The Berry Phase and Monopoles in Non-Abelian Gauge Theories

Abstract

We consider the quantum mechanical notion of the geometrical (Berry) phase in SU(2) gauge theory, both in the continuum and on the lattice. It is shown that in the coherent state basis eigenvalues of the Wilson loop operator naturally decompose into the geometrical and dynamical phase factors. Moreover, for each Wilson loop there is a unique choice of U(1) gauge rotations which do not change the value of the Berry phase. Determining this U(1) locally in terms of infinitesimal Wilson loops we define monopole-like defects and study their properties in numerical simulations on the lattice. The construction is gauge dependent, as is common for all known definitions of monopoles. We argue that for physical applications the use of the Lorenz gauge is most appropriate. And, indeed, the constructed monopoles have the correct continuum limit in this gauge. Physical consequences are briefly discussed.

18 pp., Latex2e, 4 figures, psfig.sty

References in corpus (5)

• On the Significance of the Quantity "A Squared"
• Towards Abelian-like formulation of the dual gluodynamics
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• Power Corrections from Small Distances
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• Twisted CP(N-1) instanton projectors and the N-level quantum density matrix
• Bianchi Identities and Degeneracy of Chromomagnetic Fields in SU(2) Gluodynamics
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