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Ashok Das

Publications and source records attributed to Ashok Das.

At least 73 records · Page 4Linked to original sources
arXiv2003

Kontsevich product and gauge invariance

We analyze the question of $U_{\star} (1)$ gauge invariance in a flat non-commutative space where the parameter of non-commutativity, $θ^{μν} (x)$, is a local function satisfying 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 modify 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 $θ^{2}$ while we discuss the gauge invariant Maxwell theory up to order $θ$. We show that despite the modifications in the gauge transformations, the covariant derivative and the field strength, 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 $θ^{μν}$ is a constant) which is reflected in the stress tensor not being conserved.

hep-th↗
arXiv2003

Anomalous Magnetic Moment of Electron in Chern-Simons QED

We calculate the anomalous magnetic moment of the electron in the Chern-Simons theory in 2+1 dimensions with and without a Maxwell term, both at zero temperature as well as at finite temperature. In the case of the Maxwell-Chern-Simons (MCS) theory, we find that there is an infrared divergence, both at zero as well as at finite temperature, when the tree level Chern-Simons term vanishes, which suggests that a Chern-Simons term is essential in such theories. At high temperature, the thermal correction in the MCS theory behaves as $\frac{1}β \ln βM$, where $β$ denotes the inverse temperature and $M$, the Chern-Simons coefficient. On the other hand, we find no thermal correction to the anomalous magnetic moment in the pure Chern-Simons (CS) theory.

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arXiv2003

Background field quantization and non-commutative Maxwell theory

We quantize non-commutative Maxwell theory 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 Maxwell theory. To leading order, we also give a closed form expression for the distribution function for the non-commutative $U (1)$ gauge theory at high temperature.

hep-th↗
arXiv2003

Deformed Harry Dym and Hunter-Zheng Equations

We study the deformed Harry Dym and Hunter-Zheng equations with two arbitrary deformation parameters. These reduce to various other known models in appropriate limits. We show that both these systems are bi-Hamiltonian with the same Hamiltonian structures. They are integrable and belong to the same hierarchy corresponding to positive and negative flows. We present the Lax pair description for both the systems and construct the conserved charges of negative order from the Lax operator. For the deformed Harry Dym equation, we construct the non-standard Lax representation for two special classes of values of the deformation parameters. In general, we argue that a non-standard description will involve a pseudo-differential operator of infinite order.

nlin.SI↗
arXiv2003

Light-front Schwinger Model at Finite Temperature

We study the light-front Schwinger model at finite temperature following the recent proposal in \cite{alves}. We show that the calculations are carried out efficiently by working with the full propagator for the fermion, which also avoids subtleties that arise with light-front regularizations. We demonstrate this with the calculation of the zero temperature anomaly. We show that temperature dependent corrections to the anomaly vanish, consistent with the results from the calculations in the conventional quantization. The gauge self-energy is seen to have the expected non-analytic behavior at finite temperature, but does not quite coincide with the conventional results. However, the two structures are exactly the same on-shell. We show that temperature does not modify the bound state equations and that the fermion condensate has the same behavior at finite temperature as that obtained in the conventional quantization.

hep-th↗
arXiv2003

Transport equation for the photon Wigner operator in non-commutative QED

We derive an exact quantum equation of motion for the photon Wigner operator in non-commutative QED, which is gauge covariant. In the classical approximation, this reduces to a simple transport equation which describes the hard thermal effects in this theory. As an example of the effectiveness of this method we show that, to leading order, this equation generates in a direct way the Green amplitudes calculated perturbatively in quantum field theory at high temperature.

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arXiv2003

Supersymmetric Extensions of the Harry Dym Hierarchy

We study the supersymmetric extensions of the Harry Dym hierarchy of equations. We obtain the susy-B extension, the doubly susy-B extension as well as the N=1 and the N=2 supersymmetric extensions for this system. The N=2 supersymmetric extension is particularly interesting, since it leads to new classical integrable systems in the bosonic limit. We prove the integrability of these systems through the bi-Hamiltonian formulation of integrable models and through the Lax description. We also discuss the supersymmetric extension of the Hunter-Zheng equation which belongs to the Harry Dym hierarchy of equations.

nlin.SI↗
arXiv2003

The static effective action for non-commutative QED at high temperature

In this paper, we systematically study the effective action for non-commutative QED in the static limit at high temperature. When $θp^{2}\ll 1$, where $θ$ represents the magnitude of the parameter for non-commutativity and $p$ denotes a typical external three momentum, we show that this leads naturally to a derivative expansion in this model. The study of the self-energy, in this limit, leads to nontrivial $θ$ dependent corrections to the electric and magnetic masses, which exist only above a certain critical temperature. The three point and the four point amplitudes are also studied as well as their relations to the Ward identities in this limit. We determine the closed form expression for the current involving only the spatial components of the gauge field and present the corresponding static effective action, which is gauge invariant.

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arXiv2002

On the energy-momentum tensor in non-commutative gauge theories

We study the properties of the energy-momentum tensor in non-commutative gauge theories by coupling them to a weak external gravitational field. In particular, we show that the stress tensor of such a theory coincides exactly with that derived from a theory where a Seiberg-Witten map has been implemented (namely, the procedure is commutative). Various other interesting features are also discussed.

hep-th↗
arXiv2002

Monodromy, Duality and Integrability of Two Dimensional String Effective Action

In this talk, we show how the monodromy matrix, ${\hat{\cal M}}$, can be constructed for the two dimensional tree level string effective action. The pole structure of ${\hat{\cal M}}$ is derived using its factorizability property. It is shown that the monodromy matrix transforms non-trivially under the non-compact 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, ${\hat{\cal M}}$ for the exactly solvable Nappi-Witten model, both when B=0 and $B\neq 0$, where these ideas can be directly checked.

hep-th↗
arXiv2002

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.

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arXiv2002

A Lax Equation for the Non-Linear Sigma Model

We propose a Lax equation for the non-linear sigma model which leads directly to the conserved local charges of the system. We show that the system has two infinite sets of such conserved charges following from the Lax equation, much like dispersionless systems. We show that the system has two Hamiltonian structures which are compatible so that it is truly a bi-Hamiltonian system. However, the two Hamiltonian structures act on the two distinct sets of charges to give the dynamical equations, which is quite distinct from the behavior in conventional integrable systems. We construct two recursion operators which connect the conserved charges within a given set as well as between the two sets. We show explicitly that the conserved charges are in involution with respect to either of the Hamiltonian structures thereby proving complete integrability of the system. Various other interesting features are also discussed.

hep-th↗
arXiv2002

Classical transport equation in non-commutative QED at high temperature

We show that the high temperature behavior of non-commutative QED may be simply obtained from Boltzmann transport equations for classical particles. The transport equation for the charge neutral particle is shown to be characteristically different from that for the charged particle. These equations correctly generate, for arbitrary values of the non-commutative parameter theta, the leading, gauge independent hard thermal loops, arising from the fermion and the gauge sectors. We briefly discuss the generating functional of hard thermal amplitudes.

hep-th↗
arXiv2002

Dispersion relations for the self-energy in non-commutative field theories

We study the IR/UV connection in non-commutative $ϕ^{3}$ theory as well as in non-commutative QED from the point of view of the dispersion relation for the self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of non-commutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed.

hep-th↗
arXiv2002

Vanishing magnetic mass in QED$_{3}$ with a Chern-Simons term

We show that, at one loop, the magnetic mass vanishes at finite temperature in QED in any dimension. In QED$_{3}$, even the zero temperature part can be regularized to zero. We calculate the two loop contributions to the magnetic mass in QED$_{3}$ with a Chern-Simons term and show that it vanishes. We give a simple proof which shows that the magnetic mass vanishes to all orders at finite temperature in this theory. This proof also holds for QED in any dimension.

hep-th↗
arXiv2002

Alternative dispersionless limit of N=2 supersymmetric KdV-type hierarchies

We present a systematic procedure for obtaining the dispersionless limit of a class of N=1 supersymmetric systems starting from the Lax description of their dispersive counterparts. This is achieved by starting with an N=2 supersymmetric system and scaling the fields in an alternative manner so as to maintain N=1 supersymmetry. We illustrate our method by working out explicitly the examples of the dispersionless supersymmetric two boson hierarchy and the dispersionless supersymmetric Boussinesq hierarchy.

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