3.9.13  Yang-Mills Theory

Yang-Mills fields are gauge fields used in modern physics to describe physical fields that play the role of carriers in fundamental interaction. In 1954, C.N. Yang and R.L. Mills suggested that the space of intrinsic degrees of freedom of elementary particles depends on the points of space-time, and the intrinsic spaces corresponding to different points are not canonically isomorphic. In geometrical terms, this suggestion means that the space of intrinsic degrees of freedom is a vector bundle over space-time that does not have a canonical trivialization, and physical fields are described by cross-sections of this bundle. To describe the differential evolution equation of a field one has to define a connection in the bundle, that is, a trivialization of the bundle along the curves in the base. Such a connection with a fixed holonomy group describes a physical field, usually called a Yang-Mills field. The equations for a free Yang-Mills field can be deduced from a variational principle. They are a natural non-linear generalization of Maxwell’s equations.

The most important Quantum Field Theories describing elementary particles are gauge theories formulated in terms of a principal fibre bundle over the Minkowski space-time with particular choices of the structure group. Given an arbitrary compact gauge group, does a non-trivial quantum Yang-Mills theory with a finite mass gap exist?

This problem is listed as one of the Millennium Prize Problems in mathematics given by the Clay Institute, which is to prove that for any compact simple gauge group, a non-trivial quantum Yang–Mills theory exists onand has a mass gap. Existence includes establishing strong axiomatic properties, such as those cited in Streater & Wightman (1964), Osterwalder & Schrader (1973) and Osterwalder & Schrader (1975).

As it was accurately anticipated by Jaffe and Witten in the Official Problem Description, that establishing the existence of Yang-Mills theory and mass gap requires the introduction of fundamental new ideas both in physics and in mathematics. Hence, the innovative concept of the Duality of Time and perpetual creation of space provide a dynamic granular structure of space-time which clearly indicates the existence of a minimum physical mass as a result of the coupling between at least two geometrical points, or the individual monads that are the temporal images of the only one Single Monad that is actually described by real existence at the real flow of time. Since the massless monads are abruptly bursting from vacuum to the speed of light, and because they cannot coexist together in the inner level of time, when two monads couples to form a physical particle their minimum average velocity on the normal outward level of time would equal at least half the speed of light, because the speed of each one of them must be either zero or, which gives the particle a minimum positive energy or rest mass.

The problem in most current theories is that they consider space-time as a background continuum, where particles propagate in continuous existence, which means that they can acquire any infinitesimal energy. With the new concept of the Duality of Time and perpetual creation of space, there is no motion in the common sense that the object or particle gradually leaves its place to occupy new infinitesimally adjacent places, but it is perpetually re-created in those new places. Therefore, there is no instantaneous transmutation but an average change between the discrete points of space, which also takes a discrete duration of time. These discrete instances of space-time are created dynamically to form the aether which then may condense into matter particles at some higher excited states. This dynamic aether does not contradict the null result of Michelson-Morley experiment which proved that light travels with the same speed regardless whether it was moving in the direction of the movement of the Earth or perpendicular to it. On the contrary, this constancy and invariance of the speed of light can now be explained as the speed of the dynamic creation of space, and it is the only real speed in nature, while the limited velocities of objects and matter particles are a result of averaging over the inner levels of time.