Related papers: Quantum Fields and Extended Objects in Space-Times…
The one-loop effective action for a massive self-interacting scalar field is investigated in $4$-dimensional ultrastatic space-time $ R \times H^3/\Gamma$, $H^3/\Gamma$ being a non-compact hyperbolic manifold with finite volume. Making use…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
An encyclopedia article on mathematical aspects of quantum field theory in curved spacetime. Section titles are: Introduction and preliminaries; Construction of *-algebra for a real linear scalar field on globally hyperbolic spacetimes and…
An asymptotic expansion of the trace of the heat kernel on a cone where the heat coefficients have a delta function behavior at the apex is obtained. It is used to derive the renormalized effective action and total energy of a…
We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a…
We consider the grand canonical thermodynamics of a noninteracting scalar field in a static spacetime. We take the nonrelativistic limit of thermodynamic quantities in a way that leaves the curved structure of the background geometry…
We study the classical and quantum theory of spherically symmetric spacetimes with scalar field coupling in general relativity. We utilise the canonical formalism of geometrodynamics adapted to the Painleve-Gullstrand coordinates, and…
The generator of time-translations on the solution space of the wave equation on stationary spacetimes specialises to the square root of the Laplacian on Riemannian manifolds when the spacetime is ultrastatic. Its spectral analysis…
The observed large-scale structure in our Universe is seen as a result of quantum fluctuations amplified by spacetime evolution. This, and related problems in cosmology, asks for an understanding of the quantum fields of the standard model…
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
The aim of this review is to outline a full route from the fundamental principles of algebraic quantum field theory on curved spacetime in its present-day form to explicit phenomenological applications which allow for comparison with…
We generalize the curved $N$-body problem to spheres and hyperbolic spheres whose curvature $\kappa$ varies in time. Unlike in the particular case when the curvature is constant, the equations of motion are non-autonomous. We first briefly…
We introduce a class of space-times modeling singular events such as evaporating black holes and topology changes, which we dub as semi-globally hyperbolic space-times. On these space-times we aim to study the existence of reasonable…
We use the brick wall model to calculate the free energy of quantum scalar field in a curved spacetime (D +1) dimensions. We find the thermodynamics properties of quantum scalar field in several scenaries: Minkowski spacetime, Schwarzschild…
We present some new ideas on how to design analogue models of quantum fields living in curved spacetimes using ultra-cold atoms in optical lattices. We discuss various types of static and dynamical curved spacetimes achievable by simple…
Massless and massive scalar fields and massless spinor fields are considered at arbitrary temperatures in four dimensional ultrastatic curved spacetime. Scalar models under consideration can be either conformal or nonconformal and include…
The complete form of the high-temperature expansion of the one-loop contribution to the free energy of a scalar field on a stationary gravitational background is derived. The explicit expressions for the divergent and finite parts of the…
The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schr\"{o}dinger equation…
Quantum field theory in curved space-times is a well developed area in mathematical physics which has had important phenomenological applications to the very early universe. However, it is not commonly appreciated that on time dependent…