804 research outputs found
Vacuum Radiation and Symmetry Breaking in Conformally Invariant Quantum Field Theory
The underlying reasons for the difficulty of unitarily implementing the whole
conformal group in a massless Quantum Field Theory (QFT) are
investigated in this paper. Firstly, we demonstrate that the singular action of
the subgroup of special conformal transformations (SCT), on the standard
Minkowski space , cannot be primarily associated with the vacuum radiation
problems, the reason being more profound and related to the dynamical breakdown
of part of the conformal symmetry (the SCT subgroup, to be more precise) when
representations of null mass are selected inside the representations of the
whole conformal group. Then we show how the vacuum of the massless QFT radiates
under the action of SCT (usually interpreted as transitions to a uniformly
accelerated frame) and we calculate exactly the spectrum of the outgoing
particles, which proves to be a generalization of the Planckian one, this
recovered as a given limit.Comment: 29 pages, Latex, 1 figure, to appear in Commun. Math. Phy
Conformal Spinning Quantum Particles in Complex Minkowski Space as Constrained Nonlinear Sigma Models in U(2,2) and Born's Reciprocity
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a
base for the construction of conformally invariant quantum (field) theory,
either as phase or configuration spaces. We follow a gauge-invariant Lagrangian
approach (of nonlinear sigma-model type) and use a generalized Dirac method for
the quantization of constrained systems, which resembles in some aspects the
standard approach to quantizing coadjoint orbits of a group G. Physical wave
functions, Haar measures, orthonormal basis and reproducing (Bergman) kernels
are explicitly calculated in and holomorphic picture in these Cartan domains
for both scalar and spinning quantum particles. Similarities and differences
with other results in the literature are also discussed and an extension of
Schwinger's Master Theorem is commented in connection with closure relations.
An adaptation of the Born's Reciprocity Principle (BRP) to the conformal
relativity, the replacement of space-time by the 8-dimensional conformal domain
at short distances and the existence of a maximal acceleration are also put
forward.Comment: 33 pages, no figures, LaTe
Modular Invariance on the Torus and Abelian Chern-Simons Theory
The implementation of modular invariance on the torus as a phase space at the
quantum level is discussed in a group-theoretical framework. Unlike the
classical case, at the quantum level some restrictions on the parameters of the
theory should be imposed to ensure modular invariance. Two cases must be
considered, depending on the cohomology class of the symplectic form on the
torus. If it is of integer cohomology class , then full modular invariance
is achieved at the quantum level only for those wave functions on the torus
which are periodic if is even, or antiperiodic if is odd. If the
symplectic form is of rational cohomology class , a similar result
holds --the wave functions must be either periodic or antiperiodic on a torus
times larger in both direccions, depending on the parity of .
Application of these results to the Abelian Chern-Simons is discussed.Comment: 24 pages, latex, no figures; title changed; last version published in
JM
Higher-U(2,2)-spin fields and higher-dimensional W-gravities: quantum AdS space and radiation phenomena
A physical and geometrical interpretation of previously introduced tensor
operator algebras of U(2,2) in terms of algebras of higher-conformal-spin
quantum fields on the anti-de Sitter space AdS_5 is provided. These are
higher-dimensional W-like algebras and constitute a potential gauge guide
principle towards the formulation of induced conformal gravities
(Wess-Zumino-Witten-like models) in realistic dimensions. Some remarks on
quantum (Moyal) deformations are given and potentially tractable versions of
noncommutative AdS spaces are also sketched. The role of conformal symmetry in
the microscopic description of Unruh and Hawking's radiation effects is
discussed.Comment: LaTeX, 30 pages, 2 figures, final version to appear in Class. and
Quant. Gra
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