Quantum field theory in curved spacetime has been remarkably fruitful. It can be used to explain how the large-scale structure of the universe and the anisotropies of the cosmic background radiation that we observe today first arose. Similarly, it provides a deep connection between general relativity, thermodynamics, and quantum field theory. This book develops quantum field theory in curved spacetime in a pedagogical style, suitable for graduate students. The authors present detailed, physically motivated, derivations of cosmological and black hole processes in which curved spacetime plays a key role. They explain how such processes in the rapidly expanding early universe leave observable consequences today, and how in the context of evaporating black holes, these processes uncover deep connections between gravitation and elementary particles. The authors also lucidly describe many other aspects of free and interacting quantized fields in curved spacetime.

Quantum electrodynamics describes the interactions of electrons and photons. Electric charge (the gauge coupling constant) is energy dependent, and there is a previous claim that charge is affected by gravity (described by general relativity) with the implication that the charge is reduced at high energies. But that claim has been very controversial with the situation inconclusive. Here I report an analysis (free from earlier controversies) demonstrating that that quantum gravity corrections to quantum electrodynamics have a quadratic energy dependence that result in the reduction of the electric charge at high energies, a result known as asymptotic freedom.Comment: To be published in Nature. 19 pages LaTeX, no figure

We study the question of the gauge dependence of the quantum gravity contribution to the running gauge coupling constant for electromagnetism. The calculations are performed using dimensional regularization in a manifestly gauge invariant and gauge condition independent formulation of the effective action. It is shown that there is no quantum gravity contribution to the running charge, and hence there is no alteration to asymptotic freedom at high energies as predicted by 11.10.Gh, 11.10.Hi Until fairly recently the belief that quantum gravity lay outside the realm of any conceivable experimental test was pervasive in the physics community. Important work by Donoghue [1] helped to change this pessimistic viewpoint. Donoghue proposed that the effective field theory methodology be applied to quantum gravity, with Einstein's theory viewed as an effective low energy approximation to some as yet unknown more complete theory. Since Donoghue's pioneering work, there has been considerable interest in this viewpoint. A beautiful review of the subject has been given by Burgess [2].A notable calculation was performed recently by Robinson and Wilczek [3] for Einstein gravity coupled to a gauge theory. It was claimed, as a consequence of quantum gravity corrections, that all gauge theories become asymptotically free at high energies. This includes the Einstein-Maxwell theory, and occurs below the Planck scale at which perturbative quantum gravity calculations become suspect. If the gravitational scale is sufficiently low, as predicted by many higher dimensional theories, then it is conceivable that the predictions of [3] on the running gauge coupling constant might be experimentally testable [4]. A recent analysis of the calculation [5] has cast doubt on the results of [3] by claiming that the quantum gravity correction to the running gauge coupling constant is gauge dependent, and that there is really no such effect. The calculations of [5] do demonstrate that when computed using traditional background-field methods the effective action does depend on the choice of gauge condition. Choosing a particular gauge condition, and demonstrating independence of parameters that enter this condition is not sufficient to demonstrate gauge condition independence. As we will discuss, with the choice of gauge conditions made in [3, 5] a gauge condition independent result for the effective action necessitates additional terms that are not present if the standard background-field method is employed. Because of the interest in this problem, its potential as an experimental test of quantum gravity, and the controversy surround- * URL: http://www.staff.ncl.ac.uk/d.j.toms ; Electronic address: d.j.toms@newcastle.ac.uk ing the details, we will present a different analysis to that of [3,5] that removes all question of any possible gauge dependence.There are two basic problems that need to be dealt with in any calculation in a gauge theory. The first is to ensure that the calculations are done in a way that is gauge invariant. The second is ...

We examine the lowest order quantum corrections to the effective action arising from a quantized real scalar field in the Randall-Sundrum background spacetime. The leading term is the familiar vacuum, or Casimir, energy density. The next term represents an induced gravity term that can renormalize the 4-dimensional Newtonian gravitational constant. The calculations are performed for an arbitrary spacetime dimension. Two inequivalent boundary conditions, corresponding to twisted and untwisted field configurations, are considered. A careful discussion of the regularization and renormalization of the effective action is given, with the relevant counterterms found. It is shown that the requirement of self-consistency of the Randall-Sundrum solution is not simply a matter of minimizing the Casimir energy density. The massless, conformally coupled scalar field results are obtained as a special limiting case of our results. We clarify a number of differences with previous work.

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