119290439
An alternative construction of the positive inner product in non-Hermitian quantum mechanics
Within the context of non-Hermitian quantum mechanics, we use the generators of eigenvectors of the Hamiltonian to construct a unitary inner product space. Such models have been of interest in recent years, for instance, in the context of PT symmetry, although our construction extends to the larger class of so-called pseudo-Hermitian operators. We provide a detailed example to illustrate the concept and compare with known results.
119009436
Duality and integrability of two-dimensional string effective action
Abstract We present a prescription for constructing the monodromy matrix, M (ω) , for O ( d , d ) invariant string effective actions and derive its transformation properties under the T -duality group. This allows us to construct M (ω) for new backgrounds, starting from known ones, which are related by T -duality. As an application, we derive the monodromy matrix for the exactly solvable Nappi–Witten model, both when B =0 and B ≠0.
17283472
Large gauge Ward identity
Abstract We study the question of the Ward identity for ` large' gauge invariance in 0+1 dimensional theories. We derive the relevant Ward identities for a single flavor fermion and a single flavor complex scalar field interacting with an Abelian gauge field. These identities are nonlinear. The Ward identity for any other complicated theory can be derived from these basic sets of identities. However, the structure of the Ward identity changes since these are nonlinear identities. In particular, we work out the ` large' gauge Ward identity for a supersymmetric theory involving a single flavor of fermion as well as a complex scalar field. Contrary to the effective action for the individual theories, the solution of the Ward identity in the supersymmetric theory involves an infinity of Fourier component modes. We comment on which features of this analysis are likely/unlikely to generalize to the 2+1 dimensional theory.
15910786
Supersymmetric polytropic gas dynamics
Abstract We construct the N =1 supersymmetric extension of the polytropic gas dynamics. We give both the Lagrangian as well as the Hamiltonian description of this system. We construct the infinite set of ‘‘ Eulerian" conserved charges associated with this system and show that they are in involution, thereby proving complete integrability of this system. We construct the SUSY-B extension of this system as well and comment on the similarities and differences between this system and an earlier construction of the supersymmetric Chaplygin gas. We also derive the N =1 supersymmetric extension of the elastic medium equations, which, however, do not appear to be integrable.
18666187
Topics in Finite Temperature Field Theory
We discuss a few selected topics in finite temperature field theory.
16121968
Finite temperature field theories on the light front
In this talk, we describe our present understanding of thermal field theories on the light-front with an application to Schwinger model.
121788923
An alternate characterization of integrability
This paper will show that the existence of at least three independent symplectic forms (related in a simple way) on the phase space of a dynamical system is a sufficient condition for the integrability of the system.
15405943
Behavior of the thermal gluon self-energy in the Coulomb gauge
We study, to one loop order, the behavior of the gluon self-energy in the noncovariant Coulomb gauge at finite temperature. The cancellation of the peculiar energy divergences, which arise in such a gauge, is explicitly verified in the complete two point function of the Yang-Mills theory. At high temperatures, the leading T{sup 2} term is determined to be transverse and nonlocal, in agreement with the results obtained in covariant gauges. The coefficient of the sub-leading ln(T) contribution is nontransverse but local and coincides (up to a multiplicative constant) with that of the ultraviolet pole term of the zero temperature amplitude.
17464874
A New Class of Supersymmetric Theories
We construct a class of quantum mechanical theories which are invariant under fermionic transformations similar to supersymmetry transformations. The generators of the transformations in this case, however, satisfy a BRST-like algebra.
14248110
Two-loop corrections to the topological mass term in thermal QED3
Abstract We study the radiative corrections to the Chern–Simons mass term at two loops in (2+1)-dimensional quantum electrodynamics at finite temperature. We show that, in contrast to the behavior at zero temperature, thermal effects lead to a non-vanishing contribution at this order. Using this result, as well as the large gauge Ward identity for the leading parity violating terms in the static limit, we determine the leading order parity violating effective action in this limit at two loops, which generalizes the one-loop effective action proposed earlier.
119209165
Non-commutative Supersymmetric Quantum Mechanics
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two- and three-dimensional examples are explicitly studied. The structure of the theory studied suggest other possible applications in physical systems with potentials involving spin and non-local interactions.