Towards a solution of pure Yang-Mills theory in 3+1 dimensions

Abstract

We discuss an analytic approach towards the solution of pure Yang-Mills theory in 3+1 dimensional spacetime. The approach is based on the use of local gauge invariant variables in the Schrödinger representation and the large $N$, planar limit. In particular, within this approach we point out unexpected parallels between pure Yang-Mills theory in 2+1 and 3+1 dimensions. The most important parallel shows up in the analysis of the ground state wave-functional especially in view of the numerical similarity of the existing large N lattice simulations of the spectra of 2+1 and 3+1 Yang Mills theories.

arXiv comment12 pages

References in corpus (16)

• SU(N) gauge theories in 2+1 dimensions
• SU(N) gauge theories in four dimensions: exploring the approach to N = infinity
• On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions
• A gauge-invariant Hamiltonian analysis for non-Abelian gauge theories in (2+1) dimensions
• Planar Yang-Mills theory: Hamiltonian, regulators and mass gap
• SU(N) gauge theories in 2+1 dimensions -- further results
• On the origin of the mass gap for non-Abelian gauge theories in (2+1) dimensions
• Chern-Simons Theory and the Quark-Gluon Plasma
• Glueball Regge Trajectories in (2+1) Dimensional Gauge Theories
• Hard Thermal Loops, Gauged WZNW Action and the Energy of Hot Quark-Gluon Plasma
• Hamiltonian Analysis of the Effective Action for Hard Thermal Loops in QCD
• Manifest covariance and the Hamiltonian approach to mass gap in (2+1)-dimensional Yang-Mills theory
• Two-dimensional dynamics of QCD_3
• Exactly Soluble QCD and Confinement of Quarks
• On pure Yang-Mills theory in 3+1 dimensions: Hamiltonian, vacuum and gauge invariant variables
• Towards the QCD String: 2+1 dimensional Yang-Mills theory in the planar limit

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• Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity
• Glueball masses in the large N limit
• Time and M-theory
• On the Glueball Spectrum of Pure Yang-Mills Theory in 2+1 Dimensions
• The robustness of the vacuum wave function and other matters for Yang-Mills theory
• Canonical Transformations and Loop Formulation of SU(N) Lattice Gauge Theories
• Mass gap in the weak coupling limit of $(2+1)$ SU(2) lattice gauge theory
• On the Physics of the Minimal Length: The Question of Gauge Invariance
• On pure Yang-Mills theory in 3+1 dimensions: Hamiltonian, vacuum and gauge invariant variables
• Scalar lattice gauge theory
• The Yang-Mills vacuum wave functional thirty-five years later