory is named. He is son of the physicist Hans Thirring, co-discoverer of the Lense-Thirring frame dragging effect in general relativity....
, Kurt Symanzik
Kurt Symanzik
Kurt Symanzik was a German physicist working in quantum field theory.- Life :Symanzik was born in Lyck , East Prussia, and spent his childhood in Königsberg. He started studying physics in 1946 at Universität München but after a short time moved to Werner Heisenberg at Göttingen...
, Carl Friedrich von Weizsaecker, Wolfhart Zimmermann
Wolfhart Zimmermann
Wolfhart Zimmermann is a German theoretical physicist. Zimmermann attained a doctorate in 1950 at Freiburg im Breisgau in topology . In the 1950s he was at Göttingen one of the pioneers of the mathematical quantum field theory; along with Kurt Symanzik and Harry Lehmann he developed the LSZ theory...
, Bruno Zumino
Bruno Zumino
Bruno Zumino is an Italian theoretical physicist and emeritus faculty at the University of California, Berkeley. He got his bachelor degree from the University of Rome in 1945...
, who all have made important contributions to physics at some time.
A year later, with Heisenberg's recommendation to his friend Enrico Fermi
Enrico Fermi
Enrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...
, Oehme was offered a research associate position at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
, where he worked at the Institute for Nuclear Studies. Publications associated with this
period are described below under Work. In the fall of 1956, he moved to Princeton as a member of the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
, returning in 1958 to the University of Chicago as a professor in the Department of Physics and at the Enrico Fermi Institute
Enrico Fermi Institute
The Institute for Nuclear Studies was founded September, 1945 as part of the University of Chicago with Samuel King Allison as director. On November 20, 1955 it was renamed The Enrico Fermi Institute for Nuclear Studies...
for Nuclear Studies. Since 1998, he is professor emeritus.
Visiting Professor Positions*:
University of Maryland, College Park
University of Maryland, College Park
The University of Maryland, College Park is a top-ranked public research university located in the city of College Park in Prince George's County, Maryland, just outside Washington, D.C...
, 1957; Universität Wien, Austria 1961; Imperial College, London1963-64;
Universität Karlsruhe, Germany, 1974, 1975, 1977; University of Tokyo
University of Tokyo
, abbreviated as , is a major research university located in Tokyo, Japan. The University has 10 faculties with a total of around 30,000 students, 2,100 of whom are foreign. Its five campuses are in Hongō, Komaba, Kashiwa, Shirokane and Nakano. It is considered to be the most prestigious university...
, Japan, 1976, 1988;
Research Institute of Fundamental Physics, University of Kyoto, Japan, 1976.
Visiting Positions*:
Instituto de Física Teórica, São Paulo, Brasil; Brookhaven National Laboratory
Brookhaven National Laboratory
Brookhaven National Laboratory , is a United States national laboratory located in Upton, New York on Long Island, and was formally established in 1947 at the site of Camp Upton, a former U.S. Army base...
; Lawrence Berkeley National Laboratory
Lawrence Berkeley National Laboratory
The Lawrence Berkeley National Laboratory , is a U.S. Department of Energy national laboratory conducting unclassified scientific research. It is located on the grounds of the University of California, Berkeley, in the Berkeley Hills above the central campus...
; CERN
CERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
, Geneva, Switzerland; International Centre for Theoretical Physics
International Centre for Theoretical Physics
The Abdus Salam International Centre for Theoretical Physics was founded in 1964 by Pakistani scientist and Nobel Laureate Abdus Salam after consulting with Munir Ahmad Khan. It operates under a tripartite agreement among the Italian Government, UNESCO, and International Atomic Energy Agency...
, Miramare-Trieste, Italy; Max Planck Institute for Physics
Max Planck Institute for Physics
Max Planck Institute for Physics is a physics institute in Munich, Germany that specializes in High Energy Physics and Astroparticle physics. It is part of the Max-Planck-Gesellschaft and is also known as the Werner Heisenberg Institute, after its first director.It was founded as the Kaiser Wilhelm...
, München, Germany.
Awards*:
Guggenheim Fellow, 1963-64: Humboldt Price, 1974; Japan Society (JSPS) Award, 1976.
Fellow: American Physical Society
American Physical Society
The American Physical Society is the world's second largest organization of physicists, behind the Deutsche Physikalische Gesellschaft. The Society publishes more than a dozen scientific journals, including the world renowned Physical Review and Physical Review Letters, and organizes more than 20...
.
(*For citations see corresponding publications and acknowledgements in publications.
)
Dispersion Relations, GMO Sum Rule, and Edge of the Wedge Theorem
In 1954 in Chicago, Oehme studied the analyticComplex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
properties of forward
Scattering amplitude
Scattering amplitude
In quantum physics, the scattering amplitude is the amplitude of the outgoing spherical wave relative to the incoming plane wave in the stationary-state scattering process...
s in quantum field theories. He found that particle-particle and
antiparticle
Antiparticle
Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...
-particle amplitudes are connected by analytic continuation
Analytic continuation
In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function. Analytic continuation often succeeds in defining further values of a function, for example in a new region where an infinite series representation in terms of which...
in the
complex energy plane. These results led to the paper by him with Marvin L. Goldberger
and Hironari Miyazawa on the dispersion relations for pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
-nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
scattering, which
also contains the Goldberger-Miyazawa-Oehme Sum Rule.
There is good agreement with the experimental results of the Fermi Group
at Chicago, the Lindenbaum
Lindenbaum
Lindenbaum is a surname, meaning Tilia in German; the nearest British tree name is Lime tree. It may refer to:* Adolf Lindenbaum, Polish mathematician** Lindenbaum's lemma** Lindenbaum–Tarski algebra* John Lindenbaum, musician...
Group at Brookhaven and others.
The GMO Sum Rule is often used in the analysis of the pion-nucleon system.
Oehme published a proper derivation of hadronic forward dispersion relations on the basis of
local quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
in an article published in Il Nuovo Cimento. His proof remains
valid in gauge theories with confinement
Confinement
Confinement may refer to either* Civil confinement for psychiatric patients* Color confinement, the physical principle explaining the non-observation of color charged particles like free quarks* Solitary confinement, a strict form of imprisonment...
.
The analytic
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
connection Oehme found between particle and antiparticle
Antiparticle
Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...
amplitudes is the first example of a fundamental feature of local quantum field theory
Local quantum field theory
The Haag-Kastler axiomatic framework for quantum field theory, named after Rudolf Haag and Daniel Kastler, is an application to local quantum physics of C*-algebra theory. It is therefore also known as Algebraic Quantum Field Theory...
: the crossing property. It is proven here, in a non-perturbative setting, on the basis of the analytic properties of amplitudes which are a consequence of locality
Locality
Locality may refer to:* Locality, a.k.a. human settlement* Locality of reference in computer-science data-access issue* Locality * Locality * Locality, physics concept re principle of locality* Locality in astronomy...
and spectrum
Spectrum
A spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...
, like the dispersion relations. For generalizations, one still relies mostly on perturbation theory
Perturbation theory
Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...
.
For the purpose of using the powerful methods of the theory of functions
of several complex variables
Several complex variables
The theory of functions of several complex variables is the branch of mathematics dealing with functionson the space Cn of n-tuples of complex numbers...
for the proof of non-forward dispersion relations,
and for analytic
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others...
properties of other Greens functions, Oehme formulated and proved a fundamental theorem which he called the “Edge of the Wedge Theorem” (“Keilkanten Theorem”). This work was done mainly in the Fall of 1956 at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in collaboration with Hans-Joachim Bremermann
Hans-Joachim Bremermann
Hans-Joachim Bremermann was a German-American mathematician and biophysicist. He worked on computer science and evolution, introducing new ideas of how mating generates new gene combinations...
and John G. Taylor
John G. Taylor
John Gerald Taylor, born 1931, gained a PhD from Christ's College, Cambridge . He has had a wide ranging academic career in mathematical physics and artificial intelligence. He is currently Emeritus Professor and Director of the Centre for Neural Networks at King's College London and Guest...
.
Using microscopic causality
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
and spectral properties, the BOT theorem provides
an initial region of analyticity, which can be enlarged by "Analytic Completion".
Oehme first presented these results at the Princeton University Colloquium
during the winter semester 1956/57. Independently, a different and elaborate proof of
non-forward dispersion relations has been published by Nikolay Bogoliubov and collaborators.
The Edge of the Wedge Theorem of BOT has many other applications.
For example, it can be used to show that, in the presence of (spontaneous) violations of Lorentz invariance, micro-causality (locality), together
with positivity of the energy, implies Lorentz invariance of the energy-
momentum spectrum.
Together with Marvin L. Goldberger and Yoichiro Nambu
Yoichiro Nambu
is a Japanese-born American physicist, currently a professor at the University of Chicago. Known for his contributions to the field of theoretical physics, he was awarded a one-half share of the Nobel Prize in Physics in 2008 for the discovery of the mechanism of spontaneous broken symmetry in...
, Oehme also has formulated dispersion relations
for nucleon-nucleon scattering.
Charge Conjugation Non-Conservation
On August 7, 1956, Oehme wrote a letter to C.N. Yang in which it isshown that weak interactions must violate charge conjugation conservation in the event
of a positive outcome of the polarization experiment in beta-decay. Since parity
Parity
Parity may refer to:* Parity , a symmetry property of physical quantities or processes under spatial inversion* Parity , indicates whether a number is even or odd...
conservation leads to the same restrictions, he points out that C and P must BOTH
be violated in order to get an asymmetry. Hence, at the level of ordinary weak
interactions, CP is the relevant symmetry, and not C and P individually.
Violation of C is one of the fundamental conditions for the matter-antimatter
asymmetry of the Universe.
The results of Oehme form the basis for the
later experimental effort to study CP Symmetry, and the fundamental discovery of non-conservation at a lower level of interaction strength.
As indicated above, the letter is reprinted
in the book on Selected Papers by C.N. Yang.
Prompted by the letter, T D Lee, R Oehme and C N Yang provided a detailed discussion of
the interplay of non-invariance under P, C and T, and of applications to
the Kaon
Kaon
In particle physics, a kaon is any one of a group of four mesons distinguished by the fact that they carry a quantum number called strangeness...
- anti-Kaon complex. Their results are of importance for the description of the CP violation
CP violation
In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...
discovered later. In their paper the authors already consider non-invariance under T (time reversal
Time reversal
Time reversal may refer to:* In physics, T-symmetry - the study of thermodynamics and the symmetry of certain physical laws where the concept of time is reversed — ie...
)
and hence, given the assumption of CPT symmetry
CPT symmetry
CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...
, also under CP.
Propagators and OZ Superconvergence Relations
In connection with an exact structure analysis for gauge theoryGauge theory
In physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
propagator
Propagator
In quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum. Propagators are used to represent the contribution of virtual particles on the internal...
s,
undertaken by Oehme in collaboration with Wolfhart Zimmermann
Wolfhart Zimmermann
Wolfhart Zimmermann is a German theoretical physicist. Zimmermann attained a doctorate in 1950 at Freiburg im Breisgau in topology . In the 1950s he was at Göttingen one of the pioneers of the mathematical quantum field theory; along with Kurt Symanzik and Harry Lehmann he developed the LSZ theory...
,
he obtained "Superconvergence
Superconvergence
In numerical analysis, a superconvergent method is one which converges faster than generally expected. For example in the Finite Element Method approximation to Poisson's equation in two dimensions, using piecewise linear elements, the average error in the gradient is first order...
Relations" for theories where the number of matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
fields (flavors) is below a given limit. These "Oehme-Zimmernann Relations" provide a link between long- and short-distance properties of the theory. They are of importance for gluon
Gluon
Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
confinement.
These results about propagators depend essentially only upon general principles.
Reduction of Quantum Field Theories
As a general method of imposing restrictions on quantum field theories withseveral parameters, Oehme and Zimmermann have introduced a theory of reduction
of coupling constants.
This method is based upon the renormalization group
Renormalization group
In theoretical physics, the renormalization group refers to a mathematical apparatus that allows systematic investigation of the changes of a physical system as viewed at different distance scales...
, and is more general than the
imposition of symmetries.
There are solutions of the reduction equations which do not correspond to additional symmetries, but may be related to other characteristic aspects of the theory. On the other hand, supersymmetric theories do come out as possible solutions. This is an important example for the appearance of supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
without imposing it explicitly. The reduction theory is finding many applications, theoretical
and phenomenological.
Other Contributions
Further contributions by Oehme, like those involving complex angular momentumAngular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
,
Rising Cross section
Cross section (physics)
A cross section is the effective area which governs the probability of some scattering or absorption event. Together with particle density and path length, it can be used to predict the total scattering probability via the Beer-Lambert law....
s, Broken Symmetries, Current algebra
Current algebra
Current algebra is a mathematical framework in quantum field theory where the fields form a Lie algebra under their commutation relations.For instance, in a non-Abelian Yang–Mills symmetry, where ρ is the charge density,...
s and Weak Interactions, as well as chapters in books, may be found in:
(http://home.uchicago.edu/~roehme/).