6955417
THE ZERO CURVATURE FORMULATION OF TB, sTB HIERARCHY AND TOPOLOGICAL ALGEBRAS
A particular dispersive generalization of long water wave equation in (1+1) dimensions, which is important in the study of matrix models without scaling limit, known as two-Boson (TB) equation, as well as the associated hierarchy has been derived from the zero curvature condition on the gauge group SL(2, R) ⊗ U(1). The supersymmetric extension of the two-Boson (sTB) hierarchy has similarly been derived from the zero curvature condition associated with the gauge supergroup OSp(2|2). Topological algebras arise naturally as the second Hamiltonian structure of these classical integrable systems, indicating a close relationship of these models with 2-D topological field theories.
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.
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.
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.
120503298
Systematic expansion for compact QED near weak coupling
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.
9625249
Screening length in (2+1)-dimensional Abelian Chern–Simons theories
Abstract In this Letter, we systematically study the question of screening length in Abelian Chern–Simons theories. In the Abelian Higgs theory, where there are two massive poles in the gauge propagator at the tree level, we show that the coefficient of one of them becomes negligible at high temperature and that the screening length is dominantly determined by the parity violating part of the self-energy. In this theory, static magnetic fields are screened. In the fermion theory, on the other hand, the parity conserving part of the self-energy determines the screening length and static magnetic fields are not screened. Several other interesting features are also discussed.
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.
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.
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.
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.