634 research outputs found

### Group quantization of parametrized systems II. Pasting Hilbert spaces

The method of group quantization described in the preceeding paper I is
extended so that it becomes applicable to some parametrized systems that do not
admit a global transversal surface. A simple completely solvable toy system is
studied that admits a pair of maximal transversal surfaces intersecting all
orbits. The corresponding two quantum mechanics are constructed. The similarity
of the canonical group actions in the classical phase spaces on the one hand
and in the quantum Hilbert spaces on the other hand suggests how the two
Hilbert spaces are to be pasted together. The resulting quantum theory is
checked to be equivalent to that constructed directly by means of Dirac's
operator constraint method. The complete system of partial Hamiltonians for any
of the two transversal surfaces is chosen and the quantum Schr\"{o}dinger or
Heisenberg pictures of time evolution are constructed.Comment: 35 pages, latex, no figure

### Quantizations on the circle and coherent states

We present a possible construction of coherent states on the unit circle as
configuration space. Our approach is based on Borel quantizations on S^1
including the Aharonov-Bohm type quantum description. The coherent states are
constructed by Perelomov's method as group related coherent states generated by
Weyl operators on the quantum phase space 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
and coherent states over a finite periodic chain where the quantum phase space
was Z_M x Z_M. The coherent states constructed in this work are shown to
satisfy the resolution of unity. To compare them with canonical coherent
states, also some of their further properties are studied demonstrating
similarities as well as substantial differences.Comment: 15 pages, 4 figures, accepted in J. Phys. A: Math. Theor. 45 (2012)
for the Special issue on coherent states: mathematical and physical aspect

### 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

### Curvature Dependent Diffusion Flow on Surface with Thickness

Particle diffusion in a two dimensional curved surface embedded in $R_3$ is
considered. In addition to the usual diffusion flow, we find a new flow with an
explicit curvature dependence. New diffusion equation is obtained in $\epsilon$
(thickness of surface) expansion. As an example, the surface of elliptic
cylinder is considered, and curvature dependent diffusion coefficient is
calculated.Comment: 8 pages, 8 figures, Late

### 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

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