119087410
Path integral approach to residual gauge fixing
In this paper we study the question of residual gauge fixing in the path integral approach for a general class of axial-type gauges including the light-cone gauge. We show that the two cases--axial-type gauges and the light-cone gauge--lead to very different structures for the explicit forms of the propagator. In the case of the axial-type gauges, fixing the residual symmetry determines the propagator of the theory completely. On the other hand, in the light-cone gauge there is still a prescription dependence even after fixing the residual gauge symmetry, which is related to the existence of an underlying global as well as local symmetry.
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.
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.
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.
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.
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.
7939687
Gauge field theory in the infrared regime
We propose that the low energy behavior of a pure gauge theory can be studied by simply assuming violation of Lorentz invariance which is implemented through a deformation of the canonical Poisson brackets of the theory depending on an infrared scale. The resulting theory is equivalent to a pure gauge theory with a Chern-Simons like term. It is shown that at low energies this theory can be identified with three dimensional QCD where the mass of the fermion is related to the infrared scale.
121080340
Covariant Lax operators and Kac-Moody algebras
It will be shown that covariantizing the Lax operators with a ‘‘time’’ independent non‐Abelian gauge connection leaves the dynamical equations invariant. However, the symmetries associated with the Schrodinger equation in such a case is enlarged. This is used to give a simple derivation of various Kac–Moody algebras associated with such Lax operators.
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.
34163489
NONLEPTONIC DECAYS OF CHARMED MESONS INTO TWO PSEUDOSCALAR MESONS
We investigate the nonleptonic decay of charmed meson into two pseudoscalar mesons using the vector-dominance model, and compare the results with those obtained from the factorization model. In particular, we discuss the role of the annihilation diagrams in the two models.
14145665
Path integral solubility of a general two-dimensional model
The solubility of a general two dimensional model, which reduces to various models in different limits, is studied within the path integral formalism. Various subtleties and interesting features are pointed out.