The partition function versus boundary conditions and confinement in the Yang-Mills theory

Details The partition function versus boundary conditions and confinement in the Yang-Mills theory The partition function versus boundary conditions and confinement in the Yang-Mills theory

1998-02-23

arxiv.org/abs/hep-th/9802161v1

Phys.Rev. D58 (1998) 085024

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, RevTeX, submitted to Phys. Rev. D

Scientific paper

10.1103/PhysRevD.58.085024

We analyse dependence of the partition function on the boundary condition for the longitudinal component of the electric field strength in gauge field theories. In a physical gauge the Gauss law constraint may be resolved explicitly expressing this component via an integral of the physical transversal variables. In particular, we study quantum electrodynamics with an external charge and SU(2) gluodynamics. We find that only a charge distribution slowly decreasing at spatial infinity can produce a nontrivial dependence in the Abelian theory. However, in gluodynamics for temperatures below some critical value the partition function acquires a delta-function like dependence on the boundary condition, which leads to colour confinement.

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