scholarly journals INTEGRABLE SYSTEMS ON FLAG MANIFOLD AND COHERENT STATE PATH-INTEGRAL

1995 ◽  
Vol 10 (25) ◽  
pp. 1847-1855 ◽  
Author(s):  
MYUNG-HO KIM ◽  
PHILLIAL OH
Keyword(s):  
Coherent State ◽  
Path Integral ◽  
Integrable Systems ◽  
Symplectic Structure ◽  
Flag Manifold ◽  
Exact Expression ◽  
Integrable Models ◽  
Conserved Quantities ◽  
Special Cases ◽  
State Path

We construct integrable models on flag manifold by using the symplectic structure explicitly given in the Bruhat coordinatization of flag manifold. They are noncommutative integrable and some of the conserved quantities are given by the Casimir invariants. We quantize the systems using the coherent state path-integral technique and find the exact expression for the propagator for some special cases.

scholarly journals A NOTE ON (SPIN-) COHERENT-STATE PATH INTEGRAL

1999 ◽  
Vol 13 (02) ◽  
pp. 107-140 ◽  
Author(s):  
JUNYA SHIBATA ◽  
SHIN TAKAGI
Keyword(s):  
Coherent State ◽  
Path Integral ◽  
Continuous Time ◽  
Classical Level ◽  
Classical Action ◽  
Single Spin ◽  
Spin Coherent State ◽  
Classical Path ◽  
Time Formalism ◽  
State Path

It is pointed out that there are some fundamental difficulties with the frequently used continuous-time formalism of the spin-coherent-state path integral. They arise already in a single-spin system and at the level of the "classical action" not to speak of fluctuations around the "classical path". Similar difficulties turn out to be present in the case of the (boson-)coherent-state path integral as well; although partially circumventable by an ingenious trick (Klauder's ∊-prescription) at the "classical level", they manifest themselves at the level of fluctuations. Detailed analysis of the origin of these difficulties makes it clear that the only way of avoiding them is to work with the proper discrete-time formalism. The thesis is explicitly illustrated with a harmonic oscillator and a spin under a constant magnetic field.

scholarly journals A COHERENT STATE PATH INTEGRAL FOR ANYONS

1995 ◽  
Vol 10 (12) ◽  
pp. 985-989 ◽  
Author(s):  
J. GRUNDBERG ◽  
T.H. HANSSON
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Coherent States ◽  
Integral Formula ◽  
Harmonic Potential ◽  
One Dimensional ◽  
Change Of Variables ◽  
The One ◽  
State Path

We derive an su (1, 1) coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to an su (1, 1) version of the Holstein-Primakoff transformation.

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