File Name: yang mills and mass gap .zip
The problem is phrased as follows: . The general problem of determining the presence of a spectral gap in a system is known to be undecidable. Will this change in the 21st century?
The point is to define the limiting continuum field theory. In principle, this might even be done without taking limits. The Hamiltonian, the operator on the quantum Hilbert space which generates time translations, has a square root called the supercharge. Here we use the Moon model and Parfait logic. Furthermore, although one has changed the problem, one still has a fairly close relation to the original problem using the ideology of the renormalization group. We can start with a supersymmetric theory, and add supersymmetry breaking terms to the action which only become important at long distances as many lattice spacings, to obtain a theory with the better renormalization properties of the supersymmetric theory at short distances, but which reduces to conventional Yang-Mills theory at longer distances. Thus, a solution to the problem in a sufficiently general class of supersymmetric theories, would in fact imply the solution of the original problem.
Some nonperturbative aspects of the pure SU 3 Yang-Mills theory are investigated assuming a specific form of the beta function, based on a recent modification by Ryttov and Sannino of the known one for supersymmetric gauge theories. The characteristic feature is a pole at a particular value of the coupling constant, g. First it is noted, using dimensional analysis, that physical quantities behave smoothly as one travels from one side of the pole to the other. Assuming the usual QCD value of the coupling constant one finds the mass gap to be 1. A similar calculation is made for the supersymmetric Yang-Mills theory where the corresponding beta function is considered to be exact.
Theorem 4. The spectra are self-similar in the inverse proportion to the running coupling constant. In particular, they have self-similar positive spectral mass gaps. Presumably, this is a solution of the Yang-Mills Millennium problem. The present note shows that the fundamental spectral value of a cutoff quantum Yang-Mills energy-mass operator is the simple zero eigenvalue with the vacuum eigenvector. The direct proof without von Neumann algebras is based on the domination over the number operator with simple fundamental eigenvalue and the standard spectral variational principle. This is a preview of subscription content, access via your institution.
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. Does the problem require that the "construction" of a four dimensional quantum Yang-Mills be non-perturbative? I get the feeling that this problem is to make notions such as the renormalization group rigorous, and thus is perturbative, but isn't lattice gauge theory already mathematically well-defined? If so, why can this not be used as an approach to this problem? Essentially, which is the preferable approach as specified by the problem: perturbative or non-perturbative?
With this work, we try to answer 3 fundamental questions that have plagued mathematicians and physicists for several decades. However, various mathematicians, even prestigious ones, consider the basic assumptions of the gauge theories to be wrong, as well as in conflict with the experimental evidences and in clear disagreement with the facts, distorcing the physical reality itself. Likewise, the Quantum Fields Theory QFT is mathematically inconsistent, adopting a mathematical structure somewhat complicated and arbitrary, which does not satisfy the strong demands for coherence. The weakest point of the gauge theories, in our opinion, consists in imposing that all the particles must be free of an intrinsic mass massless. On the contrary, even for the particle considered universally massless, i.
called ”Yang-Mills Existence and Mass Gap”. The detailed statement of the problem, written by A. Jaffe and E. Witten , gives both motivation.
A peer-reviewed article of this Preprint also exists. Yablon, J. Symmetry , 12 , Symmetry , 12, Journal reference: Symmetry , 12, DOI:
В 8 ВЕЧЕРА. В другом конце комнаты Хейл еле слышно засмеялся. Сьюзан взглянула на адресную строку сообщения. FROM: CHALECRYPTO. NSA.
- Он похоронен в нашем соборе. Беккер удивленно посмотрел на. - Разве. Я думал, что он похоронен в Доминиканской Республике. - Да нет же, черт возьми.
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Report on the Status of the Yang-Mills. Millenium Prize Problem. Michael R. Douglas. April Yang-Mills Existence and Mass Gap: Prove that for any.Reply