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A METHOD TO CALCULATE $Q_{\rm BRST}^2$ IN THE PATH-INTEGRAL QUANTIZATION

Y. Igarashi, Jisuke Kubo, S. Sakakibara

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Abstract

The BRST transformation of wave functional represented in a finite-time path-integral is analyzed in the generalized Hamiltonian formalism of Batalin, Fradkin, and Vilkovisky, and it is shown that the anomalous Schwinger terms that appear in the nilpotency condition and the time development of BRST charge Q BRST can be directly calculated in the path-integral quantization. We explicitly compute [Formula: see text] in a chiral Yang–Mills theory. The method is general in character, and can easily be applied to other theories.

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What this paper is about

The BRST transformation of wave functional represented in a finite-time path-integral is analyzed in the generalized Hamiltonian formalism of Batalin, Fradkin, and Vilkovisky, and it is shown that the anomalous Schwinger terms that appear in the nilpotency condition and the time development of BRST charge Q BRST can be directly calculated in the path-integral quantization. We explicitly compute [Formula: see text] in a chiral Yang–Mills theory. The method is general in character, and can easily be applied to other theories.

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Available abstract

The BRST transformation of wave functional represented in a finite-time path-integral is analyzed in the generalized Hamiltonian formalism of Batalin, Fradkin, and Vilkovisky, and it is shown that the anomalous Schwinger terms that appear in the nilpotency condition and the time development of BRST charge Q BRST can be directly calculated in the path-integral quantization. We explicitly compute [Formula: see text] in a chiral Yang–Mills theory. The method is general in character, and can easily be applied to other theories.

Key concepts: BRST quantization, Path integral formulation, Physics, Quantization (signal processing), Mathematical physics, Hamiltonian (control theory), Formalism (music), Hamiltonian formalism

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