2023/05/19 by Haba, Z.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2305.11989
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations which are the Fourier-Laplace transforms of a complex measure and for polynomials of the fotm x4n and x4n+2 (where n is a natural number). We extend the method to quantum field theory (QFT) with complex scaled spatial coordinates \bf x→ i\bf x. We show that such a complex extension of the path integral (in the real time) allows a rigorous path integral treatment of a large class of potentials including the ones unbounded from below.