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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:
 [1];  [2];  [3];  [3];  [1];  [1]
  1. Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP). Dept. of Physics
  2. Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
  3. International Centre for Theoretical Sciences (ICTS-TIFR), Bengaluru (India)
Publication Date:
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 Volume: 97; Journal Issue: 10; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
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

Citation Formats

Geracie, Michael, Haehl, Felix M., Loganayagam, R., Narayan, Prithvi, Ramirez, David M., and Rangamani, Mukund. Schwinger-Keldysh superspace in quantum mechanics. United States: N. p., 2018. Web. doi:10.1103/physrevd.97.105023.
Geracie, Michael, Haehl, Felix M., Loganayagam, R., Narayan, Prithvi, Ramirez, David M., & Rangamani, Mukund. Schwinger-Keldysh superspace in quantum mechanics. United States. https://doi.org/10.1103/physrevd.97.105023
Geracie, Michael, Haehl, Felix M., Loganayagam, R., Narayan, Prithvi, Ramirez, David M., and Rangamani, Mukund. Tue . "Schwinger-Keldysh superspace in quantum mechanics". United States. https://doi.org/10.1103/physrevd.97.105023.
@article{osti_1439370,
title = {Schwinger-Keldysh superspace in quantum mechanics},
author = {Geracie, Michael and Haehl, Felix M. and Loganayagam, R. and Narayan, Prithvi and Ramirez, David M. and Rangamani, Mukund},
abstractNote = {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.},
doi = {10.1103/physrevd.97.105023},
journal = {Physical Review. D.},
number = 10,
volume = 97,
place = {United States},
year = {2018},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/physrevd.97.105023

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Cited by: 8 works
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