Schwinger-Keldysh formalism. Part I: BRST symmetries and superspace
Schwinger-Keldysh formalism. Part I: BRST symmetries and superspace
We review the Schwinger-Keldysh, or in-in, formalism for studying quantum dynamics of systems out-of-equilibrium. The main motivation is to rephrase well known facts in the subject in a mathematically elegant setting, by exhibiting a set of BRST symmetries inherent in the construction. We show how these fundamental symmetries can be made manifest by working in a superspace formalism. We argue that this rephrasing is extremely efficacious in understanding low energy dynamics following the usual renormalization group approach, for the BRST symmetries are robust under integrating out degrees of freedom. In addition we discuss potential generalizations of the formalism that allow us to compute out-of-time-order correlation functions that have been the focus of recent attention in the context of chaos and scrambling. We also outline a set of problems ranging from stochastic dynamics, hydrodynamics, dynamics of entanglement in QFTs, and the physics of black holes and cosmology, where we believe this framework could play a crucial role in demystifying various confusions. Our companion paper arXiv:1610.01941 describes in greater detail the mathematical framework embodying the topological symmetries we uncover here.
hep-th, cond-mat.stat-mech, math-ph, math.MP
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Loganayagam, R.
18806477-1ac8-419a-9729-0e36440bd36a
Rangamani, Mukund
c6e93885-0b7e-4e8c-92e5-56227da78a81
13 June 2017
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Loganayagam, R.
18806477-1ac8-419a-9729-0e36440bd36a
Rangamani, Mukund
c6e93885-0b7e-4e8c-92e5-56227da78a81
Haehl, Felix M., Loganayagam, R. and Rangamani, Mukund
(2017)
Schwinger-Keldysh formalism. Part I: BRST symmetries and superspace.
Journal of High Energy Physics, 69 (2017).
(doi:10.1007/JHEP06(2017)069).
Abstract
We review the Schwinger-Keldysh, or in-in, formalism for studying quantum dynamics of systems out-of-equilibrium. The main motivation is to rephrase well known facts in the subject in a mathematically elegant setting, by exhibiting a set of BRST symmetries inherent in the construction. We show how these fundamental symmetries can be made manifest by working in a superspace formalism. We argue that this rephrasing is extremely efficacious in understanding low energy dynamics following the usual renormalization group approach, for the BRST symmetries are robust under integrating out degrees of freedom. In addition we discuss potential generalizations of the formalism that allow us to compute out-of-time-order correlation functions that have been the focus of recent attention in the context of chaos and scrambling. We also outline a set of problems ranging from stochastic dynamics, hydrodynamics, dynamics of entanglement in QFTs, and the physics of black holes and cosmology, where we believe this framework could play a crucial role in demystifying various confusions. Our companion paper arXiv:1610.01941 describes in greater detail the mathematical framework embodying the topological symmetries we uncover here.
Text
1610.01940v4
- Accepted Manuscript
Available under License Other.
Text
JHEP06(2017)069
- Version of Record
More information
Submitted date: 6 October 2016
Accepted/In Press date: 18 May 2017
Published date: 13 June 2017
Additional Information:
94 pages; v2: fixed typos. v3: minor clarifications and improvements. v4: further minor improvements. published version
Keywords:
hep-th, cond-mat.stat-mech, math-ph, math.MP
Identifiers
Local EPrints ID: 469969
URI: http://eprints.soton.ac.uk/id/eprint/469969
ISSN: 1126-6708
PURE UUID: 9c52555d-5631-4b41-906e-e035c85f2eb8
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Date deposited: 29 Sep 2022 16:42
Last modified: 17 Mar 2024 04:14
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Contributors
Author:
Felix M. Haehl
Author:
R. Loganayagam
Author:
Mukund Rangamani
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