602 research outputs found
Coherent states on the circle
We present a possible construction of coherent states on the unit circle as
configuration space. In our approach the phase space is the product Z x S^1.
Because of the duality of canonical coordinates and momenta, i.e. the angular
variable and the integers, this formulation can also be interpreted as coherent
states over an infinite periodic chain. For the construction we use the analogy
with our quantization over a finite periodic chain where the phase space was
Z_M x Z_M. Properties of the coherent states constructed in this way are
studied and the coherent states are shown to satisfy the resolution of unity.Comment: 7 pages, presented at GROUP28 - "28th International Colloquium on
Group Theoretical Methods in Physics", Newcastle upon Tyne, July 2010.
Accepted in Journal of Physics Conference Serie
Automorphisms of the fine grading of sl(n,C) associated with the generalized Pauli matrices
We consider the grading of by the group of
generalized Pauli matrices. The grading decomposes the Lie algebra into
one--dimensional subspaces. In the article we demonstrate that the normalizer
of grading decomposition of in is the group , where is the cyclic group of order . As an
example we consider graded by and all contractions
preserving that grading. We show that the set of 48 quadratic equations for
grading parameters splits into just two orbits of the normalizer of the grading
in
Symmetries of the finite Heisenberg group for composite systems
Symmetries of the finite Heisenberg group represent an important tool for the
study of deeper structure of finite-dimensional quantum mechanics. As is well
known, these symmetries are properly expressed in terms of certain normalizer.
This paper extends previous investigations to composite quantum systems
consisting of two subsystems - qudits - with arbitrary dimensions n and m. In
this paper we present detailed descriptions - in the group of inner
automorphisms of GL(nm,C) - of the normalizer of the Abelian subgroup generated
by tensor products of generalized Pauli matrices of orders n and m. The
symmetry group is then given by the quotient group of the normalizer.Comment: Submitted to J. Phys. A: Math. Theo
Dihedral symmetry of periodic chain: quantization and coherent states
Our previous work on quantum kinematics and coherent states over finite
configuration spaces is extended: the configuration space is, as before, the
cyclic group Z_n of arbitrary order n=2,3,..., but a larger group - the
non-Abelian dihedral group D_n - is taken as its symmetry group. The
corresponding group related coherent states are constructed and their
overcompleteness proved. Our approach based on geometric symmetry can be used
as a kinematic framework for matrix methods in quantum chemistry of ring
molecules.Comment: 13 pages; minor changes of the tex
Symmetries of finite Heisenberg groups for k-partite systems
Symmetries of finite Heisenberg groups represent an important tool for the
study of deeper structure of finite-dimensional quantum mechanics. This short
contribution presents extension of previous investigations to composite quantum
systems comprised of k subsystems which are described with position and
momentum variables in Z_{n_i}, i=1,...,k. Their Hilbert spaces are given by
k-fold tensor products of Hilbert spaces of dimensions n_1,...,n_k. Symmetry
group of the corresponding finite Heisenberg group is given by the quotient
group of a certain normalizer. We provide the description of the symmetry
groups for arbitrary multipartite cases. The new class of symmetry groups
represents very specific generalization of finite symplectic groups over
modular rings.Comment: 6 pages, to appear in Proceedings of QTS7 "Quantum Theory and
Symmetries 7", Prague, August 7-13, 201
On Representations of sl(n, C) Compatible with a Z2-grading
This paper extends existing Lie algebra representation theory related to Lie algebra gradings. The notion of a representation compatible with a given grading is applied to finite-dimensional representations of sl(n,C) in relation to its Z2-gradings. For representation theory of sl(n,C) the Gel’fand-Tseitlin method turned out very efficient. We show that it is not generally true that every irreducible representation can be compatibly graded
Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions
Mutually unbiased bases in Hilbert spaces of finite dimensions are closely
related to the quantal notion of complementarity. An alternative proof of
existence of a maximal collection of N+1 mutually unbiased bases in Hilbert
spaces of prime dimension N is given by exploiting the finite Heisenberg group
(also called the Pauli group) and the action of SL(2,Z_N) on finite phase space
Z_N x Z_N implemented by unitary operators in the Hilbert space. Crucial for
the proof is that, for prime N, Z_N is also a finite field.Comment: 13 pages; accepted in J. Phys. A: Math. Theo
The Newest Offering in the Higher Education Leadership Movement: A Model Campus-Wide Residential Program for Faculty and Staff .
The purpose of this article is to review the recent emphases by institutions of higher education on leadership development and to describe a model program for a population not yet widely addressed: faculty and staff
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