### 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 language | English (US) |
---|---|

Article number | 107 |

Journal | Journal of High Energy Physics |

Volume | 2016 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2016 |

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### Keywords

- Random systems
- Statistical methods
- Stochastic processes

### Cite this

**Generating functionals for quantum field theories with random potentials.** / Jain, Mudit; Vanchurin, Vitaly.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2016, no. 1, 107. https://doi.org/10.1007/JHEP01(2016)107

}

TY - JOUR

T1 - Generating functionals for quantum field theories with random potentials

AU - Jain, Mudit

AU - Vanchurin, Vitaly

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

KW - Random systems

KW - Statistical methods

KW - Stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=85008488013&partnerID=8YFLogxK

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U2 - 10.1007/JHEP01(2016)107

DO - 10.1007/JHEP01(2016)107

M3 - Article

AN - SCOPUS:85008488013

VL - 2016

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 1

M1 - 107

ER -