Deep reinforcement learning for complex evaluation of one-loop diagrams in quantum field theory
Abstract
n this paper we present a technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. To extract certain quantities of two-point functions, such as spectral densities, mass poles or multiparticle thresholds, it is necessary to perform an analytic continuation of the correlator in question. At one-loop level in Euclidean space, this results in the necessity to deform the integration contour of the loop integral in the complex plane of the square of the loop momentum, to avoid nonanalyticities in the integration plane. Using a toy model for which an exact solution is known, we train a reinforcement learning agent to perform the required contour deformations. Our study shows great promise for an agent to be deployed in iterative numerical approaches used to compute nonperturbative two-point functions, such as the quark propagator Dyson-Schwinger equation, or more generally, Fredholm equations of the second kind, in the complex domain.
- Authors:
-
[1];
[2];
[2]
- Washington Univ., St. Louis, MO (United States); Silicon Austria Labs, Graz (Austria)
- Silicon Austria Labs, Graz (Austria)
- Publication Date:
- Research Org.:
- Washington Univ., St. Louis, MO (United States)
- Sponsoring Org.:
- Austrian federal government; Austrian Association for the Electric and Electronics Industry; USDOE Office of Science (SC), Nuclear Physics (NP); Austrian Science Fund (FWF)
- Contributing Org.:
- Graz University
- OSTI Identifier:
- 1800308
- Alternate Identifier(s):
- OSTI ID: 1605311; OSTI ID: 1830676
- Grant/Contract Number:
- FG02-05ER41375; FG-02-05ER41375
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. E
- Additional Journal Information:
- Journal Volume: 101; Journal Issue: 3; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Physics
Citation Formats
Windisch, Andreas, Gallien, Thomas, and Schwarzlmüller, Christopher. Deep reinforcement learning for complex evaluation of one-loop diagrams in quantum field theory. United States: N. p., 2020.
Web. doi:10.1103/physreve.101.033305.
Windisch, Andreas, Gallien, Thomas, & Schwarzlmüller, Christopher. Deep reinforcement learning for complex evaluation of one-loop diagrams in quantum field theory. United States. https://doi.org/10.1103/physreve.101.033305
Windisch, Andreas, Gallien, Thomas, and Schwarzlmüller, Christopher. Wed .
"Deep reinforcement learning for complex evaluation of one-loop diagrams in quantum field theory". United States. https://doi.org/10.1103/physreve.101.033305. https://www.osti.gov/servlets/purl/1800308.
@article{osti_1800308,
title = {Deep reinforcement learning for complex evaluation of one-loop diagrams in quantum field theory},
author = {Windisch, Andreas and Gallien, Thomas and Schwarzlmüller, Christopher},
abstractNote = {n this paper we present a technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. To extract certain quantities of two-point functions, such as spectral densities, mass poles or multiparticle thresholds, it is necessary to perform an analytic continuation of the correlator in question. At one-loop level in Euclidean space, this results in the necessity to deform the integration contour of the loop integral in the complex plane of the square of the loop momentum, to avoid nonanalyticities in the integration plane. Using a toy model for which an exact solution is known, we train a reinforcement learning agent to perform the required contour deformations. Our study shows great promise for an agent to be deployed in iterative numerical approaches used to compute nonperturbative two-point functions, such as the quark propagator Dyson-Schwinger equation, or more generally, Fredholm equations of the second kind, in the complex domain.},
doi = {10.1103/physreve.101.033305},
journal = {Physical Review. E},
number = 3,
volume = 101,
place = {United States},
year = {Wed Mar 18 00:00:00 EDT 2020},
month = {Wed Mar 18 00:00:00 EDT 2020}
}
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