theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

, a spurion is a fictitious, auxiliary field in a

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

that can be used to parameterize any

symmetry breaking In physics, symmetry breaking is a phenomenon where a disordered but Symmetry in quantum mechanics, symmetric state collapses into an ordered, but less symmetric state. This collapse is often one of many possible Bifurcation theory, bifurcatio ...

and to determine all operators invariant under the symmetry. The procedure begins with finding a parameter that measures the amount of symmetry breaking. This parameter is promoted to a field, i.e. to a function of the spacetime coordinates. With this new fictitious field, operators that are invariant under the symmetry may be found by the usual group-theoretical considerations. The list of operators found in this way is complete as long as all sources of the breaking are included. The operators in the actual theory are ultimately found by setting the spurious field equal to the constant value of the parameter.

Applications

In the theory of

pion In particle physics, a pion (, ) or pi meson, denoted with the Greek alphabet, Greek letter pi (letter), pi (), is any of three subatomic particles: , , and . Each pion consists of a quark and an antiquark and is therefore a meson. Pions are the ...

s, physics often uses the

chiral perturbation theory Chiral perturbation theory (ChPT) is an effective field theory constructed with a Lagrangian (field theory), Lagrangian consistent with the (approximate) chiral symmetry of quantum chromodynamics (QCD), as well as the other symmetries of parity (ph ...

. Here, the relevant symmetry is the

isospin In nuclear physics and particle physics, isospin (''I'') is a quantum number related to the up- and down quark content of the particle. Isospin is also known as isobaric spin or isotopic spin. Isospin symmetry is a subset of the flavour symmetr ...

SU(2) symmetry. It is broken by the different masses of u and d

quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...

s as well as by their different charges. The chiral Lagrangian may be extended to an exactly SU(2)-symmetric Lagrangian by promoting these parameters (mass and charge) to fields that break the symmetry spontaneously. Calculations of observables to higher orders may be done with the spurion fields. The final result, at any order of accuracy, is obtained by substituting the right masses and charges. In the standard electroweak theory, the spurion is replaced by an actual field, the

Higgs boson The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the excited state, quantum excitation of the Higgs field, one of the field (physics), fields in particl ...

. However, in alternative theories of electroweak symmetry breaking, e.g. those based on

Technicolor Technicolor is a family of Color motion picture film, color motion picture processes. The first version, Process 1, was introduced in 1916, and improved versions followed over several decades. Definitive Technicolor movies using three black-and ...

, the spurion techniques are important to derive the physical predictions. Quantum field theory {{quantum-stub