201 research outputs found
An Elementary Construction on Nonlinear Coherent States Associated to Generalized Bargmann Spaces
Consider the space 2(ℂ,()), where ()=−||2⋀ is the
Gaussian measure, and its generalized Bargmann subspaces which are the null
kernels of the operator Δ=−2/+(/)−;
=0,1,…. In this work, we present an other construction of following the Hermite functions
which allows us to define a family of generalized Bargmann transform which maps isometrically into 2(ℝ). The generalized coherent states ∣⟩ associated to are constructed and some properties of them are given
A holomorphic representation of the Jacobi algebra
A representation of the Jacobi algebra by first order differential operators with polynomial
coefficients on the manifold is presented. The
Hilbert space of holomorphic functions on which the holomorphic first order
differential operators with polynomials coefficients act is constructed.Comment: 34 pages, corrected typos in accord with the printed version and the
Errata in Rev. Math. Phys. Vol. 24, No. 10 (2012) 1292001 (2 pages) DOI:
10.1142/S0129055X12920018, references update
Wavelets in Banach Spaces
We describe a construction of wavelets (coherent states) in Banach spaces
generated by ``admissible'' group representations. Our main targets are
applications in pure mathematics while connections with quantum mechanics are
mentioned. As an example we consider operator valued Segal-Bargmann type spaces
and the Weyl functional calculus.
Keywords: Wavelets, coherent states, Banach spaces, group representations,
covariant, contravariant (Wick) symbols, Heisenberg group, Segal-Bargmann
spaces, Weyl functional calculus (quantization), second quantization, bosonic
field.Comment: 37 pages; LaTeX2e; no pictures; 27/07/99: many small correction
Unitary Realizations of U-duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories
We review the current status of the construction of unitary representations
of U-duality groups of supergravity theories in five, four and three
dimensions. We focus mainly on the maximal supergravity theories and on the N=2
Maxwell-Einstein supergravity (MESGT) theories defined by Jordan algebras of
degree three in five dimensions and their descendants in four and three
dimensions. Entropies of the extremal black hole solutions of these theories in
five and four dimensions are given by certain invariants of their U-duality
groups. The five dimensional U-duality groups admit extensions to spectrum
generating generalized conformal groups which are isomorphic to the U-duality
groups of corresponding four dimensional theories. Similarly, the U-duality
groups of four dimensional theories admit extensions to spectrum generating
quasiconformal groups that are isomorphic to the corresponding U-duality groups
in three dimensions. We outline the oscillator construction of the unitary
representations of generalized conformal groups that admit positive energy
representations, which include the U-duality groups of N=2 MESGT's in four
dimensions. We conclude with a review of the minimal unitary realizations of
U-duality groups that are obtained by quantizations of their quasiconformal
actions.Comment: 24 pages; latex fil
Self Duality and Quantization
Quantum theory of the free Maxwell field in Minkowski space is constructed
using a representation in which the self dual connection is diagonal. Quantum
states are now holomorphic functionals of self dual connections and a
decomposition of fields into positive and negative frequency parts is
unnecessary. The construction requires the introduction of new mathematical
techniques involving ``holomorphic distributions''. The method extends also to
linear gravitons in Minkowski space. The fact that one can recover the entire
Fock space --with particles of both helicities-- from self dual connections
alone provides independent support for a non-perturbative, canonical
quantization program for full general relativity based on self dual variables.Comment: 14 page
Two-Photon Algebra Eigenstates: A Unified Approach to Squeezing
We use the concept of the algebra eigenstates that provides a unified
description of the generalized coherent states (belonging to different sets)
and of the intelligent states associated with a dynamical symmetry group. The
formalism is applied to the two-photon algebra and the corresponding algebra
eigenstates are studied by using the Fock-Bargmann analytic representation.
This formalism yields a unified analytic approach to various types of
single-mode photon states generated by squeezing and displacing
transformations.Comment: To appear in Annals of Physics, REVTeX with AMSsymbols, 27 pages, no
figures. More information on http://www.technion.ac.il/~brif/science.htm
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