15661741
Propagators with the Mandelstam-Leibbrandt prescription in the light-cone gauge
We show that the Feynman propagator in the light-cone gauge with the Mandelstam-Leibbrandt prescription has a logarithmic growth for large n-tilde{center_dot}x which is related to the presence of a residual gauge invariance. Furthermore, we show that the retarded propagator for the n-tilde{center_dot}A component of the gauge field develops a coordinate dependent mass. We argue that this feature is unphysical and may be eliminated by fixing the residual gauge degrees of freedom.
15910786
Supersymmetric polytropic gas dynamics
Abstract We construct the N =1 supersymmetric extension of the polytropic gas dynamics. We give both the Lagrangian as well as the Hamiltonian description of this system. We construct the infinite set of ‘‘ Eulerian" conserved charges associated with this system and show that they are in involution, thereby proving complete integrability of this system. We construct the SUSY-B extension of this system as well and comment on the similarities and differences between this system and an earlier construction of the supersymmetric Chaplygin gas. We also derive the N =1 supersymmetric extension of the elastic medium equations, which, however, do not appear to be integrable.
119290439
An alternative construction of the positive inner product in non-Hermitian quantum mechanics
Within the context of non-Hermitian quantum mechanics, we use the generators of eigenvectors of the Hamiltonian to construct a unitary inner product space. Such models have been of interest in recent years, for instance, in the context of PT symmetry, although our construction extends to the larger class of so-called pseudo-Hermitian operators. We provide a detailed example to illustrate the concept and compare with known results.
119327271
Duality, monodromy, and integrability of two dimensional string effective action
The monodromy matrix $\mathcal{M}^$ is constructed for the two dimensional tree level string effective action. The pole structure of $\mathcal{M}^$ is derived using its factorizability property. It is found that the monodromy matrix transforms nontrivially under the noncompact T-duality group, which leaves the effective action invariant, and this can be used to construct the monodromy matrix for more complicated backgrounds starting from simpler ones. We construct, explicitly, $\mathcal{M}^$ for the exactly solvable Nappi-Witten model, both when $B=0$ and $B\ensuremath{\ne}0,$ where these ideas can be directly checked. We consider well known charged black hole solutions in the heterotic string theory that can be generated by T-duality transformations from a spherically symmetric ``seed'' Schwarzschild solution. We construct the monodromy matrix for the Schwarzschild black hole background of the heterotic string theory.
118370691
Infrared chiral anomaly at finite temperature
Abstract We study the Schwinger model at finite temperature and show that a temperature dependent chiral anomaly may arise from the long distance behavior of the electric field. At high temperature this anomaly depends linearly on the temperature T and is present not only in the two point function, but also in all even point amplitudes.
119493925
Kontsevich product and gauge invariance
We analyze the question of ${U}_{\ensuremath{\star}}(1)$ gauge invariance in a flat noncommutative space where the parameter of noncommutativity, ${\ensuremath{\theta}}^{\ensuremath{\mu}\ensuremath{\nu}}(x),$ is a local function satisfying the Jacobi identity (and thereby leading to an associative Kontsevich product). We show that in this case both gauge transformations as well as the definitions of covariant derivatives have to be modified so as to have a gauge invariant action. We work out the gauge invariant actions for the matter fields in the fundamental and the adjoint representations up to order ${\ensuremath{\theta}}^{2}$ while we discuss the gauge invariant Maxwell theory up to order $\ensuremath{\theta}.$ We show that, despite the modifications in the gauge transformations, the covariant derivative, and the field strength, the Seiberg-Witten map continues to hold for this theory. In this theory, translations do not form a subgroup of the gauge transformations (unlike in the case when ${\ensuremath{\theta}}^{\ensuremath{\mu}\ensuremath{\nu}}$ is a constant) which is reflected in the stress tensor not being conserved.
121370801
Gauge fixing ambiguities, flux strings, and the unconstrained Yang-Mills theory
Abstract We find the inconstrained Yang-Mills Lagrangian in the variables of Goldstone and Jackiw. It takes canonical form allowing immediate path integral quantization. There are no gauge fixing ambiguities except in the presence of instantons. We generalize the Lagrangian to include point sources, and show that it is only necessary to fix the gauge along a string connecting two sources. We discuss the significance of the singularities of the Hamiltonian and suggest an interpretation.
120170788
Nonlinear gauge fixing with auxiliary fields
We study renormalizability of gauge theories in nonlinear gauges with the help of auxiliary fields. We show that the auxiliary-field formulation is particularly helpful in understanding the divergence structures in the nonlinear gauges. A quadratic gauge-fixing choice in non-Abelian gauge theory in general induces quartic ghost terms. We show that there can exist various Becchi-Rouet-Stora-invariant Lagrangians involving quartic ghosts. However, renormalizability only selects out the Lagrangian which respects the global invariance corresponding to the original gauge group.
123202189
Temperature dependent anomalous statistics
The authors show that the anomalous statistics which arises in (2+1)-dimensional Chern-Simons gauge theories can become temperature dependent in the most natural way. They analyse and show that a statistics-changing phase transition can happen in these theories only as T to infinity .
125456590
Canonical quantization of constrained systems
121579857
The zero curvature formulation of the Boussinesq equation
Abstract We derive the Boussineq equation from the zero curvature condition associated with the group SL (3, R ). We also present a connection between this formulation and the one based on a combined conformal and spin-3 flow.