Quantum field theory on a cosmological, quantum space-time

Abhay Ashtekar, Wojciech Kaminski, and Jerzy Lewandowski
Phys. Rev. D 79, 064030 – Published 27 March 2009

Abstract

In loop quantum cosmology, Friedmann-LeMaître-Robertson-Walker space-times arise as well-defined approximations to specific quantum geometries. We initiate the development of a quantum theory of test scalar fields on these quantum geometries. Emphasis is on the new conceptual ingredients required in the transition from classical space-time backgrounds to quantum space-times. These include a “relational time” à la Leibniz, the emergence of the Hamiltonian operator of the test field from the quantum constraint equation, and ramifications of the quantum fluctuations of the background geometry on the resulting dynamics. The familiar quantum field theory on classical Friedmann-LeMaître-Robertson-Walker models arises as a well-defined reduction of this more fundamental theory.

  • Received 7 January 2009

DOI:https://doi.org/10.1103/PhysRevD.79.064030

©2009 American Physical Society

Authors & Affiliations

Abhay Ashtekar1,*, Wojciech Kaminski1,2,†, and Jerzy Lewandowski1,2,‡

  • 1Institute for Gravitation and the Cosmos & Physics Department, Penn State, University Park, Pennsylvania 16802, USA
  • 2Instytut Fizyki Teoretycznej Uniwersytet Warszawski, ul.Hoza 69, PL-00 681 Warsaw, Poland

  • *ashtekar@gravity.psu.edu
  • Wojciech.Kaminski@fuw.edu.pl
  • jerzy.lewandowski@fuw.edu.pl

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Issue

Vol. 79, Iss. 6 — 15 March 2009

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