Resolving problems with the continuum limit in coherent-state path integrals

G. Kordas, Dimitrios Kalantzis, A. I. Karanikas

一幸 藤井

Emmanouil George Thrapsaniotis

Oliwier Urbański

The paper solves the problem of continuum limit in bosonic thermal coherent-state path integrals. For this purpose, exact discrete versions of the path integral are constructed for three different orderings of the Hamiltonian: normal, anti-normal and symmetric (Weyl order). Subsequently, their different continuum versions are checked on the harmonic oscillator, to choose the symmetric ordering as a possibly correct choice for all polynomial Hamiltonians. Spotted mathematical subtleties in the simple case serve as a clue to the general solution. Finally, a general justification for the symmetric order is provided by deriving the continuum path integral starting from the exact discrete case using a renormalization procedure in the imaginary time frequency domain. While the role of Weyl order has already been found, the paper provides the missing proof of its suitability for every polynomial Hamiltonian and simplifies the previously established construction by referring only to creation and annihilation operators (without position and momentum operators).

L. C. Lew Yan Voon

For a restricted class of potential problems, the Feynman path integral in the coordinate representation circumvents operator-ordering ambiguities. We will show that, in the coherent-state representation, the traditional continuum time path integral cannot resolve this issue. Using a simple solvable model, we carry out a careful analysis of the continuum limit with regularization. The latter is found to be necessary to address the operator-ordering issue.

Enrico Onofri