115132692
Hard thermal effective actions in the Schwinger formulation
We derive the properties of hard thermal effective actions in gauge theories from the point of view of Schwinger's proper time formulation. This analysis is simplified by introducing a set of generalized energy and momenta which are conserved and are nonlocal in general. These constants of motion, which embody energy-momentum exchanges between the fields and the particles along their trajectories, can be related to a class of gauge invariant or covariant potentials in the hard thermal regime. We show that in this regime the generalized energy, which is nonlocal in general, generates the characteristic nonlocal behavior of the hard thermal effective actions.
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.
119327271
Duality, monodromy, and integrability of two dimensional string effective action
The monodromy matrix $\mathcal{M}^$ is constructed for the two dimensional tree level string effective action. The pole structure of $\mathcal{M}^$ is derived using its factorizability property. It is found that the monodromy matrix transforms nontrivially under the noncompact T-duality group, which leaves the effective action invariant, and this can be used to construct the monodromy matrix for more complicated backgrounds starting from simpler ones. We construct, explicitly, $\mathcal{M}^$ for the exactly solvable Nappi-Witten model, both when $B=0$ and $B\ensuremath{\ne}0,$ where these ideas can be directly checked. We consider well known charged black hole solutions in the heterotic string theory that can be generated by T-duality transformations from a spherically symmetric ``seed'' Schwarzschild solution. We construct the monodromy matrix for the Schwarzschild black hole background of the heterotic string theory.
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.
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.
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.
118735341
The response of laser interferometers to a gravitational wave
Laser interferometer detectors are widely used in the extensive effort to detect gravitational waves. The interaction of a gravitational wave with light in the interferometer is usually explained in terms of the motion of the “free” mirrors that form the interferometer arms. It is instructive to show that the same result can be obtained by calculating the propagation of an electromagnetic plane wave between free mirrors in the curved space-time induced by the gravitational wave. We find that the plane wave acquires frequency modulation sidebands at the frequency of the gravitational wave. Such sidebands are equivalent to the time-dependent phase shift imposed on the plane wave, as obtained in the conventional calculation.
119440690
Thermal operator representation of finite temperature graphs. II
Using the mixed space representation (t,p{yields}) in the context of scalar field theories, we prove in a simple manner that the Feynman graphs at finite temperature are related to the corresponding zero temperature diagrams through a simple thermal operator, both in the imaginary time as well as in the real time formalisms. This result is generalized to the case when there is a nontrivial chemical potential present. Several interesting properties of the thermal operator are also discussed.
123020230
New Renormalization Program for Broken Gauge Theories
We derive a new renormalization-group theorem which expressly relates the parameters of the symmetric high-energy theory to the parameters of the broken, low-energy theory. The relation is an analytic one. It summarizes the threshold effects by leapfrogging across each threshold and provides a connection formula. The relation is derived for an arbitrary group hierarchy structure.
15684496
The supersymmetric two boson hierarchies
Abstract We construct the most general supersymmetric two boson system that is integrable. We obtain the Lax operator and the nonstandard Lax representation for this system. We show that, under appropriate redefinition of variables, this reduces to the supersymmetric nonlinear Schrodinger equation without any arbitrary parameter which is known to be integrable. We show that this supersymmetric system has three local Hamiltonian structures just like the bosonic counterpart and we show how the supersymmetric KdV equation can be embedded into this system.
119835460
Derivative expansion and the parity violating effective action for thermal (2+1)-dimensional QED at higher orders
We systematically study induced higher order corrections to the parity violating part in thermal QED{sub 2+1}, in the static limit, using the method of derivative expansion. We explicitly calculate the parity violating parts of the quadratic, cubic and the quartic terms (in fields) of the effective action which is linear in the magnetic field. We show that each of these actions can be summed, in principle, to all orders in the derivatives. However, such a structure is complicated and not very useful. On the other hand, at every order in the powers of the derivatives, we show that the effective action can also be summed to all orders in the A{sub 0} fields. The resulting thermal parity violating actions can be expressed in terms of the leading order effective action in the static limit. We prove gauge invariance, both large and small of the resulting effective actions, within the framework of derivative expansion. Various other features of the theory are also brought out.