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9 - Metric Correlations at One-Loop: In-In and Large N

from Part III - Stochastic Gravity

Published online by Cambridge University Press:  20 January 2020

Bei-Lok B. Hu
Affiliation:
University of Maryland, College Park
Enric Verdaguer
Affiliation:
Universitat de Barcelona
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Summary

As a short introduction to this chapter we first briefly summarize the in-in or closed-time-path (CTP) functional formalism and evaluate the CTP effective action for a scalar field in Minkowski spacetime. We then consider N quantum matter fields interacting with the gravitational field assuming an effective field theory approach to quantum gravity and consider the quantization of metric perturbations around a semiclassical background in the CTP formalism. A suitable prescription is given to select an asymptotic initial vacuum state of the interacting theory; this prescription plays an important role in calculations in later chapters. We derive expressions for the two-point metric correlations, which are conveniently written in terms of the CTP effective action that results from integrating out the matter fields by rescaling the gravitational constant and performing a 1/N expansion. These correlations include loop corrections from matter fields but no graviton loops. This is achieved consistently in the 1/N expansion, and is illustrated in a simplified model of matter–gravity interaction.

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Chapter
Information
Semiclassical and Stochastic Gravity
Quantum Field Effects on Curved Spacetime
, pp. 317 - 336
Publisher: Cambridge University Press
Print publication year: 2020

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