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.
18810830
The sTB-B hierarchy
Abstract We construct a new supersymmetric two boson (sTB-B) hierarchy and study its properties. We derive the conserved quantities and the Hamiltonian structures (proving the Jacobi identity) for the system. We show how this system gives the sKdV-B equation and its Hamiltonian structures upon appropriate reduction. We also describe the zero curvature formulation of this hierarchy both in the superspace as well as in components.
120503298
Systematic expansion for compact QED near weak coupling
119380448
DYNAMICAL SUPERSYMMETRY
We show, in a simple quantum mechanical model, how a theory can become supersymmetric in the presence of interactions even when the free theory is not. This dynamical generation of supersymmetry relaxes the condition on the equality of masses of the superpartners which would be of phenomenological interest.
123610301
The hamiltonian structures of the KP hierarchy
Abstract We obtain the two hamiltonian structures of the KP hierarchy following the method of Drinfeld and Sokolov. We point out how the second structure of Drinfeld and Sokolov needs to be modified in the present case. We briefly comment on the connection between these structures and the W 1+∞ algebra.
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.
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.
119076261
New nonlocal charges in SUSY-B integrable models
Abstract In this Letter, we study systematically the general properties of the B -extension of any integrable model. In addition to discussing the general properties of Hamiltonians, Hamiltonian structures etc, we also clarify the origin of “exotic” charges in such models. We show that, in such models, there exist at least two sets of non-local conserved charges (and more if N >1 supersymmetry is present) and that the “exotic” charges are part of this non-local charge hierarchy. The construction of these non-local charges from the Lax operator is explained.
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.
15081073
Supersymmetric Moyal-Lax representation
The super Moyal–Lax representation and the super Moyal momentum algebra are introduced and the properties of simple and extended supersymmetric integrable models are systematically investigated. It is shown that, much like in the bosonic cases, the super Moyal–Lax equation can be interpreted as a Hamiltonian equation and can be derived from an action. Similarly, we show that the parameter of non-commutativity, in this case, is related to the central charge of the second Hamiltonian structure of the system. The super Moyal– Lax description allows us to go to the dispersionless limit of these models in a singular limit and we discuss some of the properties of such systems.
119417489
Generalized Benney lattice and the heavenly equation
We generalize the Benney lattice and show that the new system of equations can be reduced to a generalized Chaplygin gas as well as the heavenly equation. We construct two infinite sets of conserved charges and show that one of the sets can be obtained from the Lax function. The conserved densities are related to Legendre polynomials and we present closed form expressions for the generating functions for these densities which also determines the Riemann invariants of the problem. We prove that the system is bi-Hamiltonian and that the conserved charges are in involution with respect to either of the Hamiltonian structures. We show that the associated generalized elastic medium equations are bi-Hamiltonian as well. We also bring out various other interesting features of our model.