How to increase the applicability of integral transform approaches in physics?

TL;DR

This paper discusses expanding the use of integral transform methods in physics beyond the Laplace kernel, emphasizing the potential of bell-shaped kernels like the Lorentz kernel to improve ab initio calculations of many-body systems.

Contribution

It highlights the need for developing new kernels suitable for many-body problems to enhance the applicability of integral transform approaches in physics.

Findings

Lorentz kernel enables ab initio continuum calculations in nuclear physics.

Bell-shaped kernels improve the inversion problem of integral transforms.

Potential for integral transforms to become primary tools in many-body physics.

Abstract

Integral transform approaches are numerous in many fields of physics, but in most cases limited to the use of the Laplace kernel. However, it is well known that the inversion of the Laplace transform is very problematic, so that the function related to the physical observable is in most cases unaccessible. The great advantage of kernels of bell-shaped form has been demonstrated in few-body nuclear systems. In fact the use of the Lorentz kernel has allowed to overcome the stumbling block of the ab initio description of reactions to the full continuum of systems of more than three particles. The problem of finding kernels of similar form, applicable to many-body problems deserves particular attention. If this search were successful the integral transform approach might represent the only viable ab initio access to many observables that are not calculable directly.