10995613
Deformed Harry Dym and Hunter–Zheng equations
We study the deformed Harry Dym and Hunter–Zheng equations with two arbitrary deformation parameters. These reduce to various other known models in appropriate limits. We show that both these systems are bi-Hamiltonian with the same Hamiltonian structures. They are integrable and belong to the same hierarchy corresponding to positive and negative flows. We present the Lax pair description for both the systems and construct the conserved charges of negative order from the Lax operator. For the deformed Harry Dym equation, we construct the nonstandard Lax representation for two special classes of values of the deformation parameters. In general, we argue that a nonstandard description will involve a pseudodifferential operator of infinite order.
120503298
Systematic expansion for compact QED near weak coupling
28025238
Dirac quantization in superspace.
We extend the method of Dirac quantization to superspace. We study simple models like the supersymmetric quantum mechanics as well as the supersymmetric nonlinear \ensuremath{\sigma} model in 1+1 dimensions. Although in both these cases the matrix representing the Poisson brackets between the constraints is singular, we show, following the spirit of Dirac, that one can still define Dirac brackets and that the resulting quantization is consistent with those of the component fields.
124322319
A simple and direct method for generating travelling wave solutions for nonlinear integrable equations
4019389
Retarded Green’s functions and forward scattering amplitudes in thermal field theory
In this paper, we give a simple diagrammatic identification of the unique combination of the causal {ital n}-point vertex functions in the real time formalism that would coincide with the corresponding functions obtained in the imaginary time formalism. Furthermore, we give a simple calculational method for evaluating the temperature dependent parts of the retarded vertex functions, to one loop, by identifying them with the forward scattering amplitudes of on-shell thermal particles. As an application of the method, we calculate and show that the temperature-dependent parts of all the retarded functions vanish at one loop order for (1+1)-dimensional massless QED. We further point out that, in this model, in fact, the temperature-dependent parts of all the retarded vertex functions vanish to all orders in perturbation theory. {copyright} {ital 1999} {ital The American Physical Society}
121912240
Chiral Schwinger model in curved space-time
We extend the method of path integrals to obtain the solution of the chiral Schwinger model in curved space-time and compare it with the flat space-time solution.
119054229
Colliding string waves and duality
Abstract The collision of plane waves corresponding to massless states of closed string is considered in D -dimensional space–time. The reduced tree level effective action is known to be manifestly O ( d , d ) invariant, d being the number of transverse spatial dimensions in the collision process. We adopt a coset space reformulation of the effective two-dimensional theory and discuss the relation of this process with classical integrable systems in two dimensions in the presence of gravity. We show how it is possible to generate new backgrounds for the scattering process, from known background solutions to the equations of motion, in the coset reformulation. We present explicit calculations for the case of four space–time dimensions as an illustrative example.
119040018
Large gauge invariance and finite temperature
In this talk, I summarize the status of our understanding of the puzzle of large gauge invariance at finite temperature.
7266877
Dispersionless fermionic KdV
Abstract We analyze the dispersionless limits of the Kupershmidt equation, the SUSY KdV-B equation and the SUSY KdV equation. We present the Lax description for each of these models and bring out various properties associated with them as well as discuss open questions that need to be addressed in connection with these models.
46280608
SELECTED TOPICS IN INTEGRABLE MODELS
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
16449376
Lucas Polynomials and a Standard Lax Representation for the Polytropic Gas Dynamics
A standard Lax representation for the polytropic gas dynamics is derived by exploiting various properties of the Lucas and Fibonacci polynomials. The two infinite sets of conserved charges are derived from this representation and shown to coincide with the ones derived from the known non-standard representation. The same Lax function is shown to also give the standard Lax description for the elastic medium equations. In addition, some results on possible dispersive extensions of such models are presented.