Abstract
The Hamiltonian path integral for reggeon quantum mechanics with cubic and quartic interactions is unambiguously defined. On the basis of a recursion formula on the time lattice, a generalized Trotter formula is given and proven to be equivalent to a Lagrangian path integral for a Schroedinger problem in an interval. The potential occuring in this formula is the same found in previous papers, and the corresponding path integral exists also in the limit of vanishing quartic coupling. This provides a regularization procedure for the purely cubic case for both α(0) less or greater than one. All previous results are confirmed, in particular the tunnel-like energy gap.
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