# Solving the path integral for $(ax)^4-(bx)^2$ potential

I need help in solving the path integral of potential given by the form $(ax)^4-(bx)^2$

This potential is maybe known as Ginzberg Landau potential

I tried using the approximation in which the integral reduces to a function of time times an exponential factor carrying ($i/h$)(Classical action). (see Quantum Mechanics and Path Integrals, Feyman, Hibbs; section 3-5: Gaussian Integrals) It still gives an integration which is difficult to handle.

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There's no exact solution of this path integral in four dimensions. Pick up any field theory text and read its treatment of the perturbation theory of the $\phi^{4}$ potential, which should be the first example given in the textbook. – Jerry Schirmer Feb 11 at 17:02