2016/10/19 by Stan Gudder, Gudder, Stan
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #General Physics (physics.gen-ph) #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.1610.07877
openalex publication_date 2016/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We begin with a description of spacetime by a 4-dimensional cubic lattice \sscript. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space \sscripthat corresponds to a cubic lattice of energy-momentum. This description implies that there is a discrete set of possible particle masses. We then define discrete scalar quantum fields on \sscript. These fields are employed to define interaction Hamiltonians and scattering operators. Although the scattering operator S cannot be computed exactly, approximations are possible. Whether S is unitary is an unsolved problem. Besides the definitions of these operators, our main assumption is conservation of energy-momentum for a scattering process. This article concludes with various examples of perturbation approximations. These include simplified versions of electron-electron and electron-proton scattering as well as simple decay processes. We also define scattering cross-sections, decay rates and lifetimes within this formalism.