Mass Operator and Gauge Field Theory with Five-variable Field Functions

Key words: 
• mass operator /
• gauge eld /
• scalar coupling

Abstract: To investigate the mass generating problem without Higgs mechanism we present a model in which a new scalar gauge coupling is naturally introduced. Because of the existence of production and annihilation for particles in quantum eld theory, we extend the number of independent variables from conventional four space-time dimensions to ve ones in order to describe all degrees of freedom for eld functions while the conventional space-time is still retained to be the background. The potential fth variable is nothing but the proper time of particles. In response, a mass operator should be introduced. After that, the lagrangian for free fermion elds in terms of ve independent variables and mass operator is written down. By applying the gauge principle, three kinds of vector
gauge couplings and one kind of scalar gauge coupling are naturally introduced. In the current scenario,the mass spectrum for all fundamental particles is accounted for in principle by solving the eigenvalue of mass operator under the function of all kinds of interactions. Moreover, there no any auxiliary mechanism including spontaneous symmetry breaking get involved in the model. Therefore, traditional problems in the standard model such as the vacuum energy problem are removed from our model, as well as the hierarchy problem on the mass spectrum for fundamental particles.