119273464
Thermal operator and dispersion relation in QED at finite temperature and chemical potential
Combining the thermal operator representation with the dispersion relation in QED at finite temperature and chemical potential, we determine the complete retarded photon self-energy only from its absorptive part at zero temperature. As an application of this method, we show that, even for the case of a nonzero chemical potential, the temperature dependent part of the one loop retarded photon self-energy vanishes in (1+1) dimensional massless QED.
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.
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.
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.
13275637
Two‐dimensional supersymmetric harmonic oscillator carrying a representation of the GL(2|1) graded Lie algebra
We study a supersymmetric two‐dimensional harmonic oscillator which carries a representation of the general graded Lie algebra GL(2|1), formulate it on the superspace, and discuss its physical spectrum.
119440690
Thermal operator representation of finite temperature graphs. II
Using the mixed space representation (t,p{yields}) in the context of scalar field theories, we prove in a simple manner that the Feynman graphs at finite temperature are related to the corresponding zero temperature diagrams through a simple thermal operator, both in the imaginary time as well as in the real time formalisms. This result is generalized to the case when there is a nontrivial chemical potential present. Several interesting properties of the thermal operator are also discussed.
121624438
The Hamiltonian structures associated with a generalized Lax operator
It is shown that with every Lax operator, which is a pseudodifferential operator of nonzero leading order, is associated a KP hierarchy. For each such operator, we construct the second Gelfand–Dikii bracket associated with the Lax equation and show that it defines a Hamiltonian structure. When the leading order is positive the corresponding compatible first Hamiltonian structure, which turns out, in general, to be different from the naive first Gelfand–Dikii bracket is derived. The corresponding Hamiltonian structures for the constrained Lax operator, where the next to leading‐order term vanishes or has a constant coefficient, is discussed.
199681358
Finite temperature effective actions
In this lecture we will describe a systematic method for evaluating effective actions at finite temperature. The method will be illustrated with the effective actions for the 0 + 1 dimensional massive QED as well as for the 1 + 1 dimensional QED with massless or massive fermions.
120430897
ZERO CURVATURE CONDITION OF OSp(2/2) AND THE ASSOCIATED SUPERGRAVITY THEORY
The N=2 fermionic extensions of the KdV equations are derived from the zero curvature condition associated with the graded Lie algebra of OSp(2/2). These equations lead to two bi-Hamiltonian systems, one of which is supersymmetric. We also derive the one-parameter family of N=2 supersymmetric KdV equations without a bi-Hamiltonian structure in this approach. Following our earlier proposal, we interpret the zero curvature condition as a gauge anomaly equation which brings out the underlying current algebra for the corresponding 2D supergravity theory. This current algebra is then used to obtain the operator product expansions of various fields of this theory.