Derivation of the cutoff length from the quantum quadratic enhancement of a mass in vacuum energy constant Lambda

Abstract

Ultraviolet self-interaction energies in field theory sometimes contain meaningful physical quantities. The self-energies in such as classical electrodynamics are usually subtracted from the rest mass. For the consistent treatment of energies as sources of curvature in the Einstein field equations, this study includes these subtracted self-energies into vacuum energy expressed by the constant Lambda (used in such as Lambda-CDM). In this study, the self-energies in electrodynamics and macroscopic classical Einstein field equations are examined, using the formalisms with the ultraviolet cutoff scheme. One of the cutoff formalisms is the field theory in terms of the step-function-type basis functions, developed by the present authors. The other is a continuum theory of a fundamental particle with the same cutoff length. Based on the effectiveness of the continuum theory with the cutoff length shown in the examination, the dominant self-energy is the quadratic term of the Higgs field at a quantum level (classical self-energies are reduced to logarithmic forms by quantum corrections). The cutoff length is then determined to reproduce today's tiny value of Lambda for vacuum energy. Additionally, a field with nonperiodic vanishing boundary conditions is treated, showing that the field has no zero-point energy.