Abstract
Abstract Wilson's quantum field theory (QFT) 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 QFT in less than 4 dimensions, Newton–Leibniz's differential-integral formulas must be extended to the noninteger 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.
Highlights
Wilson’s quantum field theory (QFT) 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 QFT in less than 4 dimensions, Newton–Leibniz’s differential-integral formulas must be extended to the noninteger 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
The Higgs particle is an important part of the standard model of particle physics, and it has been recently discovered at CERN [1, 2]
Summary
The Higgs particle is an important part of the standard model of particle physics, and it has been recently discovered at CERN [1, 2]. To avoid the awkward situation of fractional-dimensional space-time, Halpern and Huang [4, 5] searched for alternatives to the trivial λφ field theory by considering nonpolynomial potentials. They found that the existence of nontrivial fixed points (i.e., ultraviolet fixed points) is associated with the nonpolynomial potentials. The main purpose of this paper is just to propose some methods for testing the validity of Wilson’s proposal within the framework of particle physics To this end, let us remind that Wilson’s QFT in less than 4 dimensions lacks rigid mathematical foundation. According to Tao’s suggestion, if xðl À jDlÞ represents the point on a m-dimensional fractal curve and j 1⁄4 0; 1; 2; ..., the distance between points xðlÞ and xðl À DlÞ should yield: jDm1⁄2xðlÞ; xðl À D lÞj ð3Þ
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