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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:
; ; ; ; ;
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 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

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. doi: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. doi: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
DOI: 10.1103/PhysRevD.97.105023

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Cited by: 4 works
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Works referenced in this record:

Equilibrium and nonequilibrium formalisms made unified
journal, February 1985


Topological sigma models & dissipative hydrodynamics
journal, April 2016

  • Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund
  • Journal of High Energy Physics, Vol. 2016, Issue 4
  • DOI: 10.1007/JHEP04(2016)039

Cutkosky rules for superstring field theory
journal, October 2016


Schwinger-Keldysh formalism. Part I: BRST symmetries and superspace
journal, June 2017

  • Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund
  • Journal of High Energy Physics, Vol. 2017, Issue 6
  • DOI: 10.1007/JHEP06(2017)069

Brownian Motion of a Quantum Oscillator
journal, May 1961

  • Schwinger, Julian
  • Journal of Mathematical Physics, Vol. 2, Issue 3
  • DOI: 10.1063/1.1703727

Channel-state duality
journal, February 2013


Two sum rules for the thermal n -point functions
journal, December 2005


Effective field theory of dissipative fluids
journal, September 2017

  • Crossley, Michael; Glorioso, Paolo; Liu, Hong
  • Journal of High Energy Physics, Vol. 2017, Issue 9
  • DOI: 10.1007/JHEP09(2017)095

The theory of a general quantum system interacting with a linear dissipative system
journal, October 1963


The fluid manifesto: emergent symmetries, hydrodynamics, and black holes
journal, January 2016

  • Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)184

Renormalization in open quantum field theory. Part I. Scalar field theory
journal, November 2017

  • Baidya, Avinash; Jana, Chandan; Loganayagam, R.
  • Journal of High Energy Physics, Vol. 2017, Issue 11
  • DOI: 10.1007/JHEP11(2017)204

Schwinger-Keldysh formalism. Part II: thermal equivariant cohomology
journal, June 2017

  • Haehl, Felix M.; Loganayagam, R.; Rangamani, Mukund
  • Journal of High Energy Physics, Vol. 2017, Issue 6
  • DOI: 10.1007/JHEP06(2017)070

    Works referencing / citing this record:

    A panoply of Schwinger-Keldysh transport
    journal, January 2018