Massless Scalar QED with Non-minimal Chern Simons Coupling

2+1 dimensional massless scalar QED with $(\phi^*\phi)^3$ scalar self-coupling is modified by the addition of a non- minimal Chern-Simons term that couples the dual of the electromagnetic field strength to the covariant current of the complex scalar field. The theory is shown to be fully one- loop renormalizable. The one loop effective potential for the scalar field gives rise to spontaneous symmetry breaking which induces masses for both the scalar and vector fields. At high temperature there is a symmetry restoring phase transition.Comment: 18 pages, latex, preprint WIN-93-1

Dynamical mass generation of a two-component fermion in Maxwell-Chern-Simons QED_3: The lowest ladder approximation

Dynamical mass generation of a two-component fermion in $QED_3$ with a Chern-Simons term is investigated by solving the Schwinger-Dyson equation formulated in the lowest ladder approximation. Dependence of the dynamical fermion mass on a gauge-fixing parameter, a gauge coupling constant, and a topological mass is examined by approximated analytical and also numerical methods. The inclusion of the Chern-Simons term makes impossible to choose a peculiar gauge in which a wave function renormalization is absent. The numerical evaluation shows that the wave function renormalization is fairly close to 1 in the Landau gauge. It means that this gauge is still a specific gauge where the Ward-Takahashi identity is satisfied approximately. We also find that the dynamical mass is almost constant if the topological mass is larger than the coupling constant, while it decreases when the topological mass is comparable to or smaller than the coupling constant and tends to the value in $QED_3$ without the Chern-Simons term.Comment: 22 pages, 9 figures, Version to appear in Phys. Rev.

Anyon in External Electromagnetic Field: Hamiltonian and Lagrangian Formulations

We propose a simple model for a free relativistic particle of fractional spin in 2+1 dimensions which satisfies all the necessary conditions. The canonical quantization of the system leads to the description of one- particle states of the Poincare group with arbitrary spin. Using the Hamil- tonian formulation with the set of constraints, we introduce the electro- magnetic interaction of a charged anyon and obtain the Lagrangian. The Casimir operator of the extended algebra, which is the first-class constraint, is obtained and gives the equation of motion of the anyon. In particular, from the latter it follows that the gyromagnetic ratio for a charged anyon is two due to the parallelness of spin and momentum of the particle in 2+1 dimensions. The canonical quantization is also considered in this case.Comment: 9 pages, Latex, HU-SEFT R 1993-1

Quantum fluctuations of the Chern-Simons theory and dynamical dimensional reduction

We consider a large-N Chern-Simons theory for the attractive bosonic matter (Jackiw-Pi model) in the Hamiltonian collective-field approach based on the 1/N expansion. We show that the dynamics of low-lying density excitations around the ground-state vortex configuration is equivalent to that of the Sutherland model. The relationship between the Chern-Simons coupling constant lambda and the Calogero-Sutherland statistical parameter lambda_s signalizes some sort of statistical transmutation accompanying the dimensional reduction of the initial problem.Comment: 10 pages, 2 figure

Reconstruction of field theory from excitation spectra of defects

We show how to reconstruct a field theory from the spectrum of bound states on a topological defect. We apply our recipe to the case of kinks in 1+1 dimensions with one or two bound states. Our recipe successfully yields the sine-Gordon and $\lambda \phi^4$ field theories when suitable bound state spectra are assumed. The recipe can also be used to globally reconstruct the inflaton potential of inflationary cosmology if the inflaton produces a topological defect. We discuss how defects can provide ``smoking gun'' evidence for a class of inflationary models.Comment: 10 pages, 4 figures. Included proof (Appendix B) that wall fluctuation potentials have supersymmetric form. Added reference

Effective QED Actions: Representations, Gauge Invariance, Anomalies and Mass Expansions

We analyze and give explicit representations for the effective abelian vector gauge field actions generated by charged fermions with particular attention to the thermal regime in odd dimensions, where spectral asymmetry can be present. We show, through $\zeta-$function regularization, that both small and large gauge invariances are preserved at any temperature and for any number of fermions at the usual price of anomalies: helicity/parity invariance will be lost in even/odd dimensions, and in the latter even at zero mass. Gauge invariance dictates a very general ``Fourier'' representation of the action in terms of the holonomies that carry the novel, large gauge invariant, information. We show that large (unlike small) transformations and hence their Ward identities, are not perturbative order-preserving, and clarify the role of (properly redefined) Chern-Simons terms in this context. From a powerful representation of the action in terms of massless heat kernels, we are able to obtain rigorous gauge invariant expansions, for both small and large fermion masses, of its separate parity even and odd parts in arbitrary dimension. The representation also displays both the nonperturbative origin of a finite renormalization ambiguity, and its physical resolution by requiring decoupling at infinite mass. Finally, we illustrate these general results by explicit computation of the effective action for some physical examples of field configurations in the three dimensional case, where our conclusions on finite temperature effects may have physical relevance. Nonabelian results will be presented separately.Comment: 36 pages, RevTeX, no figure

Stochastic collective dynamics of charged--particle beams in the stability regime

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by $\lambda_c\sqrt{N}$, where $N$ is the number of particles in the beam and $\lambda_c$ the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schr\"odinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so--called ``quantum--like approaches'' to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam--field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.Comment: 15 pages, 9 figure

Current Algebra in Three Dimensions

We study a three dimensional analogue of the Wess--Zumino--Witten model, which describes the Goldstone bosons of three dimensional Quantum Chromodynamics. The topologically non--trivial term of the action can also be viewed as a nonlinear realization of Chern--Simons form. We obtain the current algebra of this model by canonical methods. This is a three dimensional generalization of the Kac--Moody algebra.Comment: 11 pages, UR-1266, ER40685-72

Three-dimensional N=4 supersymmetry in harmonic N=3 superspace

We consider the map of three-dimensional N=4 superfields to N=3 harmonic superspace. The left and right representations of the N=4 superconformal group are constructed on N=3 analytic superfields. These representations are convenient for the description of N=4 superconformal couplings of the Abelian gauge superfields with hypermultiplets. We analyze the N=4 invariance in the non-Abelian N=3 Yang-Mills theory.Comment: Latex file, 22 pages; v2 two references adde

Higher Derivative CP(N) Model and Quantization of the Induced Chern-Simons Term

We consider higher derivative CP(N) model in 2+1 dimensions with the Wess-Zumino-Witten term and the topological current density squared term. We quantize the theory by using the auxiliary gauge field formulation in the path integral method and prove that the extended model remains renormalizable in the large N limit. We find that the Maxwell-Chern-Simons theory is dynamically induced in the large N effective action at a nontrivial UV fixed point. The quantization of the Chern-Simons term is also discussed.Comment: 8 pages, no figure, a minor change in abstract, added Comments on the quantization of the Chern-Simons term whose coefficient is also corrected, and some references are added. Some typos are corrected. Added a new paragraph checking the equivalence between (3) and (5), and a related referenc