17559703
Properties of Moyal-Lax representation
The Moyal-Lax representation and the Moyal momentum algebra are presented. The Moyal-Lax equation can be interpreted as a Hamiltonian equation. The Moyal-Lax description leads in a natural manner to the dispersionless limit and provides the second Hamiltonian structure of dispersionless integrable models.
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.
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.
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.
121933320
Strong-coupling calculation of the mass ratio in supersymmetric field theory
Abstract The purpose of this paper is to demonstrate the suitability of strong-coupling expansions as a technique for obtaining useful numerical information from a supersymmetric field theory. Strong-coupling methods involve introducing a lattice which explicitly breaks supersymmetry invariance. However, we present compelling evidence that supersymmetry is restored in the continuum limit. Specifically, we calculate the ratio of the fermion mass to the boson mass and show that to seventh order in perturbation theory this ratio approaches one to within one percent.
2690850
A Lax representation for the Born-Infeld equation
Abstract We study the Born-Infeld equation from a Lagrangian point of view emphasizing the duality symmetry present in such systems. We obtain the Hamiltonian formulation directly from the Lagrangian. We also show that this system admits a dispersionless nonstandard Lax representation which directly leads to all the conserved charges (including the ones not previously obtained). We also present the generating function for these charges and point out various other properties of this system.
39204644
Thermal Operator and Cutting Rules at Finite Temperature and Chemical Potential
In the context of scalar field theories, both real and complex, we derive the cutting description at finite temperature (with zero/finite chemical potential) from the cutting rules at zero temperature through the action of a simple thermal operator. We give an alternative algebraic proof of the largest time equation which brings out the underlying physics of such a relation. As an application of the cutting description, we calculate the imaginary part of the one-loop retarded self-energy at zero/finite temperature and finite chemical potential and show how this description can be used to calculate the dispersion relation as well as the full physical self-energy of thermal particles.
119397088
Absence of higher order corrections to the non-Abelian topological mass term
We study the Yang-Mills-Chern-Simons theory systematically in an effort to generalize the Coleman-Hill result to the non-Abelian case. We show that, while the Chern-Simons coefficient is in general gauge dependent in a non-Abelian theory, it takes on a physical meaning in the axial gauge. Using the non-Abelian Ward identities as well as the analyticity of the amplitudes in the momentum variables, we show that, in the axial gauge, the Chern-Simons coefficient does not receive any quantum correction beyond one loop. This allows us to deduce that the ratio 4{pi}m/g{sup 2} is unrenormalized, in a non-Abelian theory, beyond one loop in any infrared safe gauge. This is the appropriate generalization of the Coleman-Hill result to non-Abelian theories. Various other interesting properties of the theory are also discussed.
122033381
On the “current” algebra of the KdV equation
Abstract We study the algebra of the conserved densities of the KdV equation. We obtain general conditions which show that the algebra does not close in general. A nontrivial example where the algebra closes is presented.