Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism

Details Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism

2008-12-02

arxiv.org/abs/0812.0580v2

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, typos corrected, preprint of P.N. Lebedev Physical Institute, No. 39, 1975

Scientific paper

We obtain the Ward identities and the gauge-dependence of Green's functions in non-Abelian gauge theories by using only the canonical commutation relations and the equations of motion for the Heisenberg operators. The consideration is applicable to theories both with and without spontaneous symmetry breaking. We present a definition of a generalized statistical average which ensures that the Fourier images of temperature Green's functions of the Fermionic fields have only even-valued frequencies. This makes it possible to set up a procedure of gauge-invariant statistical averaging in terms of the Hamiltonian and the field operators.

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