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1 results

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

  • from Part III - Stochastic Gravity
  • Bei-Lok B. Hu, University of Maryland, College Park, Enric Verdaguer, Universitat de Barcelona
  • Book:
    Semiclassical and Stochastic Gravity
    Published online:
    20 January 2020
    Print publication:
    05 March 2020, pp 317-336

  • 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.