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Coherent State Path Integral for the Harmonic Oscillator and a Spin Particle in a Constant Magnetic field
Author(s) -
Bergeron Mario
Publication year - 1992
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190400203
Subject(s) - path integral formulation , coherent states , harmonic oscillator , physics , relation between schrödinger's equation and the path integral formulation of quantum mechanics , quantum mechanics , free particle , creation and annihilation operators , spin (aerodynamics) , feynman diagram , mathematics , quantum , thermodynamics
Definition and formulas for harmonic oscillator coherent states and spin coherent states are reviewed in detail. The path integral formalism and its relation with the partition function of a system are also reviewed. The harmonic oscillator coherent state path integral is evaluated exactly at the discrete level and then used to find its continuum limit using various regularizations. The computation of the path integral for a particle of spin s put in a constant magnetic field is carried out using harmonic oscillator coherent states and spin coherent states, with a careful analysis of infinitesimal terms (in 1/ N where N is the number of time slices) appearing in the Lagrangian. A mapping of the spin system into a CP 1 model is shown explicitly. The theory of a spinless particle in the field of a magnetic monopole and its relation with the spin system are explained. The equivalence of these two models is established up to infinitesimal order by the introduction of an external field correction. This gives a new representation of a coherent state path integral in terms of a more familiar Feynman path integral.