10568329
SELF-DUALITY AND THE KdV HIERARCHY
We derive the entire KdV hierarchy as well as the recursion relations from the self-duality condition on gauge fields in four dimensions.
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.
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.
120503298
Systematic expansion for compact QED near weak coupling
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.
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.
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.
14979556
LIGHTFRONT HAMILTONIAN STRUCTURES FOR THE NONLINEAR SIGMA MODEL
We derive the Dirac brackets for the O(N) nonlinear sigma model in the lightfront description with and without constraint. We bring out various subtleties that arise including the fact that antiperiodic boundary condition seems to be preferred.
17610218
A Nonlinearly Dispersive Fifth Order Integrable Equation and its Hierarchy
Abstract In this paper, we study the properties of a nonlinearly dispersive integrable system of fifth order and its associated hierarchy. We describe a Lax representation for such a system which leads to two infinite series of conserved charges and two hierarchies of equations that share the same conserved charges. We construct two compatible Hamiltonian structures as well as their Casimir functionals. One of the structures has a single Casimir functional while the other has two. This allows us to extend the flows into negative order and clarifies the meaning of two different hierarchies of positive flows. We study the behavior of these systems under a hodograph transformation and show that they are related to the Kaup-Kupershmidt and the Sawada-Kotera equations under appropriate Miura transformations. We also discuss briefly some properties associated with the generalization of second, third and fourth order Lax operators.
121344490
Bosonic Reduction of Susy Generalized Harry Dym Equation
In this paper, we construct the two-component supersymmetric generalized Harry Dym equation which is integrable and study various properties of this model in the bosonic limit. In particular, in the bosonic limit we obtain a new integrable system which, under a hodograph transformation, reduces to a coupled three-component system. We show how the Hamiltonian structure transforms under a hodograph transformation and study the properties of the model under a further reduction to a two-component system. We find a third Hamiltonian structure for this system (which has been shown earlier to be a bi-Hamiltonian system) making this a genuinely tri-Hamiltonian system. The connection of this system to the modified dispersive water wave equation is clarified. We also study various properties in the dispersionless limit of our model.
119355685
Forward scattering amplitudes and the thermal operator representation
We develop systematically to all orders the forward scattering description for retarded amplitudes in field theories at zero temperature. Subsequently, through the application of the thermal operator, we establish the forward scattering description at finite temperature. We argue that, beyond providing a graphical relation between the zero temperature and the finite temperature amplitudes, this method is calculationally quite useful. As an example, we derive the important features of the one-loop retarded gluon self-energy in the hard thermal loop approximation from the corresponding properties of the zero temperature amplitude.