Testing for Wilson’s Quantum Field Theory in Less Than 4 Dimensions

Abstract

Wilson’s quantum field theory in less than 4 dimensions has achieved a great success in the study of critical phenomenon, but is still not tested within the scope of particle physics. To guarantee the validity of Wilson’s quantum field theory in less than 4 dimensions, Newton-Leibniz’s differential-integral formulas must be extended to the non-integer dimensional situation. We show that this leads to a new prediction that Planck’s constant will be expressed in terms of three fundamental constants: critical time scale, dimension of time axis and total energy of universe. We propose the corresponding methods to measure these three constants. It will be thus interesting to compare the well-known value of Planck’s constant with the potential theoretical value consisting of three fundamental constants.