General relativity as an effective field theory: The leading quantum corrections

I describe the treatment of gravity as a quantum effective field theory. This allows a natural separation of the (known) low energy quantum effects from the (unknown) high energy contributions. Within this framework, gravity is a well behaved quantum field theory at ordinary energies. In studying the class of quantum corrections at low energy, the dominant effects at large distance can be isolated, as these are due to the propagation of the massless particles (including gravitons) of the theory and are manifested in the nonlocal/nonanalytic contributions to vertex functions and propagators. These leading quantum corrections are parameter-free and represent necessary consequences of quantum gravity. The methodology is illustrated by a calculation of the leading quantum corrections to the gravitational interaction of two heavy masses.Comment: 34 pages, Latex, UMHEP-40

Appearing Out of Nowhere: The Emergence of Spacetime in Quantum Gravity

Quantum gravity is understood as a theory that, in some sense, unifies general relativity (GR) and quantum theory, and is supposed to replace GR at extremely small distances (high-energies). It may be that quantum gravity represents the breakdown of spacetime geometry described by GR. The relationship between quantum gravity and spacetime has been deemed "emergence", and the aim of this thesis is to investigate and explicate this relation. After finding traditional philosophical accounts of emergence to be inappropriate, I develop a new conception of emergence by considering physical case studies including condensed matter physics, hydrodynamics, critical phenomena and quantum field theory understood as effective field theory. This new conception of emergence is independent of reduction and derivation. Instead, a low-energy theory is understood as emergent from a high-energy theory if it is novel and autonomous compared to the high-energy theory, and the low-energy physics is dependent (in a particular, minimal sense) on the high-energy physics (this dependence is revealed by the techniques of effective field theory and the renormalisation group). These ideas are important in exploring the relationship between quantum gravity and GR, where GR is understood as an effective, low-energy theory of quantum gravity. Without experimental data or a theory of quantum gravity, we rely on principles and techniques from other areas of physics to guide the way. As well as considering the idea of emergence appropriate to treating GR as an effective field theory, I investigate the emergence of spacetime (and other aspects of GR) in several concrete approaches to quantum gravity, including examples of the condensed matter approaches, the "discrete approaches" (causal set theory, causal dynamical triangulations, quantum causal histories and quantum graphity) and loop quantum gravity.Comment: PhD thesis submitted to the University of Sydne

The Quantum Theory of General Relativity at Low Energies

In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in ``non-renormalizable'' theories, using only the degrees of freedom and interactions appropriate for those energies. Whether or not general relativity is truly fundamental, at low energies it is automatically described as a quantum effective field theory and this allows a consistent framework for quantum gravity at ordinary energies. I briefly describe the nature and limits of the technique.Comment: 9 pages, Latex, talk presented at Journees Relativistes 96, Ascona, Switzerland, May 1996. To be published in Helv. Phys. Act

Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory

This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems. Contents: 1. Introduction 2. Effective Field Theories 3. Low-Energy Quantum Gravity 4. Explicit Quantum Calculations 5. ConclusionsComment: 56 pages, 2 figures, JHEP style, Invited review to appear in Living Reviews of Relativit

Quantum Field Theory Is Not Merely Quantum Mechanics Applied to Low Energy Effective Degrees of Freedom

It is commonly assumed that quantum field theory arises by applying ordinary quantum mechanics to the low energy effective degrees of freedom of a more fundamental theory defined at ultra-high-energy/short-wavelength scales. We shall argue here that, even for free quantum fields, there are holistic aspects of quantum field theory that cannot be properly understood in this manner. Specifically, the ``subtractions'' needed to define nonlinear polynomial functions of a free quantum field in curved spacetime are quite simple and natural from the quantum field theoretic point of view, but are at best extremely ad hoc and unnatural if viewed as independent renormalizations of individual modes of the field. We illustrate this point by contrasting the analysis of the Casimir effect, the renormalization of the stress-energy tensor in time-dependent spacetimes, and anomalies from the point of quantum field theory and from the point of view of quantum mechanics applied to the independent low energy modes of the field. Some implications for the cosmological constant problem are discussed.Comment: Latex, 8 Pages, 5th Prize Essay, Gravity Research Foundatio

Covariant Loop Quantum Gravity, Low Energy Perturbation Theory, and Einstein Gravity with High Curvature UV Corrections

A low-energy perturbation theory is developed from the nonperturbative framework of covariant Loop Quantum Gravity (LQG) by employing the background field method. The resulting perturbation theory is a 2-parameter expansion in the semiclassical and low-energy regime. The two expansion parameters are the large spin and small curvature. The leading order effective action coincides with the Einstein-Hilbert action. The subleading corrections organized by the two expansion parameters give the modifications of Einstein gravity in quantum and high-energy regime from LQG. The perturbation theory developed here shows for the first time that covariant LQG produces the high curvature corrections to Einstein gravity. This result means that LQG is not a naive quantization of Einstein gravity, but rather provides the UV modification. The result of the paper may be viewed as the first step toward understanding the UV completeness of LQG.Comment: 5 pages, 1 figure, presentation improved, references adde

Quantum generation of Schwarzschild-de Sitter (Nariai) black holes in effective dilaton-Maxwell gravity

Dilaton coupled electromagnetic field is essential element of low-energy string effective action or it may be considered as result of spherical compactification of Maxwell theory in higher dimensions. The large $N$ and large curvature effective action for $N$ dilaton coupled vectors is calculated. Adding such quantum correction to classical dilaton gravity action we show that effective dilaton-Maxwell gravity under consideration may generate Schwarzschild-de Sitter black holes (SdS BHs) with constant dilaton as solutions of the theory. That suggests a mechanism (alternative to BHs production) for quantum generation of SdS BHs in early universe (actually, for quantum creation of inflationary Universe) due to back-reaction of dilaton coupled matter. The possibility of proliferation of anti-de Sitter space is briefly discussed.Comment: LaTeX file, 11 page