Functional integral for the molecular polaron withq2coupling

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Abstract
The density matrix of a two-state electronic system coupled quadratically to an oscillator is expressed as functional integrals over commuting and anticommuting (Grassmann) elements satisfying one-sided boundary conditions. The functional integral over the oscillator coordinates is evaluated in closed form, and the resultant electronic integral which contains effective retarded interactions is evaluated in the semiclassical approximation. In the case of physical interest, N=1, we find that the semiclassical approximation already incorporates the essential physical features of the exact solution, for all values of the interaction strength and of the temperature.