Modification of special relativity and formulation of convergent and invariant quantum field theory

Abstract

Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, the special theory of relativity uses another assumption. This other assumption concerns the Euclidean structure of gravity-free space and the homogeneity of gravity-free time in the usual inertial coordinate system. Introducing the primed inertial coordinate system, in addition to the usual inertial coordinate system, for each inertial frame of reference, we assume the Euclidean structures of gravity-free space and time in the primed inertial coordinate system and their generalized Finslerian structures in the usual inertial coordinate system. We combine the alternative assumption with the two postulates (i) and (ii) to modify the special theory of relativity. The modified special relativity theory involves two versions of the light speed, infinite c′ in the primed inertial coordinate system and finite c in the usual inertial coordinate system. It also involves the c′-type Galilean transformation between any two primed inertial coordinate systems and the localized Lorentz transformation between two corresponding usual inertial coordinate systems. Since all our experimental data are collected and expressed in the usual inertial coordinate system, the physical principle is: the c′-type Galilean invariance in the primed inertial coordinate system plus the transformation from the primed inertial coordinate system to the usual inertial coordinate system. This principle is applied to a reformulation of mechanics, field theory and quantum field theory. Relativistic mechanics in the usual inertial coordinate system is unchanged, while field theory is developed and divergence-free. Any c′-type Galilean-invariant field system can be quantized by using the canonical quantization method in the primed inertial coordinate system. We establish a transformation law for quantized field systems as they are transformed from the primed to the usual inertial coordinate system. It is shown that the modified special relativity theory, together with quantum mechanics, leads to a convergent and invariant quantum field theory, in full agreement with experimental facts. The formulation of this quantum field theory does not demand departures from the concepts such as local Lorentz invariance in the usual inertial coordinate system, locality of interactions, and local or global gauge symmetries.