Modular degeneracy of vacuum zero potential point and gauge transformations

This paper presents an extended gauge theory which can contain the Higgs mechanism, considering ⁴ field theory as an example. It can introduce interaction into different vacuum modular degeneracy states and break modular degeneracy. At the same time we can obtain both massless and massive vector bosons. According to the extended gauge theory, gauge transformations can be classified into two kinds: those with fixed parameter, called simply definite gauge transformations, which have a function of breaking modular degeneracy, and indefinite gauge transformations, which have a function of keeping phase degeneracy.