Toward Quantization of Inhomogeneous Field Theory (original) (raw)

Refined Algebraic Quantization and Quantum Field Theory in Curved Space-Time

Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The construction can be made rigorous for a general globally hyperbolic space-time, but the quasifree state so obtained turns out to be unphysical in general. We exhibit a closely related pair of Fock representations that is also defined generically and conforms to the notion of in- and outgoing states in those situations where particle creation by the external field is expected. 1 1 Introduction In the early years of quantum field theory in curved space-time the two most important foundational problems were deemed to be the following: First, how to generalize the notion of vacuum in Minkowski space to space-times with a lesser degree of symmetries, and second, how to get rid of the divergencies that appear in the expectation value of the energy-momentum ten...

Canonical quantization, spacetime noncommutativity and deformed symmetries in field theory

Journal of Physics A: Mathematical and Theoretical, 2007

Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are introduced by making use of the reparametrization invariance of the action and of an arbitrary non-canonical symplectic structure. This construction implies that the constraints need to be deformed, resulting in an automatic Drinfeld twisting of the generators of the symmetries associated with the reparametrized theory. We illustrate our procedure for the case of a scalar field in 1+1-spacetime dimensions, but it can be readily generalized to arbitrary dimensions and arbitrary types of fields.

Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity

2009

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.

Quantization of Scalar Field Theory with Internal Symmetry

2011

We consider the simple theoretical model of scalar fields in one spatial dimension with an internal symmetry. We use the Schr\"{o}dinger picture to describe the quantum properties of localized solutions. Making use of collective coordinates method allows to develop a perturbation theory, which exactly describes symmetry properties of theory. As examples the U(1) and SU(2) symmetries are analyzed and dependence

On the Emergence of Non Locality for Quantum Fields Enjoying Κ-Poincaŕe Symmetries

2008

A novel perspective developed in [arXiv:0710.1083] by M. Arzano underlies the deep relation between "quantum groups" and Planck-scale-suppressed non locality (determined by dynamical quantum gravity) in quantum field theory. Far from locality, symmetries of the theory cannot be described in terms of Lie algebras but need a new language, provided by non co-commutative Hopf algebras or "quantum groups". This kind of "quantized" symmetries, acting on non commutative space-times, emerges in the low-energy limit of certain quantum gravity models. Within this perspective, we give here an insight to the issue of "physically" characterizing space-time symmetries of "quantum groups"-type and investigating quantum fields enjoying them. We focus on κ-Minkowski non commutative space-time and discuss how symmetries can be described by the κ-Poincaré Hopf algebra. We then show how working on the symplectic structure of classical κ-fields suggests a new approach to the canonical quantization of mass-less free fields and present results obtained in [arXiv:0707.1329] via deformed Fock space construction. Based on preliminary work with G. Amelino-Camelia and M. Arzano, we discuss some general expectations concerning the structure of multi-particle states in the quantum-gravity realm, introducing the first elements of a toy model based on the κ-deformed bosonic symmetrization of Fock space here summarized.

Quantization of field theories in the presence of boundaries

1996

This paper reviews the progress made over the last five years in studying boundary conditions and semiclassical properties of quantum fields about 4-realdimensional Riemannian backgrounds. For massless spin-1 2 fields one has a choice of spectral or supersymmetric boundary conditions, and the corresponding conformal anomalies have been evaluated by using zeta-function regularization. For Euclidean Maxwell theory in vacuum, the mode-by-mode analysis of BRST-covariant Faddeev-Popov amplitudes has been performed for relativistic and non-relativistic gauge conditions. For massless spin-3 2 fields, the contribution of physical degrees of freedom to one-loop amplitudes, and the 2-spinor analysis of Dirac and Rarita-Schwinger potentials, have been obtained. In linearized gravity, gauge modes and ghost modes in the de Donder gauge have been studied in detail. This program may lead to a deeper understanding of different quantization techniques for gauge fields and gravitation, to a new vision of gauge invariance, and to new points of view in twistor theory.

Algebraic Quantum Field Theory in Curved Spacetimes

Mathematical Physics Studies, 2015

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 category of (C *)-algebras obeying supplementary conditions. Among other things: (a) the key idea of relative Cauchy evolution is described in detail, and related to the stress-energy tensor; (b) a systematic 'rigidity argument' is used to generalise results from flat to curved spacetimes; (c) a detailed discussion of the issue of selection of physical states is given, linking notions of stability at microscopic, mesoscopic and macroscopic scales; (d) the notion of subtheories and global gauge transformations are formalised; (e) it is shown that the general framework excludes the possibility of there being a single preferred state in each spacetime, if the choice of states is local and covariant. Many of the ideas are illustrated by the example of the free Klein-Gordon theory, which is given a new 'universal definition'.