Felix Alexandrovich Berezin was a Soviet

Soviet Union

The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....

 Russian

Russians

The Russian people are an East Slavic ethnic group native to Russia, speaking the Russian language and primarily living in Russia and neighboring countries....

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 and physicist

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 his contributions to the theory 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...

 and supermanifold

Supermanifold

In physics and mathematics, supermanifolds are generalizations of the manifold concept based on ideas coming from supersymmetry. Several definitions are in use, some of which are described below.- Physics :...

s as well as to the path integral formulation

Path integral formulation

The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...

 of 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...

.

Berezin studied at the Moscow State University

Moscow State University

Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...

, but was not allowed to do his graduate studies there on account of his Jewish origin (his mother was Jewish). For the next three years Berezin taught at Moscow high schools. He continued to study mathematical physics under direction of Israel Gelfand

Israel Gelfand

Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand was a Soviet mathematician who made major contributions to many branches of mathematics, including group theory, representation theory and functional analysis...

. After Khrushchev

Nikita Khrushchev

Nikita Sergeyevich Khrushchev led the Soviet Union during part of the Cold War. He served as First Secretary of the Communist Party of the Soviet Union from 1953 to 1964, and as Chairman of the Council of Ministers, or Premier, from 1958 to 1964...

's liberalization, he joined the Department of Mathematics at the Moscow State University at the age of 25.

The Berezin integral

Berezin integral

In mathematical physics, a Grassmann integral, or, more correctly, Berezin integral, is a way to define integration for functions of Grassmann variables. It is not an integral in the Lebesgue sense; it is called integration because it has analogous properties and since it is used in physics as a...

 over anticommuting Grassmann variables is named for him, as is the closely related construction of the Berezinian

Berezinian

In mathematics and theoretical physics, the Berezinian or superdeterminant is a generalization of the determinant to the case of supermatrices. The name is for Felix Berezin...

 which may be regarded as the "super"-analog of the determinant

Determinant

In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific arithmetic expression, while other ways to determine its value exist as well...

.

Berezin drowned during a summer trip in Kolyma

Kolyma

The Kolyma region is located in the far north-eastern area of Russia in what is commonly known as Siberia but is actually part of the Russian Far East. It is bounded by the East Siberian Sea and the Arctic Ocean in the north and the Sea of Okhotsk to the south...

 region.

Works

• The Method of Second Quantization, Academic Press (1966).
• Introduction to Superanalysis, Springer (1987).

External links