Logical Foundations of Local Gauge Symmetry and Symmetry Breaking

Abstract

Quantum field theory has successfully generated a number of general conclusions. It seems meaningful to disclose the logical forms of these conclusions. The present paper reports two results. The first result shows the logic of local gauge symmetry and indefinability of mass. The second result shows the logic of Higgs mechanism and definability of mass. The results are obtained by integrating four components, namely, gauge symmetry and Higgs mechanism in quantum field theory, and incompleteness theorem and indefinability theorem in mathematical logic. Godel numbering is the key for arithmetic modeling applied in this paper.