Abstract:
I study the response of a detector that is coupled non-linearly to a quantized complex scalar field in different types of classical electromagnetic backgrounds. Assuming that the quantum field is in the vacuum state, I show that, when in {\it inertial} motion, the detector responds {\it only} when the electromagnetic background produces particles. However, I find that the response of the detector is {\it not} proportional to the number of particles produced by the background.

Abstract:
We give a rigorous description of a model of the quantized electromagnetic field interacting with quantized current fields. In the special case of classical currents our results agree with common knowledge about the problem. A toy model of a quantum current is studied as well.

Abstract:
In this paper, we probe the validity of the tunnelling interpretation that is usually called forth in literature to explain the phenomenon of particle production by time independent classical electromagnetic backgrounds. We show that the imaginary part of the effective lagrangian is zero for a complex scalar field quantized in a time independent, but otherwise arbitrary, magnetic field. This result implies that no pair creation takes place in such a background. But we find that when the quantum field is decomposed into its normal modes in the presence of a spatially confined and time independent magnetic field, there exists a non-zero tunnelling probability for the effective Schr{\" o}dinger equation. According to the tunnelling interpretation, this result would imply that spatially confined magnetic fields can produce particles, thereby contradicting the result obtained from the effective lagrangian. This lack of consistency between these two approaches calls into question the validity of attributing a non-zero tunnelling probability for the effective Schr{\" o}dinger equation to the production of particles by the time independent electromagnetic backgrounds. The implications of our analysis are discussed.

Abstract:
The predictions of the semiclassical description of particle creation based on QFT in classical backgrounds may be significantly modified when the source of the classical background is also quantized and backreaction is taken into account. In the cases of a stable charged particle, expanding empty (Milne) universe, and de Sitter universe with a true cosmological constant, the semiclassical particle creation is completely blocked up.

Abstract:
The predictions of the semiclassical description of particle creation based on QFT in classical backgrounds may be significantly modified when the source of the classical background is also quantized and backreaction is taken into account. In the cases of a stable charged particle, expanding empty (Milne) universe, and de Sitter universe with a true cosmological constant, the semiclassical particle creation is completely blocked up.

Abstract:
This paper offers an expository account of some ideas, methods, and conjectures concerning quantized coordinate rings and their semiclassical limits, with a particular focus on primitive ideal spaces. The semiclassical limit of a family of quantized coordinate rings of an affine algebraic variety V consists of the classical coordinate ring O(V) equipped with an associated Poisson structure. Conjectured relationships between primitive ideals of a generic quantized coordinate ring A and symplectic leaves in V (relative to a semiclassical limit Poisson structure on O(V)) are discussed, as are breakdowns in the connections when the symplectic leaves are not algebraic. This prompts replacement of the differential-geometric concept of symplectic leaves with the algebraic concept of symplectic cores, and a reformulated conjecture is proposed: The primitive spectrum of A should be homeomorphic to the space of symplectic cores in V, and to the Poisson-primitive spectrum of O(V). Various examples, including both quantized coordinate rings and enveloping algebras of solvable Lie algebras, are analyzed to support the choice of symplectic cores to replace symplectic leaves.

Abstract:
We compare the different approaches presently available in literature to probe the vacuum structure of quantum fields in classical electromagnetic and gravitational backgrounds. We compare the results from the Bogolubov transformations and the effective Lagrangian approach with the response of monopole detectors (of the Unruh-DeWitt type) in non-inertial frames in flat spacetime and in inertial frames in different types of classical electromagnetic backgrounds. We also carry out such a comparison in inertial and rotating frames when boundaries are present in flat spacetime. We find that the results from these different approaches do not, in general, agree with each other. We attempt to identify the origin of these differences and then go on to discuss its implications for classical gravitational backgrounds.

Abstract:
The semiclassical theory for the large-N field models is developed from an unusual point of view. Analogously to the procedure of the second quantization in quantum mechanics, the functional Schrodinger large-N equation is presented in a third-quantized form. The third-quantized creation and annihilation operators depend on the field $\phi({\bf x})$. If the coefficient of the $\phi^4$-term is of order 1/N (this is a usual condition of applicability of the 1/N-expansion), one can rescale the third-quantized operators in such a way that their commutator will be small, while the Heisenberg equations will not contain large or small parameters. This means that classical equation of motion is an equation on the functional $\Phi[\phi(\cdot)]$. This equation being a nonlinear analog of the functional Schrodinger equation for the one-field theory is investigated. The exact solutions are constructed and the renormalization problem is analysed. We also perform a quantization procedure about found classical solutions. The corresponding semiclassical theory is a theory of a variable number of fields. The developed third-quantized semiclassical approach is applied to the problem of finding the large-N spectrum. The results are compared with obtained by known methods. We show that not only known but also new energy levels can be found.

Abstract:
The perturbative solutions to the semiclassical Einstein field equations describing spherically-symmetric and static lukewarm black hole are constructed. The source term is composed of the (classical) stress-energy tensor of the electromagnetic field and the renormalized stress-energy tensor of the quantized massive scalar field in a large mass limit. We used two different parametrizations. In the first parametrization we calculated the zeroth-order solution. Subsequently, making use of the quantum part of the total stress-energy tensor constructed in the classical background we calculated the corrections to the metric potentials and the corrections to the horizons. This procedure can be thought of as switching the quantized field on and analyzing its influence on the classical background via the back-reaction. In the second parametrization we are looking for a self-consistent lukewarm solution from the very beginning. This requires knowledge of a generic tensor which depends functionally on the metric tensor. The transformation formulas relating the line element in both parametrizations are given.

Abstract:
A nonlocal method of extracting the positive (or the negative) frequency part of a field, based on knowledge of a 2-point function, leads to certain natural generalizations of the normal ordering of quantum fields in classical gravitational and electromagnetic backgrounds and illuminates the origin of the recently discovered nonlocalities related to a local description of particles. A local description of particle creation by gravitational backgrounds is given, with emphasis on the case of black-hole evaporation. The formalism reveals a previously hidden relation between various definitions of the particle current and those of the energy-momentum tensor. The implications to particle creation by classical backgrounds, as well as to the relation between vacuum energy, dark matter, and cosmological constant, are discussed.