The Hamiltonian Analysis for Yang-Mills Theory on $R\times S^2$

Abstract

Pure Yang-Mills theory on $\mathbb{R}\times S^2$ is analyzed in a gauge-invariant Hamiltonian formalism. Using a suitable coordinatization for the sphere and a gauge-invariant matrix parametrization for the gauge potentials, we develop the Hamiltonian formalism in a manner that closely parallels previous analysis on ${\mathbb{R}}^3$. The volume measure on the physical configuration space of the gauge theory, the nonperturbative mass-gap and the leading term of the vacuum wave functional are discussed using a point-splitting regularization. All the results carry over smoothly to known results on ${\mathbb{R}}^3$ in the limit in which the sphere is de-compactified to a plane.

References in corpus (6)

• A precise calculation of the fundamental string tension in SU(N) gauge theories in 2+1 dimensions
• On the Glueball Spectrum of Pure Yang-Mills Theory in 2+1 Dimensions
• Yang-Mills Theory in 2+1 Dimensions: Coupling of Matter Fields and String-breaking Effects
• The robustness of the vacuum wave function and other matters for Yang-Mills theory
• A second order deconfinement transition for large N 2+1 dimensional Yang-Mills theory on a small two-sphere
• On the deconfining limit in (2+1)-dimensional Yang-Mills theory

Cited by in corpus (9)

• The Hamiltonian Approach to Yang-Mills (2+1): An Expansion Scheme and Corrections to String Tension
• Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis
• SU(2|2) for Theories with Sixteen Supercharges at Weak and Strong Coupling
• Analytic non-homogeneous condensates in the $(2+1)$-dimensional Yang-Mills-Higgs-Chern-Simons theory at finite density
• On the Gauge-invariant Functional Measure for Gauge Fields on CP^2
• Gauge and Scalar Fields on ${\mathbb{CP}}^2$: A Gauge-invariant Analysis I. The effective action from chiral scalars
• The Hamiltonian Approach to Yang-Mills (2+1): An Update and Corrections to String Tension
• A Supersymmetry Preserving Mass-Deformation of N=1 Super Yang-Mills in D=2+1
• Holomorphicity, Vortex Attachment, Gauge Invariance and the Fractional Quantum Hall Effect