## Path integrals on finite sets.(English)Zbl 0853.58026

The author uses the formalism of the Feynman path integral to “solve” $-{1 \over i} {\partial \over \partial t} \phi_t = H_0 \phi_t$ where $$H_0$$ is a self-adjoint operator on $$L^2(M) = \mathbb{C}^M$$, $$M$$ being a finite set. The paths are functions of $$\mathbb{R}$$ with values in $$M$$. The path integral here is a family of measures parametrized by $$t'$$ and $$t$$ with values in the space of operators on $$L^2(M)$$. The relationship of these measures to the measures of a Markov process is studied and it is shown that these measures are concentrated on a certain set of step measures. Some applications to certain hypothetical systems are also considered.

### MSC:

 58D30 Applications of manifolds of mappings to the sciences 81S40 Path integrals in quantum mechanics 46G10 Vector-valued measures and integration
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### References:

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