Related papers: Refined Algebraic Quantization and Quantum Field T…
It is well-known that there exist infinitely-many inequivalent representations of the canonical (anti)-commutation relations of Quantum Field Theory (QFT). A way out, suggested by Algebraic QFT, is to instead define the quantum theory as…
The method of refined algebraic quantization of constrained systems which is based on modification of the inner product of the theory rather than on imposing constraints on the physical states is generalized to the case of constrained…
Algebraic quantization has been applied on the class of globally hyperbolic spacetime for many decades, leading to remarkable results. Nonetheless, the presence of a boundary calls for a separate treatment, since, in general, it breaks…
The problem of defining and constructing representations of the Canonical Commutation Relations can be systematically approached via the technique of {\it algebraic quantization}. In particular, when the phase space of the system is linear…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
The Dirac quantization `procedure' for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular interpretation of the Dirac procedure known as…
Quantum field theory in curved spacetimes suffers in general from an infinite ambiguity in the choice of Fock representation and associated vacuum. In cosmological backgrounds, the requirement of a unitary implementation of the field…
It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The…
Some algebraic aspects of field quantization in space-time with boundaries are discussed. We introduce an associative algebra, whose exchange properties are inferred from the scattering processes in integrable models with reflecting…
Some basic ideas of the Refined Algebraic Quantization scheme are outlined at an intuitive level, using a class of simple models with a single wave equation as quantum constraint. In addition, hints are given how the scheme is applied to…
It is generally known that linear (free) field theories are one of the few QFT that are exactly soluble. In the Schroedinger functional description of a scalar field on flat Minkowski spacetime and for flat embeddings, it is known that the…
In this article we give an introduction to the Fock quantization of the Maxwell field. At the classical level, we treat the theory in both the covariant and canonical phase space formalisms. The approach is general since we consider…
In this article we propose a `second quantization' scheme especially suitable to deal with non-trivial, highly symmetric phase spaces, implemented within a more general Group Approach to Quantization, which recovers the standard Quantum…
We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot…
A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent…
We study the Fock quantization of scalar fields in (generically) time dependent scenarios, focusing on the case in which the field propagation occurs in --either a background or effective-- spacetime with spatial sections of flat compact…
This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a…
This monograph provides a largely self--contained and broadly accessible exposition of two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…