Functional integrals for spin‐Bose systems

The problem of obtaining the propagator of a spin‐Bose system consisting of spins‐ 1/2 and several radiation modes in interaction is reduced to developing a bosonized Hamiltonian for the system from the propagator of which, by appropriate projection, the propagator relating to the original Hamiltoni...

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Bibliographic Details
Published in:Journal of mathematical physics 1986-01, Vol.27 (1), p.221-228
Main Author: Papadopoulos, G. J.
Format: Article
Language:English
Subjects:
Boson systems
Exact sciences and technology
Physics
Quantum statistical mechanics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary:The problem of obtaining the propagator of a spin‐Bose system consisting of spins‐ 1/2 and several radiation modes in interaction is reduced to developing a bosonized Hamiltonian for the system from the propagator of which, by appropriate projection, the propagator relating to the original Hamiltonian is extracted. The analysis proceeds via functional integration involving the evaluation of two auxiliary propagators of Schrödinger equations whose Hamiltonians depend separately on radiation operators, and bosonized spin operators. These propagators are coupled through a complex field and the functional average of their product against a Gaussian measure of the field leads to the bosonized system’s propagator. The procedure is applied to the propagator for a single spin‐Bose system which is obtained as a power series in the spin flipping energy. The analysis is also applied for an explicit evaluation in the case of a simplified spin‐Bose Hamiltonian.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.527365