Path Integrals, Coherent States, and Geometric Quantization

1980 ◽  
pp. 125-142 ◽  
Author(s):  
H. P. Berg ◽  
Jan Tarski
Keyword(s):  
Coherent States ◽  
Path Integrals ◽  
Geometric Quantization

COHERENT STATES WITHOUT GROUPS: QUANTIZATION ON NONHOMOGENEOUS MANIFOLDS

1993 ◽  
Vol 08 (18) ◽  
pp. 1735-1738 ◽  
Author(s):  
JOHN R. KLAUDER
Keyword(s):  
Phase Space ◽  
Coherent State ◽  
Wide Class ◽  
Coherent States ◽  
Path Integrals ◽  
Killing Vector ◽  
Single Variable ◽  
Holomorphic Representation ◽  
Representation Spaces ◽  
State Path

A wide class of single-variable holomorphic representation spaces are constructed that are associated with very general sets of coherent states defined without the use of transitively acting groups. These representations and states are used to define coherent-state path integrals involving phase-space manifolds having one Killing vector but a quite general curvature otherwise.

Path Integrals and Coherent States of SU(2) and SU(1,1)

10.1142/1404 ◽  
1992 ◽  
Author(s):  
A Inomata ◽  
H Kuratsuji ◽  
C C Gerry
Keyword(s):  
Coherent States ◽  
Path Integrals

scholarly journals SU(2) COHERENT STATE PATH INTEGRALS LABELED BY A FULL SET OF EULER ANGLES: BASIC FORMULATION

2012 ◽  
Vol 26 (29) ◽  
pp. 1250143 ◽  
Author(s):  
MASAO MATSUMOTO
Keyword(s):  
Integral Representation ◽  
Coherent State ◽  
Path Integral ◽  
Coherent States ◽  
Path Integrals ◽  
Euler Angles ◽  
Geometric Phases ◽  
Path Integral Representation ◽  
General Systems ◽  
State Path

We develop a basic formulation of the spin (SU(2)) coherent state path integrals based not on the conventional highest or lowest weight vectors but on arbitrary fiducial vectors. The coherent states, being defined on a 3-sphere, are specified by a full set of Euler angles. They are generally considered as states without classical analogues. The overcompleteness relation holds for the states, by which we obtain the time evolution of general systems in terms of the path integral representation; the resultant Lagrangian in the action has a monopole-type term à la Balachandran et al. as well as some additional terms, both of which depend on fiducial vectors in a simple way. The process of the discrete path integrals to the continuous ones is clarified. Complex variable forms of the states and path integrals are also obtained. During the course of all steps, we emphasize the analogies and correspondences to the general canonical coherent states and path integrals that we proposed some time ago. In this paper we concentrate on the basic formulation. The physical applications as well as criteria in choosing fiducial vectors for real Lagrangians, in relation to fictitious monopoles and geometric phases, will be treated in subsequent papers separately.

Remarks on the geometric quantization of Landau levels

2016 ◽  
Vol 13 (10) ◽  
pp. 1650122 ◽  
Author(s):  
Andrea Galasso ◽  
Mauro Spera
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Coherent States ◽  
Geometric Quantization ◽  
Index Theory ◽  
Landau Levels ◽  
Translational Symmetry ◽  
Vertical Polarization ◽  
Lowest Landau Level ◽  
Theoretic Description

In this note, we resume the geometric quantization approach to the motion of a charged particle on a plane, subject to a constant magnetic field perpendicular to the latter, by showing directly that it gives rise to a completely integrable system to which we may apply holomorphic geometric quantization. In addition, we present a variant employing a suitable vertical polarization and we also make contact with Bott’s quantization, enforcing the property “quantization commutes with reduction”, which is known to hold under quite general conditions. We also provide an interpretation of translational symmetry breaking in terms of coherent states and index theory. Finally, we give a representation theoretic description of the lowest Landau level via the use of an [Formula: see text]-equivariant Dirac operator.

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