In
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
, the quantum effective action is a modified expression for the
classical action
Action may refer to:
* Action (narrative), a literary mode
* Action fiction, a type of genre fiction
* Action game, a genre of video game
Film
* Action film, a genre of film
* ''Action'' (1921 film), a film by John Ford
* ''Action'' (1980 fil ...
taking into account quantum corrections while ensuring that the
principle of least action
The stationary-action principle – also known as the principle of least action – is a variational principle that, when applied to the '' action'' of a mechanical system, yields the equations of motion for that system. The principle states tha ...
applies, meaning that extremizing the effective action yields the
equations of motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...
for the
vacuum expectation values of the quantum fields. The effective action also acts as a
generating functional
In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary series ...
for one-particle irreducible
correlation functions
The cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors. The cross-correlation matrix is used in various digital signal processing algorithms.
D ...
. The potential component of the effective action is called the effective potential, with the expectation value of the true vacuum being the minimum of this potential rather than the classical potential, making it important for studying
spontaneous symmetry breaking
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the ...
.
It was first defined
perturbatively by
Jeffrey Goldstone
Jeffrey Goldstone (born 3 September 1933) is a British theoretical physicist and an ''emeritus'' physics faculty member at the MIT Center for Theoretical Physics.
He worked at the University of Cambridge until 1977. He is famous for the discove ...
and
Steven Weinberg
Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interactio ...
in 1962, while the non-perturbative definition was introduced by
Bryce DeWitt
Bryce Seligman DeWitt (January 8, 1923 – September 23, 2004), was an American theoretical physicist noted for his work in gravitation and quantum field theory.
Life
He was born Carl Bryce Seligman, but he and his three brothers, including ...
in 1963 and independently by
Giovanni Jona-Lasinio
Giovanni Jona-Lasinio (born 1932), sometimes called Gianni Jona, is an Italian theoretical physicist, best known for his works on quantum field theory and statistical mechanics. He pioneered research concerning spontaneous symmetry breaking, and ...
in 1964.
The article describes the effective action for a single
scalar field
In mathematics and physics, a scalar field is a function (mathematics), function associating a single number to every point (geometry), point in a space (mathematics), space – possibly physical space. The scalar may either be a pure Scalar ( ...
, however, similar results exist for multiple scalar or
fermionic
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
fields.
Generating functionals
''These generation functionals also have applications in
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
and
information theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
, with slightly different factors of
and sign conventions.''
A quantum field theory with action