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An investigation of coherent state path integrals as applied to a harmonic oscillator and a single spin Voon, Lok Chong Lew Yan


In this project two steps involved in the handling of path integrals are reexamined in detail for coherent state path integals. They concern the continuum limit approximation and the regularization of the formal path integrals. Restricting oneself to the harmonic oscillator, the technique of time splitting is used to set up the coherent state path integrals and the proper way to pass to the continuum limit is demonstrated. The manipulation of these path integrals calls for regularization procedures and the validity of discrete, Riemann zeta function and 'derivative' regularization methods is observed. A modification to a fermionic theory is briefly mentioned and, finally, the above results are implemented in writing down a path integral for a single spin.

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