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Yang-Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics,…
In a previous paper we introduced two linear spinor equations equivalent to the Lorentz Force and stated that these equations were fairly general and could be applied to any force field compatible with Special Relativity. In this paper, via…
We study the gravitational duals of $d$-dimensional Yang-Mills theories with $d\leq 6$ in the presence of an ${\cal O} (N^2)$ density of heavy quarks, with $N$ the number of colors. For concreteness we focus on maximally supersymmetric…
We solve a generalization of ordinary N=1 super Yang-Mills theory with gauge group U(N) and an adjoint chiral multiplet X for which we turn on both an arbitrary tree-level superpotential term \int d^{2}\theta Tr W(X) and an arbitrary…
We discuss $SL(2,Z)$ subgroups appropriate for the study of $N=2$ Super Yang-Mills with $N_f=2n$ flavors. Hyperelliptic curves describing such theories should have coefficients that are modular forms of these subgroups. In particular,…
We propose a new reformulation of Yang-Mills theory in which three- and four-gluon self-interactions are eliminated at the price of introducing a sufficient number of auxiliary fields. We discuss the validity of this reformulation in the…
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 of the infrared asymptotics of propagators in…
The classical Yang-Mills equations are solved for arbitrary semi-simple gauge groups in the Schwinger-Fock gauge. A new class of SU(N) instantons is presented which are not embeddings of SU(N-1) instantons but have non-trivial SU(N) color…
In this talk, we examine the physical unitarity in a massive Yang-Mills theory without the Higgs field in which the color gauge symmetry is not spontaneously broken and kept intact. For this purpose, we use a new framework proposed one of…
The quantum mechanics of spatially constant SU(2) Yang-Mills- and Dirac-fields minimally coupled to each other is investigated as the strong coupling limit of 2-color-QCD. Using a canonical transformation of the quark and gluon fields,…
The N=4 superconformal Yang-Mills theory on flat four-dimensional Minkowski space is a de-confined gauge theory in the sense that the string tension for fundamental representation coloured quarks vanishes. In fact, static fundamental…
Planar maximally supersymmetric Yang-Mills theory (N=4 SYM) is a special quantum field theory. A few of its remarkable features are conformal symmetry at the quantum level, evidence of integrability and, moreover, it is a prime example of…
Supersymmetry provides a well-established theoretical framework for extensions of the standard model of particle physics and the general understanding of quantum field theories. We summarise here our investigations of N=1 supersymmetric…
In a recent note we presented a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. In this paper we show that a natural formulation also exists for a massless…
We present a classification and an explicit form of all constant solutions of the Yang-Mills equations with ${\rm SU}(2)$ gauge symmetry for an arbitrary constant non-Abelian current in pseudo-Euclidean space ${\mathbb R}^{p,q}$ of…
The canonical quantization is performed at a light-front surface for the SU(N) Yang-Mills theory. The Weyl gauge is imposed as a gauge condition. The suitable parameterization is chosen for the transverse gauge field components in order to…
We propose the reformulations of the $SU(N)$ Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the $SU(N)$ Yang-Mills theory using new field variables. This includes the…
The analyticity property of de Sitter's quantum Yang-Mills theory in the framework of Kerin space quantization, including quantum metric fluctuation, is demonstrated. This property completes our previous work regarding quantum Yang-Mills…
We investigate the $(2+1)$-dimensional $q$-deformed $\mathrm{SU}(N)_k$ Yang-Mills theory in the lattice Hamiltonian formalism, which is characterized by three parameters: the number of colors $N$, the coupling constant $g$, and the level…
Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging $T(4) \times [SU(3)]_{color} $ in flat space-time, we have a unified…