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}
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.
124322319
A simple and direct method for generating travelling wave solutions for nonlinear integrable equations
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.
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.
120503298
Systematic expansion for compact QED near weak coupling
118982028
Light front field theories at finite temperature
We study the question of generalizing light-front field theories to finite temperature. We show that the naive generalization has serious problems and we identify the source of the difficulty. We provide a proper generalization of these theories to finite temperature based on a relativistic description of thermal field theories, both in the real and the imaginary time formalisms. Various issues associated with scalar and fermion theories, such as non-analyticity of self-energy, tensor decomposition are discussed in detail.
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.
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.
18219085
Background field quantization and non-commutative QED
We quantize non-commutative QED canonically in the background field gauge for weak and slowly varying background fields. We determine the complete basis for expansion under such an approximation. As an application, we derive the Wigner function which determines the leading order high temperature behavior of the perturbative amplitudes of non-commutative QED. To leading order, we also give a closed form expression for the distribution function for non-commutative QED at high temperature.
119183441
The structure of supersymmetry in PT symmetric quantum mechanics
The structure of supersymmetry is analyzed systematically in PT symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one-dimensional PT symmetric quantum mechanical theories. We show that there is a richer structure present in these theories compared to the conventional theories associated with Hermitian Hamiltonians. We bring out various properties associated with these supersymmetric systems and generalize such quantum mechanical theories to higher dimensions as well as to the case of one-dimensional shape invariant potentials.