Treatment of a two-level system with a pseudo-Hermitian Hamiltonian by the spin coherent state path integral approach

2013 ◽  
Author(s):  
Mekki Aouachria ◽  
Farida Halimi ◽  
Rima Rekik
Keyword(s):  
Coherent State ◽  
Path Integral ◽  
Integral Approach ◽  
Level System ◽  
Path Integral Approach ◽  
Spin Coherent State ◽  
State Path

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.

Quantization on the circle

2006 ◽  
Vol 84 (5) ◽  
pp. 335-344
Author(s):  
M Merad
Keyword(s):  
Magnetic Field ◽  
External Field ◽  
Coherent State ◽  
Path Integral ◽  
Free Particle ◽  
Integral Approach ◽  
Topological Properties ◽  
Path Integral Approach ◽  
Second Stage ◽  
The Magnetic Field

We present, via the path-integral approach, the quantum study of a particle without spin constrained to move on a circle and subjected to the action of an external field (V, A). In the first stage, we follow the Faddeev–Senjanovic constraints technique that is essentially based on the Dirac algorithm; and in the second stage, we use the path-integral coherent state relative to the circle, compatible with the topological properties. In the two cases, the free particle and the problem of the magnetic field are shown as an illustrative calculation.PACS Nos.: 03.65–w, 03.65Ca, 03.65.Db

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