We present a new type of spherically symmetric monopole and dyon solutions with the magnetic charge 4π/e in the standard Weinberg-Salam model. The monopole (and dyon) could be interpreted as a non-trivial hybrid between the abelian Dirac monopole and non-abelian 't Hooft-Polyakov monopole (with an electric charge). We discuss the possible physical implications of the electroweak dyon.Typeset using REVT E X 1

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We present anyonic vortex solutions made of real electrons which could be interpreted as nontopological solitons of the (2 + 1)-dimensional Chern-Simons electrodynamics. The n-soliton solutions, which we obtain by imposing an effective axial symmetry on the (3+ 1)-dimensional quantum electrodynamics, have 4n real parameters which represent the position, size, and phase of each soliton.PACS number(s): 11.15. -q, 03.50.Kk, 12.20.Ds, 74.65. +n The axially symmetric vortex solutions which exist in ( 3 + 1 )-dimensional gauge theories have played a very important role in physics. They describe the quantized magnetic flux lines in superconductivity [I], the string model in hadrodynamics [2], and the large-scale cosmic strings in cosmology [3]. Similar vortex solutions also exist in the ( 2 + 1 )-dimensional Chern-Simons gauge theory[4]. In all these solutions, however, the presence of scalar fields has played a crucial role in providing the source of the vortices. So far no vortex solution made of a fermionic source has been constructed, although the fermionic bound states coupled to an arbitrary external magnetic vortex have been discussed by many authors [5]. The purpose of this paper is to show the existence of axially symmetric vortex solutions in which a fermion field provides the source of the vortices, and to discuss the physical implication of the solutions.The system we discuss is the one derived from the (3+ 1)-dimensional quantum electrodynamics which has an effective axial symmetry described in the following. With the symmetry one can reduce the theory to the ( 2 + 1 )-dimensional Maxwell electrodynamics which has two interacting fermionic sources: the right-handed and the left-handed fermions. Furthermore, when the effective axial symmetry is chosen in such a way to violate parity, one may add the Chern-Simons interaction to the theory. This is because the Chern-Simons interaction could be induced by the higher-order quantum correction of the fermions when a parity-violating interaction is present [ 6 ] . In this case the theory becomes Maxwell-Chern-Simons electrodynamics, but again with two fermionic sources. This means that, in the longdistance limit in which the Chern-Simons term dominates the Maxwell term, the theory can be approximated to an effective Chern-Simons electrodynamics. In this limit we show that the theory admits vortex solutions made offermions.Let us start with ( 3 + 1 )-dimensional quantum electrodynamics. In the chiral representation in which y 5 becomes diagonal one can describe the Dirac spinor \V with two two-components spinors where \V+ and \V-are the right-handed and the lefthanded Weyl spinors. Now we impose the effective axial symmetry 2nd assume that the Weyl spinors \ V, are periodic in the z coordinate (with different periodicities), but the gauge potential is independent of the z coordinate. With this effective axial symmetry one can easily reduce the theory to ( 2 + 1 )-dimensional electrodynamics.After the dimensional reduction by integrating out the z dependence, we o...

We discuss the quantization of the restricted gauge theory of SU(2) QCD regarding it as a second-class constraint system, and construct the BRST symmetry of the constrained system in the framework of the improved Dirac quantization scheme. Our analysis tells that one could quantize the restricted QCD as if it is a first-class constraint system.