Title: Schwinger-Keldysh superspace in quantum mechanics

Abstract

We examine, in a quantum mechanical setting, the Hilbert space representation of the Becchi, Rouet, Stora, and Tyutin (BRST) symmetry associated with Schwinger-Keldysh path integrals. This structure had been postulated to encode important constraints on influence functionals in coarse-grained systems with dissipation, or in open quantum systems. Operationally, this entails uplifting the standard Schwinger-Keldysh two-copy formalism into superspace by appending BRST ghost degrees of freedom. These statements were previously argued at the level of the correlation functions. We provide herein a complementary perspective by working out the Hilbert space structure explicitly. Our analysis clarifies two crucial issues not evident in earlier works: first, certain background ghost insertions necessary to reproduce the correct Schwinger-Keldysh correlators arise naturally, and, second, the Schwinger-Keldysh difference operators are systematically dressed by the ghost bilinears, which turn out to be necessary to give rise to a consistent operator algebra. We also elaborate on the structure of the final state (which is BRST closed) and the future boundary condition of the ghost fields.

Authors:

Geracie, Michael; Haehl, Felix M.; Loganayagam, R.; Narayan, Prithvi; Ramirez, David M.; Rangamani, Mukund

Publication Date:

Tue May 29 00:00:00 EDT 2018

Research Org.:

Univ. of California, Davis, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:

1439370

Alternate Identifier(s):

OSTI ID: 1498876

Grant/Contract Number:  

SC0009999

Resource Type:

Published Article

Journal Name:

Physical Review D

Additional Journal Information:

Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 10; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; quantum field theory (low energy); topological field theories; many-body techniques