Generating functionals for quantum field theories with random potentials

Mudit Jain, Vitaly Vanchurin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.

Original languageEnglish (US)
Article number107
JournalJournal of High Energy Physics
Volume2016
Issue number1
DOIs
StatePublished - Jan 2016

Bibliographical note

Funding Information:
The authors are grateful to Thorsten Battefeld, Yi-Zen Chu and Alex Kamenev for very useful discussions and comments on the manuscript. The work was supported in part by Templeton Foundation and Foundational Questions Institute (FQXi).

Publisher Copyright:
© The Authors.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Keywords

  • Random systems
  • Statistical methods
  • Stochastic processes

Fingerprint

Dive into the research topics of 'Generating functionals for quantum field theories with random potentials'. Together they form a unique fingerprint.

Cite this