Paul Finkler

Path integrals with arbitrary generators and the eigenfunction problem

Abstract We generalize the path integral formalism of quantum mechanics to include the use of arbitrary infinitesimal generators, thus providing explicit expressions for solutions of a wide class of differential equations. In particular, we develop a method of calculating the eigenfunctions of a large class of operators.

On the Relation between Hard-Core and Velocity-Dependent Potentials: An Application to the Photonuclear Sum Rules

A canonical transformation relating hard-core and velocity-dependent nucleon-nucleon potentials is applied to the Srivastava potential and an equivalent hard-core potential is found. It is shown that the deuteron photonuclear electric-dipole integrated and bremsstrahlung-weighted cross sections resulting from the two equivalent potentials are essentially the same. The reasons for this agreement suggest that differences between the two sets of cross sections may remain small in other nuclei employing this type of potential.

Bilinear equation for the cylinder with overlap and the Pomeron residue

A bilinear integral equation for the cylinder is derived within the meson sector of the theory of dual topological unitarization. The equation is more general than conventional linear cylinder equations since it includes regions of phase space in which produced particles overlap in rapidity. The equation also permits a simple treatment of phase space which corresponds to that of the planar bootstrap problem. Two classes of solutions are found, only one of which results in the Pomeron-f identity. This treatment also indicates that the residue of the Pomeron may be twice as large as that suggested by earlier calculations but in agreement with a more recent calculation.