In 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...

, a tadpole is a one-loop Feynman diagram

Feynman diagram

Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...

 with one external leg, giving a contribution to a one-point correlation function

Correlation function (quantum field theory)

In quantum field theory, the matrix element computed by inserting a product of operators between two states, usually the vacuum states, is called a correlation function....

 (i.e., the field's vacuum expectation value

Vacuum expectation value

In quantum field theory the vacuum expectation value of an operator is its average, expected value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle...

). One-loop diagrams with a 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...

 that connects back to its originating vertex are often also referred as tadpoles. For many massless theories, these graphs vanish in dimensional regularization

Dimensional regularization

In theoretical physics, dimensional regularization is a method introduced by Giambiagi and Bollini for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of an auxiliary complex parameter d, called the...

 (by dimensional analysis

Dimensional analysis

In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...

 and the absence of any inherent mass scale in the loop integral

Loop integral

In quantum field theory and statistical mechanics, loop integrals are the integrals which appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta....

).



The physics of tadpoles and the word tadpole was invented by Sidney Coleman

Sidney Coleman

Sidney Richard Coleman was an American theoretical physicist who studied under Murray Gell-Mann.- Life and work :Sidney Coleman grew up on the Far North Side of Chicago...

. The editor was not satisfied, but he changed his mind once Sidney Coleman proposed spermion instead. Both words are derived from the shape of the Feynman diagram: a circle with a line interval attached to its external side. Tadpole diagrams, in this sense, first appear in the above-mentioned article by Coleman and Glashow, Physical Review v. 134, p.B671 (1964).