Corpus ID: 119321302

Four Dimensional Quantum Yang-Mills Theory and Mass Gap

@article{Farinelli2014FourDQ,
  title={Four Dimensional Quantum Yang-Mills Theory and Mass Gap},
  author={Simone Farinelli},
  journal={arXiv: General Mathematics},
  year={2014}
}
A quantization procedure for the Yang-Mills equations for the Minkowski space $\mathbf{R}^{1,3}$ is carried out in such a way that field maps satisfying Wightman's axioms of Constructive Quantum Field Theory can be obtained. Moreover, the spectrum of the corresponding QCD Hamilton operator is proven to be positive and bounded away from zero except for the case of the vacuum state which has vanishing energy level. The particles corresponding to all solution fields are bosons. As expected from… Expand
1 Citations

Tables from this paper

Abstract Wiener measure using abelian Yang-Mills action on $\mathbb{R}^4$.
Let $\mathfrak{g}$ be the Lie algebra of a compact Lie group. For a $\mathfrak{g}$-valued 1-form $A$, consider the Yang-Mills action \begin{equation} S_{\rm YM}(A) = \int_{\mathbb{R}^4} \left|dA + AExpand

References

SHOWING 1-10 OF 99 REFERENCES
Mass gap in a Yang-Mills theory in the strong coupling limit
We prove that in the limit of the coupling going to infinity a Yang-Mills theory is equivalent to a $\lambda\phi^4$ theory with the dynamics ruled just by a homogeneous equation. This givesExpand
Mass gap in quantum energy-mass spectrum of relativistic Yang-Mills fields
A non-perturbative relativistic quantum Yang-Mills theory with a semisimple compact gauge Lie group on the four-dimensional Minkowski spacetime is set up in a Schroedinger representation withExpand
Quantum Yang-Mills-Weyl Dynamics in Schroedinger paradigm
Inspired by F. Wilczek's QCD Lite, quantum Yang-Mills-Weyl Dynamics (YMWD) describes quantum interaction between gauge bosons (associated with a simple compact gauge Lie group $\mathbb{G}$) and larksExpand
Nonperturbative results for Yang-Mills theories
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 oneExpand
The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space
In this paper we complete the proof of global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space by showing that an appropriate norm of the solutions cannot blow up in a finiteExpand
Nonperturbative aspects of Yang-Mills theory
In this thesis, several aspects of Yang-Mills theory are studied. It begins with the constrained quantization in the Coulomb gauge, using the Dirac bracket formalism. A nonperturbative analysis ofExpand
Hamiltonian formulations of Yang- Mills theory and gauge ambiguity in quantization
A general formulation of the Hamiltonian in non-Abelian Yang-Mills theory is given. The subject of gauge-fixing ambiguity is investigated. It is shown how this type of degeneracy affects theExpand
Mass in Quantum Yang-Mills Theory
Among seven problems, proposed for XXI century by Clay Mathematical Institute, there are two stemming from physics. One of them is called "Yang-Mills Existence and Mass Gap". The detailed statementExpand
Quantum Yang-Mills theory
Since the early part of the twentieth century, it has been understood that the description of nature at the subatomic scale requires quantum mechanics. In quantum mechanics, the position and velocityExpand
Quantization of non-Abelian gauge theories
Abstract It is shown that the fixing of the divergence of the potential in non-Abelian theories does not fix its gauge. The ambiguity in the definition of the potential leads to the fact that, whenExpand
...
1
2
3
4
5
...