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Register a new userGauge Invariance and Lattice Monopoles
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Authors
Adriano Di Giacomo
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The number and the location of monopoles in Lattice configurations depend on the choice of the gauge, in contrast to the obvious requirement that monopoles, as physical objects, have a gauge-invariant status. It is proved, starting from non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and well understood way.
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The long standing problem is solved why the number and the location of monopoles observed in Lattice configurations depend on the choice of the gauge used to detect them, in contrast to the obvious requirement that monopoles, as physical objects, must have a gauge-invariant status. It is proved, by use of non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and controllable way.
The number and the location of the monopoles observed on the lattice in QCD configurations happens to depend strongly on the choice of the gauge used to expose them, in contrast to the physical expectation that monopoles be gauge invariant objects. It is proved by use of the non abelian Bianchi identities (NABI) that monopoles are indeed gauge invariant, but the method used to detect them depends, in a controllable way, on the choice of the abelian projection. Numerical checks are presented.
We investigate SU(2) lattice gauge theory in four dimensions in the maximally abelian projection. Studying the effects on different lattice sizes we show that the deconfinement transition of the fields and the percolation transition of the monopole currents in the three space dimensions are precisely related. To arrive properly at this result the uses of a mathematically sound characterization of the occurring networks of monopole currents and of an appropriate method of gauge fixing turn out to be crucial. In addition we investigate detailed features of the monopole structure in time direction.
We study monopoles and corresponding t Hooft tensor in a generic gauge theory. This issue is relevant to the understanding of color confinement.
The properties of the thermal Abelian color-magnetic monopoles in the maximally Abelian gauge are studied in the vicinity of the confinement-deconfinement phase transition in the lattice $SU(3)$ gluodynamics and lattice QCD. We compute the density and interaction parameters of the thermal monopoles. We find that the density of the thermal monopoles $rho(T)$ jumps up near the transition temperature $T_c$. Additionally we present new results on the percolation transition in $SU(3)$ gluodynamics which is known to coincide in gluodynamics with the confinement-deconfinement phase transition.
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