33 research outputs found
Examples of Berezin-Toeplitz Quantization: Finite sets and Unit Interval
We present a quantization scheme of an arbitrary measure space based on
overcomplete families of states and generalizing the Klauder and the
Berezin-Toeplitz approaches. This scheme could reveal itself as an efficient
tool for quantizing physical systems for which more traditional methods like
geometric quantization are uneasy to implement. The procedure is illustrated by
(mostly two-dimensional) elementary examples in which the measure space is a
-element set and the unit interval. Spaces of states for the -element set
and the unit interval are the 2-dimensional euclidean and hermitian
\C^2 planes
One-loop approximation of Moller scattering in Krein-space quantization
It has been shown that the negative-norm states necessarily appear in a
covariant quantization of the free minimally coupled scalar field in de Sitter
spacetime [1,2]. In this processes ultraviolet and infrared divergences have
been automatically eliminated [3]. A natural renormalization of the one-loop
interacting quantum field in Minkowski spacetime () has been
achieved through the consideration of the negative-norm states defined in Krein
space. It has been shown that the combination of quantum field theory in Krein
space together with consideration of quantum metric fluctuation, results in
quantum field theory without any divergences [4]. Pursuing this approach, we
express Wick's theorem and calculate M{\o}ller scattering in the one-loop
approximation in Krein space. The mathematical consequence of this method is
the disappearance of the ultraviolet divergence in the one-loop approximation.Comment: 10 page
"Massless" vector field in de Sitter Universe
In the present work the massless vector field in the de Sitter (dS) space has
been quantized. "Massless" is used here by reference to conformal invariance
and propagation on the dS light-cone whereas "massive" refers to those dS
fields which contract at zero curvature unambiguously to massive fields in
Minkowski space. Due to the gauge invariance of the massless vector field, its
covariant quantization requires an indecomposable representation of the de
Sitter group and an indefinite metric quantization. We will work with a
specific gauge fixing which leads to the simplest one among all possible
related Gupta-Bleuler structures. The field operator will be defined with the
help of coordinate independent de Sitter waves (the modes) which are simple to
manipulate and most adapted to group theoretical matters. The physical states
characterized by the divergencelessness condition will for instance be easy to
identify. The whole construction is based on analyticity requirements in the
complexified pseudo-Riemanian manifold for the modes and the two-point
function.Comment: 33 pages, 3 figure
Tree-level Scattering Amplitude in de Sitter Space
In previous papers [1,2], it was proved that a covariant quantization of the
minimally coupled scalar field in de Sitter space is achieved through addition
of the negative norm states. This causal approach which eliminates the infrared
divergence, was generalized further to the calculation of the graviton
propagator in de Sitter space [3] and one-loop effective action for scalar
field in a general curved space-time [4]. This method gives a natural
renormalization of the above problems. Pursuing this approach, in the present
paper the tree-level scattering amplitudes of the scalar field, with one
graviton exchange, has been calculated in de Sitter space. It is shown that the
infrared divergence disappears and the theory automatically reaches a
renormalized solution of the problem.Comment: 6 page
De Sitter Waves and the Zero Curvature Limit
We show that a particular set of global modes for the massive de Sitter
scalar field (the de Sitter waves) allows to manage the group representations
and the Fourier transform in the flat (Minkowskian) limit. This is in
opposition to the usual acceptance based on a previous result, suggesting the
appearance of negative energy in the limit process. This method also confirms
that the Euclidean vacuum, in de Sitter spacetime, has to be preferred as far
as one wishes to recover ordinary QFT in the flat limit.Comment: 9 pages, latex no figure, to appear in Phys. Rev.
Power Spectrum in Krein Space Quantization
The power spectrum of scalar field and space-time metric perturbations
produced in the process of inflation of universe, have been presented in this
paper by an alternative approach to field quantization namely, Krein space
quantization [1,2]. Auxiliary negative norm states, the modes of which do not
interact with the physical world, have been utilized in this method. Presence
of negative norm states play the role of an automatic renormalization device
for the theory.Comment: 8 pages, appear in Int. J. Theor. Phy
A natural fuzzyness of de Sitter space-time
A non-commutative structure for de Sitter spacetime is naturally introduced
by replacing ("fuzzyfication") the classical variables of the bulk in terms of
the dS analogs of the Pauli-Lubanski operators. The dimensionality of the fuzzy
variables is determined by a Compton length and the commutative limit is
recovered for distances much larger than the Compton distance. The choice of
the Compton length determines different scenarios. In scenario I the Compton
length is determined by the limiting Minkowski spacetime. A fuzzy dS in
scenario I implies a lower bound (of the order of the Hubble mass) for the
observed masses of all massive particles (including massive neutrinos) of spin
s>0. In scenario II the Compton length is fixed in the de Sitter spacetime
itself and grossly determines the number of finite elements ("pixels" or
"granularity") of a de Sitter spacetime of a given curvature.Comment: 16 page
Auxiliary "massless" spin-2 field in de Sitter universe
For the tensor field of rank-2 there are two unitary irreducible
representation (UIR) in de Sitter (dS) space denoted by and
[1]. In the flat limit only the coincides
to the UIR of Poincar\'e group, the second one becomes important in the study
of conformal gravity. In the pervious work, Dirac's six-cone formalism has been
utilized to obtain conformally invariant (CI) field equation for the "massless"
spin-2 field in dS space [2]. This equation results in a field which
transformed according to , we name this field the auxiliary
field. In this paper this auxiliary field is considered and also related
two-point function is calculated as a product of a polarization tensor and
"massless" conformally coupled scalar field. This two-point function is de
Sitter invariant.Comment: 16 page