#### Thales

**Registered Member**

This thread shall become about starting to consider the many open questions pertaining to the

The Clay Mathematics Institute page contains a [.pdf] of the "Official Problem Description", as well as another document concerning "The Status of The Problem" by Michael Douglas. There is additionally a supplementary lecture by Lorenzo Sadun located directly under the "Related links" sub-header. And, of course, the Wikipedia page likewise provides a working statement of the problem:

I recently happened upon this

Put differently, what should I read about this sort of 'topicality'

A heartfelt "thanks"- truly - for your effort,

**Yang–Mills and Mass Gap**. That will be the generic "purpose" of this post, rather than attempting to cause a proof of it to appear, immediately. As such, it remains an unsolved problem in the field of 'mathematical physics', and one of seven Millennium Prize Problems as defined by the Clay Mathematics Institute. Here is a__link__to the CMI description of the__Yang-Mills existence and mass gap__problem:The laws of quantum physics stand to the world of elementary particles in the way that Newton's laws of classical mechanics stand to the macroscopic world. Almost half a century ago, Yang and Mills introduced a remarkable new framework to describe elementary particles using structures that also occur in geometry. Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the "mass gap": the quantum particles have positive masses, even though the classical waves travel at the speed of light. This property has been discovered by physicists from experiment and confirmed by computer simulations, but it still has not been understood from a theoretical point of view. Progress in establishing the existence of the Yang-Mills theory and a mass gap will require the introduction of fundamental new ideas both in physics and in mathematics.

The Clay Mathematics Institute page contains a [.pdf] of the "Official Problem Description", as well as another document concerning "The Status of The Problem" by Michael Douglas. There is additionally a supplementary lecture by Lorenzo Sadun located directly under the "Related links" sub-header. And, of course, the Wikipedia page likewise provides a working statement of the problem:

The problem is phrased as follows:[1]

Yang–Mills Existence and Mass Gap. Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists onand has a mass gap Δ > 0. Existence includes establishing axiomatic properties at least as strong as those cited in Streater & Wightman (1964), Osterwalder & Schrader (1973) and Osterwalder & Schrader (1975).

I recently happened upon this

*n*Lab page for "mass gap" and admittedly I am left at a bit of a "loss" since I am wholly unclear as to what specific background is requisite so as to be actually able to apprehend, properly summarize, or have any*real*putative access to this seemingly important issue. What happened, historiographically, in that wide area of mathematical physics?Put differently, what should I read about this sort of 'topicality'

*first*? How should one*begin*to learn 'non-perturbative quantum field theory'? That said, SciForum, I am just writing right now to sound off this initial inquiry: What are your most intelligent thoughts surrounding Yang-Mills and "mass gap"? Are there any available insights into how to best approach this problem, that you would wish to discuss?A heartfelt "thanks"- truly - for your effort,

*Thales*
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