Title: 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.