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

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 assump tion concerns the Euclidean structure of gravity-free space and the homogen eity of gravity-free time in the usual inertial coordinate system. Introduc ing the primed inertial coordinate system, in addition to the usual inertia l coordinate system, for each inertial frame of reference, we assume the Eu clidean structures of gravity-free space and time in the primed inertial co ordinate system and their generalized Finslerian structures in the usual in ertial coordinate system. We combine the alternative assumption with the tw o postulates (i) and (ii) to modify the special theory of relativity. The m odified special relativity theory involves two versions of the light speed, infinite c' in the primed inertial coordinate system and finite c in the u sual inertial coordinate system. It also involves the c'-type Galilean tran sformation between any two primed inertial coordinate systems and the local ized Lorentz transformation between two corresponding usual inertial coordi nate systems. Since all our experimental data are collected and expressed i n the usual inertial coordinate system, the physical principle is: the c'-t ype Galilean invariance in the primed inertial coordinate system plus the t ransformation from the primed inertial coordinate system to the usual inert ial coordinate system. This principle is applied to a reformulation of mech anics, field theory and quantum field theory. Relativistic mechanics in the usual inertial coordinate system is unchanged, while field theory is devel oped and divergence-free. Any c'-type Galilean-invariant field system can b e quantized by using the canonical quantization method in the primed inerti al coordinate system. We establish a transformation law for quantized field systems as they are transformed from the primed to the usual inertial coor dinate system. It is shown that the modified special relativity theory, tog ether with quantum mechanics, leads to a convergent and invariant quantum f ield 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, local ity of interactions, and local or global gauge symmetries. (C) 2001 Elsevie r Science Ltd. All rights reserved.