Phase Transition in the Higgs Model of Scalar Dyons

In the present paper we investigate the phase transition “Coulomb–confinement” in the Higgs model of abelian scalar dyons – particles having both, electric e and magnetic g, charges. It is shown that by dual symmetry this theory is equivalent to scalar fields with the effective squared electric charge e∗2 = e2 + g2. But the Dirac relation distinguishes the electric and magnetic charges of dyons. The following phase transition couplings are obtained in the one–loop approximation: αcrit = ecrit/4π ≈ 0.19, α̃crit = g 2 crit/4π ≈ 1.29 and α ∗ crit ≈ 1.48. ∗ [email protected] † [email protected], [email protected] 1. In the present paper we consider dyons – the particles with electric e and magnetic g charges. As it was shown in Refs. [1, 3–6], dyons play an essential role in physics of nonabelian theories (in particular, in QCD). The local field theory of electrically and magnetically charged particles, so called “QuantumElectroMagnetoDynamics” (QEMD) [7], is presented by the Zwanziger formalism [8,9], (see also [10] and [11]), which considers two vector potentials Aμ(x) and Bμ(x), describing one physical photon with two physical degrees of freedom. Here Bμ is the magnetic gauge potential, which is dual to the electric gauge potential Aμ. This formalism symmetrically contains non–dual and dual interactions of gauge fields with the corresponding currents: j · A and j · B, where j μ and j m μ are electric and magnetic currents, respectively. Dyons are described by the field Φ, having charges n1e and n2g (n1, n2 ∈ Z). The total system of gauge fields and dyons is given by the partition function having the following form in Euclidean space: Z = ∫ [DA][DB][DΦ][DΦ]e, (1) where S = ∫ dxL(x) = SZw(A,B) + Sgf + S(matter). (2) The Zwanziger action SZw(A,B) is given by: SZw(A,B) = ∫