5 research outputs found
Dirac Strings and Monopoles in the Continuum Limit of SU(2) Lattice Gauge Theory
Magnetic monopoles are known to emerge as leading non-perturbative
fluctuations in the lattice version of non-Abelian gauge theories in some
gauges. In terms of the Dirac quantization condition, these monopoles have
magnetic charge |Q_M|=2. Also, magnetic monopoles with |Q_M|=1 can be
introduced on the lattice via the 't Hooft loop operator. We consider the
|Q_M|=1,2 monopoles in the continuum limit of the lattice gauge theories. To
substitute for the Dirac strings which cost no action on the lattice, we allow
for singular gauge potentials which are absent in the standard continuum
version. Once the Dirac strings are allowed, it turns possible to find a
solution with zero action for a monopole--antimonopole pair. This implies
equivalence of the standard and modified continuum versions in perturbation
theory. To imitate the nonperturbative vacuum, we introduce then a nonsingular
background. The modified continuum version of the gluodynamics allows in this
case for monopoles with finite non-vanishing action. Using similar techniques,
we construct the 't Hooft loop operator in the continuum and predict its
behavior at small and large distances both at zero and high temperatures.Comment: 24 pp., Latex2e, no figures. Minor correction
On the Emerging Phenomenology of <(A_\mu)^2>
We discuss phenomenology of the vacuum condensate in pure gauge
theories, where A_\mu is the gauge potential. Both Abelian and non-Abelian
cases are considered. In case of the compact U(1) the non-perturbative part of
the condensate is saturated by monopoles. In the non-Abelian case,
a two-component picture for the condensate is presented according to which
finite values of order \Lambda_{QCD}^2 are associated both with large and short
distances. We obtain a lower bound on the by considering its change
at the phase transition. Numerically, it produces an estimate similar to other
measurements. Possible physical manifestations of the condensate are discussed.Comment: 17 pp., Latex2e, 3 figure
The Berry Phase and Monopoles in Non-Abelian Gauge Theories
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.Comment: 18 pp., Latex2e, 4 figures, psfig.st
Towards Abelian-like formulation of the dual gluodynamics
We consider gluodynamics in case when both color and magnetic charges are
present. We discuss first short distance physics, where only the fundamental
|Q|=1 monopoles introduced via the `t Hooft loop can be considered
consistently. We show that at short distances the external monopoles interact
as pure Abelian objects. This result can be reproduced by a Zwanziger-type
Lagrangian with an Abelian dual gluon. We introduce also an effective dual
gluodynamics which might be a valid approximation at distances where the
monopoles |Q|=2 can be considered as point-like as well. Assuming the monopole
condensation we arrive at a model which is reminiscent in some respect of the
Abelian Higgs model but, unlike the latter leaves space for the Casimir
scaling.Comment: 28+1 pp., Latex2e, 1 figur