Chern-simon type photon mass from fermion electric dipole moments at finite temperature in 3+1 dimensions

We study the low energy effective field theory of fermions with electric and magnetic dipole moments at finite temperature. We find that at one loop there is an interaction term of the Chern-Simon form ${\cal L_I}=m_\mu\>A_\nu {\tilde F}^{\mu\nu}$. The four vector $m_\mu \simeq d_i \mu_i m_i^2 ~{\partial_\mu}\>(ln T)$ is interpreted as a Chern- Simon type mass of photons, which is determined by the electric (magnetic) dipole moments $d_i$ ($\mu_i$) of the fermions in the vacuum polarisation loop diagram. The physical consequence of such a photon mass is that, photons of opposite circular polarisations, propagating through a hot medium, have different group velocities. We estimate that the time lag between the arrival times of the left and right circularly polarised light signals from pulsars. If the light propagates through a hot plasma (where the temperature in some regions is $T \sim 100 MeV$) then the time lag between the two circularly polarised signals of frequency $\omega$ will be $\Delta t(\omega) \simeq 10^{-6} /\omega$. It may be possible to observe this effect in pulsar signals which propagate through nebula at high temperatures.Comment: plain TeX, 9 page

Schr\"{o}dinger Fields on the Plane with non-Abelian Chern-Simons Interactions

Physical content of the nonrelativistic quantum field theory with non-Abelian Chern-Simons interactions is clarified with the help of the equivalent first- quantized description which we derive in any physical gauge.Comment: 12 pages, LaTex, SNUTP 94-1

Understanding Radiatively Induced Lorentz-CPT Violation in Differential Regularization

We have investigated the perturbative ambiguity of the radiatively induced Chern-Simons term in differential regularization. The result obtained in this method contains all those obtained in other regularization schemes and the ambiguity is explicitly characterized by an indefinite ratio of two renormalization scales. It is argued that the ambiguity can only be eliminated by either imposing a physical requirement or resorting to a more fundamental principle. Some calculation techniques in coordinate space are developed in the appendices.Comment: RevTex, 14 pages, one figure drawn by FEYNMAN, several references are modified and a paragraph about a general choice on the mass scales is added in page

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

Quantum Aspects of Supersymmetric Maxwell Chern-Simons Solitons

We study the various quantum aspects of the $N=2$ supersymmetric Maxwell Chern-Simons vortex systems. The fermion zero modes around the vortices will give rise the degenerate states of vortices. We analyze the angular momentum of these zero modes and apply the result to get the supermultiplet structures of the vortex. The leading quantum correction to the mass of the vortex coming from the mode fluctuations is also calculated using various methods depending on the value of the coefficient of the Chern-Simons term $\kappa$ to be zero, infinite and finite, separately. The mass correction is shown to vanish for all cases. Fermion numbers of vortices are also discussed.Comment: 40 pages, ReVTeX, HYUPT-94/04 SNUTP 94-6

Central charge and renormalization in supersymmetric theories with vortices

Some quantum features of vortices in supersymmetric theories in 1+2 dimensions are studied in a manifestly supersymmetric setting of the superfield formalism. A close examination of the supercurrent that accommodates the central charge and super-Poincare charges in a supermultiplet reveals that there is no genuine quantum anomaly in the supertrace identity and in the supercharge algebra, with the central-charge operator given by the bare Fayet-Iliopoulos term alone. The central charge and the vortex spectrum undergo renormalization on taking the expectation value of the central-charge operator. It is shown that the vortex spectrum is exactly determined at one loop while the spectrum of the elementary excitations receives higher-order corrections.Comment: 9 pages, revte

The Topological Unitarity Identities in Chern-Simons Theories

Starting from the generating functional of the theory of relativistic spinors in 2+1 dimensions interacting through the pure Chern-Simons gauge field, the S-matrix is constructed and seen to be formally the same as that of spinor quantum electrodynamics in 2+1 dimensions with Feynman diagrams having external photon lines excluded, and with the propagator of the topological Chern-Simons photon substituted for the Maxwell photon propagator. It is shown that the absence of real topological photons in the complete set of vector states of the total Hilbert space leads in a given order of perturbation theory to topological unitarity identities that demand the vanishing of the gauge-invariant sum of the imaginary parts of Feynman diagrams with a given number of internal on-shell free topological photon lines. It is also shown, that these identities can be derived outside the framework of perturbation theory. The identities are verified explicitly for the scattering of a fermion-antifermion pair in one-loop order.Comment: 13 pages, LaTex file, one figure (not included

Mode regularization of the susy sphaleron and kink: zero modes and discrete gauge symmetry

To obtain the one-loop corrections to the mass of a kink by mode regularization, one may take one-half the result for the mass of a widely separated kink-antikink (or sphaleron) system, where the two bosonic zero modes count as two degrees of freedom, but the two fermionic zero modes as only one degree of freedom in the sums over modes. For a single kink, there is one bosonic zero mode degree of freedom, but it is necessary to average over four sets of fermionic boundary conditions in order (i) to preserve the fermionic Z$_2$ gauge invariance $\psi \to -\psi$, (ii) to satisfy the basic principle of mode regularization that the boundary conditions in the trivial and the kink sector should be the same, (iii) in order that the energy stored at the boundaries cancels and (iv) to avoid obtaining a finite, uniformly distributed energy which would violate cluster decomposition. The average number of fermionic zero-energy degrees of freedom in the presence of the kink is then indeed 1/2. For boundary conditions leading to only one fermionic zero-energy solution, the Z$_2$ gauge invariance identifies two seemingly distinct `vacua' as the same physical ground state, and the single fermionic zero-energy solution does not correspond to a degree of freedom. Other boundary conditions lead to two spatially separated $\omega \sim 0$ solutions, corresponding to one (spatially delocalized) degree of freedom. This nonlocality is consistent with the principle of cluster decomposition for correlators of observables.Comment: 32 pages, 5 figure

Physically meaningful and not so meaningful symmetries in Chern-Simons theory

We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action both BRS invariant and Landau supersymmetric and an effective action only BRS invariant is a finite field redefinition. Having established this, we use a BRS invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift k \to k+\cv of the bare Chern-Simons parameter $k$ in conncection with the Landau supersymmetry. Finally, to convince ourselves that the shift above is not an accident of our regularization method, we comment on the fact that all BRS invariant regulators used as yet yield the same value for the shift.Comment: phyzzx, 21 pages, 2 figures in one PS fil

Exact calculation of the radiatively-induced Lorentz and CPT violation in QED

Radiative corrections arising from the axial coupling of charged fermions to a constant vector b_\mu can induce a Lorentz- and CPT-violating Chern-Simons term in the QED action. We calculate the exact one-loop correction to this term keeping the full b_\mu dependence, and show that in the physically interesting cases it coincides with the lowest-order result. The effect of regularization and renormalization and the implications of the result are briefly discussed.Comment: LaTex, 8 pages; minor correction