Group-renormalization approach in quantum field theory in curved spacetime with torsion

The nature of the interaction of the gauge models SU(N) and O(N) with an external torsion field is studied from the group-renormalization point of view. Consideration of the radiation corrections to the nonminimal interaction gives a possible explanation for the absence of a torsion field in observational data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 34–38, October, 1990.The authors thank I. L. Buchbinder for discussion of the work.     

Spectral asymmetry and quantum field theory in curved spacetime

I discuss cosmological particle production in spaces with spectral asymmetry. A change in the amount of spectral symmetry sufficient to produce a level crossing will result in the creation of neutrino pairs rather than neutrino, antineutrino pairs; the net excess of fermions being given by the number of level crossing. A symmetric Bianchi IX model is treated in detail and for large initial anisotropy the number of neutrinos produced is ($\text{1}\text{256}$) exp 12β₊ where β₊ is a measure of the initial anisotropy. The relation of this phenomenon to chiral anomalies and to the Atiyah-Patodi-Singer index theorem for manifolds with boundary is described. The effect of spectral asymmetry on photons is discussed and it is shewn that no level crossing can occur.     

Vilkovisky-de Witt effective action in quantum field theory in curved spacetime

The potentialities of the application of the Vilkovisky-de Witt effective action in quantum field theory in curved spacetime are discussed. A number of examples is given, in which this effective action eliminates problems related to the standard effective action.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 107–110, April, 1990.The author thanks I. L. Buchbinder for discussion of the work.     

Quantum field theory in curved spacetime

Quantum field theory predicts a number of unusual physical effects in non-Minkowskian manifolds (flat or curved) that have no immediate analogs in Minkowski spacetime. The following examples are reviewed: (1) The Casimir effect; (2) Radiation from accelerating conductors; (3) Particle production in manifolds with horizons, including both stationary black holes and black holes formed by collapse. In the latter examples curvature couples directly to matter through the stress tensor and induces the creation of real particles. However, it also induces serious divergences in the vacuum stress. These divergences are analyzed, and methods for handling them are reviewed.     

On quantum radiation in curved spacetime

In the context of quantum field theories in curved spacetime, we compute the effective action of the transition amplitude from vacuum to vacuum in the presence of an external gravitational field. The imaginary part of the resulted effective action determines the probability of vacuum decay via a quantum tunneling process, giving the rate and spectrum of particle creations. We show that (i) the gravitational field polarizes the vacuum and discretizes its spectrum; (ii) vacuum gains gravitational energy by such a polarization. On the basis of gravitational vacuum polarization, we discuss the quantum origin of vacuum decay in curved spacetime as pair-creations of particles and anti-particles. The thermal spectrum of particle creations is attributed to (i) the CPT invariance of pair-creations (annihilations) from (into) vacuum and (ii) vacuum acts as a reserve with the temperature determined by gravitational energy-gain.     

Modular inclusion,the Hawking temperature,and quantum field theory in curved spacetime

A recent result by Borchers connecting geometric modular action, modular inclusion and spectrum condition, is applied in quantum field theory on spacetimes with a bifurcate Killing horizon (these are generalizations of black-hole spacetimes, comprising the familiar black-hole spacetime models). Within this framework, we give sufficient, model-independent conditions ensuring that the temperature of thermal equilibrium quantum states is the Hawking temperature.     

Micro-local approach to the Hadamard condition in quantum field theory on curved space-time

For the two-point distribution of a quasi-free Klein-Gordon neutral scalar quantum field on an arbitrary four dimensional globally hyperbolic curved space-time we prove the equivalence of (1) the global Hadamard condition, (2) the property that the Feynman propagator is a distinguished parametrix in the sense of Duistermaat and Hörmander, and (3) a new property referred to as the wave front set spectral condition (WFSSC), because it is reminiscent of the spectral condition in axiomatic quantum field theory on Minkowski space. Results in micro-local analysis such as the propagation of singularities theorem and the uniqueness up toC of distinguished parametrices are employed in the proof. We include a review of Kay and Wald's rigorous definition of the global Hadamard condition and the theory of distinguished parametrices, specializing to the case of the Klein-Gordon operator on a globally hyperbolic space-time. As an alternative to a recent computation of the wave front set of a globally Hadamard two-point distribution on a globally hyperbolic curved space-time, given elsewhere by Köhler (to correct an incomplete computation in [32]), we present a version of this computation that does not use a deformation argument such as that used in Fulling, Narcowich and Wald and is independent of the Cauchy evolution argument of Fulling, Sweeny and Wald (both of which are relied upon in Köhler's proof). This leads to a simple micro-local proof of the preservation of Hadamard form under Cauchy evolution (first shown by Fulling, Sweeny and Wald) relying only on the propagation of singularities theorem. In another paper [33], the equivalence theorem is used to prove a conjecture by Kay that a locally Hadamard quasi-free Klein-Gordon state on any globally hyperbolic curved space-time must be globally Hadamard.To my parents     

Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes

In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel’d twists. We construct deformed quadratic action functionals and compute the corresponding equation of motion operators. The Green’s operators and the fundamental solution of the deformed equation of motion are obtained in terms of formal power series. It is shown that, using the deformed fundamental solution, we can define deformed *-algebras of field observables, which in general depend on the spacetime deformation parameter. This dependence is absent in the special case of Killing deformations, which include in particular the Moyal-Weyl deformation of the Minkowski spacetime.     

Axioms for renormalization in Euclidean quantum field theory

A set of axioms which fix Euclidean renormalizations up to a finite renormalization is proposed. There exists a one to one correspondence between Euclidean renormalizations and renormalizations in Minkowski space-time satisfying Hepp's axioms. No restrictions on masses are imposed.     

Optical theorem in curved space-time quantum field theory

A structural analysis is given of the optical theorem in theS-matrix approach to mutually interacting quantum fields in classical Robertson-Walker universes. As a case study, theφψ ²-interaction of conformally coupled massive (φ) and massless (φ) Klein-Gordon particles is studied. Based on the outgoing massless particles as indicator configuration, the physical interpretation is reduced to the corresponding added-up probabilities. Several examples are discussed in an in-in scheme which has the advantage that only a few non-Minkowskian in-in Feynman diagrams are involved.     

Convergent perturbation expansions for Euclidean quantum field theory

Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean quantum field theory to arbitrary accuracy, including nonper-turbative contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional ⁴-theory (in continuous space). They are not essentially more complicated than standard perturbation theory. Then ^th order term is expressed in terms ofO(n)-dimensional integrals, and is of order ^k if 4k–3n4k.Dedicated to the memory of Kurt Symanzik     

Euclidean formulation of quantum field theory without positivity

General properties of local quantum field theories (QFT) without positivity are discussed in connection with their euclidean formulation. Modified euclidean axioms for local QFT's without positivity are presented, which allow us to recover by analytic continuation Wightman functions satisfying the modified Wightman axioms for indefinite metric QFT's.     

Functional approach to scattering in quantum field theory

A functional approach to scattering theory in quantum field theory is developed by deriving an explicit functional expression fortransition amplitudes. In applications, the formalism avoids dealing with noncommutativity problems of field operators, avoids solving the field equations, avoids dealing with the often quite complicated continual (path) integrals, and avoids combinatoric problems associated with Feynman rules and the old-fashioned Wick's theorem. Finally, it avoids explicitly taking mass shell limits as in the LSZ formalism. The basic idea of the formalism is to use the quantum action principle followed by a systematic analysis of the concept of stimulated emissions as applied to particles of any spin, and is a generalization of an earlier method applied by the author to the much simpler situation of quantum mechanics.     

Local incompatibility of the microlocal spectrum condition with the KMS property along spacelike directions in quantum field theory on curved spacetime

Letters in Mathematical Physics - States of a generic quantum field theory on a curved spacetime are considered which satisfy the KMS condition with respect to an evolution associated with a...