Date: Apr 1, 2013 2:18 PM
Author: Rock Brentwood
Subject: Solution to the Mass Gap Problem in submission to Annalen der Physik

A long-standing open problem in axiomatic quantum field theory, it is
widely believed that the intractibility of the Mass Gap Problem
reflects a gap in the knowledge or understanding of foundational
principles in physics; and has attracted the attention of the Clay
Math foundation, which placed a bounty on the solution of the problem,
expressing the hopes and expectation that its resolution will involve
the formulation of some kind of newer foundation to quantum field
theory, itself.

The following is the extended abstract of a paper awaiting submission
to Annalen der Physik, which contains such a far-reaching
reformulation that involves a simultaneous resolution to the Coleman-
Mandula Theorem, Raifeartaigh Theorem, Leutwyler ("No Interaction")
Theorem and Haag Theorem; and entails, as a consequence of the
resolution of the latter theorem, a reformulation of Quantum Field
Theory that contains a solution to the Mass Gap Problem.

Reference:
M.W. Hopkins, "Unification of Galilei, Poincare and Euclidean
Symmetry",
Quantum Topology / Hopf Algebra Seminar, UI-Chicago, 2008 October 7,
http://www.math.uic.edu/seminars/view_seminar?id=998

On the Relativistic Dynamics of Moving Bodies
Extended Abstract
In the 20th century we came to a revised understanding of just what
classical physics actually was, over three centuries after its initial
formulation by Newton. Unfortunately, it came a few decades after the
older paradigm had already been superseded by the theory of
relativity.

More unfortunately, still, is that this newer understanding was never
properly reintegrated into the newer paradigm, thereby unwittingly
cutting the moorings loose from any simple formulation of the
Correspondence Limit. Had our revised view originally been present in
the formative 1905-1908 period, it would have also entailed an altered
course in the development of relativity, leading to an outcome that,
itself, represents an upward revision of what we presently understand
it to be.

Consequently, the development of the theory of relativity is not yet
complete.

When the revision is made (restoring a more cohesive form of the
Correspondence Limit in the process), the result is that the paradoxes
comprising the Haag Theorem, Coleman-Mandula Theorem, Raifeartaigh
Theorem and Leutwyler (?No Interaction?) Theorem can all be resolved,
thereby leading the way to a bona fide relativistic dynamics of
interacting bodies ? both in the classical and quantum settings. In
the latter case, this entails non-trivially interacting quantum
systems composed of a finite number of degrees of freedom per unit
volume and leads directly to a reformulation of a quantum field theory
free of infinities, in which the mass gap problem may be resolved in
the affirmative.

This modification represents the integration of Newton's Third Law
into relativity, where it has been conspicuously absent up to now;
with the integration containing the kernel of the A-R approach to the
Self-Force problem, as a consequence.

It leads to a unified framework that not only encompasses relativistic
and non-relativistic dynamics, but also the (similarly revised)
descriptions of free and interacting systems that conform to the
(anti-)De Sitter, Newton-Hooke, Para-Poincare', Para-Galilei, Carroll,
Static, Euclidean, Spherical and Hyperbolic groups, in the process
also providing two separate routes of connection and transformation
between the 3+1 Lorentzian and 4+0 Euclidean forms of dynamics.

In this paper we will spell out the details of the modification, the
revised formulation of dynamics and, within the new unified framework,
shall construct counter-examples to each of the four No Go theorems
cited. The most important of these counter-examples is of the Coleman-
Mandula theorem and involves a reconstruction of the electroweak Higgs
model that contains a predicted value for the Higgs mass that falls
within the currently established experimental bounds. We will also lay
out a reformulation of quantum field theory and prove, within this
reformulation, the existence of a mass gap for gauge theories
constructed from a large family of Langrangians that includes the Yang-
Mills Lagrangans.