Path Integrals and Coherent States

1985 ◽  
pp. 449-521
Keyword(s):  
Coherent States ◽  
Path Integrals

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.

Parametric-time coherent states for Morse potential

2002 ◽  
Vol 80 (8) ◽  
pp. 875-881 ◽  
Author(s):  
N Unal
Keyword(s):  
Coherent States ◽  
Morse Potential ◽  
Potential Problem ◽  
Path Integrals ◽  
Harmonic Oscillators

We transform the Lagrangian of the Morse-potential problem into two harmonic oscillators in a new parametric time and quantize this system by using path integrals over holomorphic coordinates of oscillators and derive coherent states. PACS Nos.: 31.15-p, 03.65Ca, 03.65Ge

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