On the Point-Splitting Method of the Commutator Anomaly of the Gauss Law Operators

We analyze the generalized point-splitting method and Jo's result for the commutator anomaly. We find that certain classes of general regularization kernels satisfying integral conditions provide a unique result, which, however differs from Faddeev's cohomological result.Comment: 16 pages, RevTex, 1 figure + 1 table, uses psbox.te

Induced Parity Breaking Term at Finite Temperature

We compute the exact induced parity-breaking part of the effective action for 2+1 massive fermions in $QED_3$ at finite temperature by calculating the fermion determinant in a particular background. The result confirms that gauge invariance of the effective action is respected even when large gauge transformations are considered.Comment: to be published in Physical Review Letters. 5 pages, Revtex, no figure

Abelian and Non-Abelian Induced Parity Breaking Terms at Finite Temperature

We compute the exact canonically induced parity breaking part of the effective action for 2+1 massive fermions in particular Abelian and non Abelian gauge field backgrounds. The method of computation resorts to the chiral anomaly of the dimensionally reduced theory.Comment: 13 pages, RevTeX, no figure

Enhancement of bulk second-harmonic generation from silicon nitride films by material composition

We present a comprehensive tensorial characterization of second-harmonic generation from silicon nitride films with varying composition. The samples were fabricated using plasma-enhanced chemical vapor deposition, and the material composition was varied by the reactive gas mixture in the process. We found a six-fold enhancement between the lowest and highest second-order susceptibility, with the highest value of approximately 5 pm/V from the most silicon-rich sample. Moreover, the optical losses were found to be sufficiently small (below 6 dB/cm) for applications. The tensorial results show that all samples retain in-plane isotropy independent of silicon content, highlighting the controllability of the fabrication process.Comment: 4 pages, 3 figures, 2 tables; Re-submitted to Optics Letter

Generalised chiral QED2 : Anomaly and Exotic Statistics

We study the influence of the anomaly on the physical quantum picture of the generalized chiral Schwinger model defined on the circle. We show that the anomaly i) results in the background linearly rising electric field and ii) makes the spectrum of the physical Hamiltonian nonrelativistic without a massive boson. The physical matter fields acquire exotic statistics . We construct explicitly the algebra of the Poincare generators and show that it differs from the Poincare one. We exhibit the role of the vacuum Berry phase in the failure of the Poincare algebra to close. We prove that, in spite of the background electric field, such phenomenon as the total screening of external charges characteristic for the standard Schwinger model takes place in the generalized chiral Schwinger model, too.Comment: LATEX file, 36 pp., to appear in Phys.Rev.

Shafranov's virial theorem and magnetic plasma confinement

Shafranov's virial theorem implies that nontrivial magnetohydrodynamical equilibrium configurations must be supported by externally supplied currents. Here we extend the virial theorem to field theory, where it relates to Derrick's scaling argument on soliton stability. We then employ virial arguments to investigate a realistic field theory model of a two-component plasma, and conclude that stable localized solitons can exist in the bulk of a finite density plasma. These solitons entail a nontrivial electric field which implies that purely magnetohydrodynamical arguments are insufficient for describing stable, nontrivial structures within the bulk of a plasma.Comment: 9 pages no figure

Bound states of neutral particles in external electric fields

Neutral fermions of spin $\frac 12$ with magnetic moment can interact with electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation for such a fermion coupled to a spherically symmetric or central electric field can be reduced to two simultaneous ordinary differential equations by separation of variables in spherical coordinates. For a wide variety of central electric fields, bound-state solutions of critical energy values can be found analytically. The degeneracy of these energy levels turns out to be numerably infinite. This reveals the possibility of condensing infinitely many fermions into a single energy level. For radially constant and radially linear electric fields, the system of ordinary differential equations can be completely solved, and all bound-state solutions are obtained in closed forms. The radially constant field supports scattering solutions as well. For radially linear fields, more energy levels (in addition to the critical one) are infinitely degenerate. The simultaneous presence of central magnetic and electric fields is discussed.Comment: REVTeX, 14 pages, no figur

Note on Moufang-Noether currents

The derivative Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal'ltsev algebra of an analytic Moufang loop.Comment: LaTeX2e, 6 pages, no figures, presented on "The XVth International Colloquium on Integrable Systems and Quantum Symmetries, Prague, 15-17 June, 2006

Gauge Invariance, Finite Temperature and Parity Anomaly in D=3

The effective gauge field actions generated by charged fermions in $QED_3$ and $QCD_3$ can be made invariant under both small and large gauge transformations at any temperature by suitable regularization of the Dirac operator determinant, at the price of parity anomalies. We resolve the paradox that the perturbative expansion is not invariant, as manifested by the temperature dependence of the induced Chern-Simons term, by showing that large (unlike small) transformations and hence their Ward identities, are not perturbative order-preserving. Our results are illustrated through concrete examples of field configurations.Comment: 4 pages, RevTe

Thermal Fluctuations of Induced Fermion Number

We analyze the phemomenon of induced fermion number at finite temperature. At finite temperature, the induced fermion number $$ is a thermal expectation value, and we compute the finite temperature fluctuations, $(\Delta N)^2=-^2$. While the zero temperature induced fermion number is topological and is a sharp observable, the finite temperature induced fermion number is generically nontopological, and is not a sharp observable. The fluctuations are due to the mixing of states inherent in any finite temperature expectation value. We analyze in detail two different cases in 1+1 dimensional field theory: fermions in a kink background, and fermions in a chiral sigma model background. At zero temperature the induced fermion numbers for these two cases are very similar, but at finite temperature they are very different. The sigma model case is generic and the induced fermion number is nontopological, but the kink case is special and the fermion number is topological, even at finite temperature. There is a simple physical interpretation of all these results in terms of the spectrum of the fermions in the relevant background, and many of the results generalize to higher dimensional models.Comment: 17 pgs, 9 figs, RevTex