Toward construction of a consistent field theory with Poincare covariance in terms of step-function-type basis functions showing confinement/deconfinement, mass-gap and Regge trajectory for non-pure/pure non-Abelian gauge fields

摘要

This article is a review by the authors concerning the construction of aPoincar${\rm \acute{e}}$ covariant (owing to spacetime continuum)field-theoretic formalism in terms of step-function-type basis functionswithout ultraviolet divergences. This formalism analytically derivesconfinement/deconfinement, mass-gap and Regge trajectory for non-Abelian gaugefields, and gives solutions for self-interacting scalar fields. Fieldspropagate in spacetime continuum and fields with finite degrees of freedomtoward continuum limit have no ultraviolet divergence. Basis functions definedin a parameter spacetime are mapped to real spacetime. The authors derive a newsolution comprised of classical fields as a vacuum and quantum fluctuations,leading to the linear potential between the particle and antiparticle from theWilson loop. The Polyakov line gives finite binding energies and reveals thedeconfining property at high temperatures. The quantum action yields positivemass from the classical fields and quantum fluctuations produces the Coulombpotential. Pure Yang-Mills fields show the same mass-gap owing to theparticle-antiparticle pair creation. The Dirac equation under linear potentialis analytically solved in this formalism, reproducing the principal propertiesof Regge trajectories at a quantum level. Further outlook mentions apossibility of the difference between conventional continuum and present wavefunctions responsible for the cosmological constant.