Hamiltonian vs Lagrangian Embedding of a Massive Spin-one Theory Involving 2-form Field

We consider the Hamiltonian and Lagrangian embedding of a first-order, massive spin-one, gauge non-invariant theory involving anti-symmetric tensor field. We apply the BFV-BRST generalised canonical approach to convert the model to a first class system and construct nil-potent BFV-BRST charge and an unitarising Hamiltonian. The canonical analysis of the St\"uckelberg formulation of this model is presented. We bring out the contrasting feature in the constraint structure, specifically with respect to the reducibility aspect, of the Hamiltonian and the Lagrangian embedded model. We show that to obtain manifestly covariant St\"uckelberg Lagrangian from the BFV embedded Hamiltonian, phase space has to be further enlarged and show how the reducible gauge structure emerges in the embedded model.Comment: Revtex, 13 pages, no figure, to appear in Int. J. Mod. Phys.

Born-Infeld Chern-Simons Theory: Hamiltonian Embedding, Duality and Bosonization

In this paper we study in detail the equivalence of the recently introduced Born-Infeld self dual model to the Abelian Born-Infeld-Chern-Simons model in 2+1 dimensions. We first apply the improved Batalin, Fradkin and Tyutin scheme, to embed the Born-Infeld Self dual model to a gauge system and show that the embedded model is equivalent to Abelian Born-Infeld-Chern-Simons theory. Next, using Buscher's duality procedure, we demonstrate this equivalence in a covariant Lagrangian formulation and also derive the mapping between the n-point correlators of the (dual) field strength in Born-Infeld Chern-Simons theory and of basic field in Born-Infeld Self dual model. Using this equivalence, the bosonization of a massive Dirac theory with a non-polynomial Thirring type current-current coupling, to leading order in (inverse) fermion mass is also discussed. We also re-derive it using a master Lagrangian. Finally, the operator equivalence between the fermionic current and (dual) field strength of Born-Infeld Chern-Simons theory is deduced at the level of correlators and using this the current-current commutators are obtained.Comment: 27 pages, One reference added, minor changes in presentation and typos corrected. To appear in Nucl. Phys.

Aspects of Noncommutative Scalar/Tensor Duality

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U(1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in $\theta$. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order $\theta$ is also derived.Comment: 7 pages, typos corrected, a footnote removed and a sentence added in the tex

A deterministic width function model

International audienceUse of a deterministic fractal-multifractal (FM) geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture and their observed power-law scaling on their power spectra. It is then shown, via two natural river networks (Racoon and Brushy creeks in the United States), that the FM approach may also be used to closely approximate existing width functions

On the equivalence between topologically and non-topologically massive abelian gauge theories

We analyse the equivalence between topologically massive gauge theory (TMGT) and different formulations of non-topologically massive gauge theories (NTMGTs) in the canonical approach. The different NTMGTs studied are St\"uckelberg formulation of (A) a first order formulation involving one and two form fields, (B) Proca theory, and (C) massive Kalb-Ramond theory. We first quantise these reducible gauge systems by using the phase space extension procedure and using it, identify the phase space variables of NTMGTs which are equivalent to the canonical variables of TMGT and show that under this the Hamiltonian also get mapped. Interestingly it is found that the different NTMGTs are equivalent to different formulations of TMGTs which differ only by a total divergence term. We also provide covariant mappings between the fields in TMGT to NTMGTs at the level of correlation function.Comment: One reference added and a typos corrected. 15 pages, To appear in Mod. Phys. Lett.

Modeling geophysical complexity: a case for geometric determinism

International audienceIt has been customary in the last few decades to employ stochastic models to represent complex data sets encountered in geophysics, particularly in hydrology. This article reviews a deterministic geometric procedure to data modeling, one that represents whole data sets as derived distributions of simple multifractal measures via fractal functions. It is shown how such a procedure may lead to faithful holistic representations of existing geophysical data sets that, while complementing existing representations via stochastic methods, may also provide a compact language for geophysical complexity. The implications of these ideas, both scientific and philosophical, are stressed

Correlation among QPO frequencies and Quiescence-state Duration in Black Hole Candidate GRS 1915+105

We discover a definite correlation between the frequency of the quasi-periodic oscillations (QPO) in quiescence states and the duration of the quiescence state of the transient X-ray source GRS 1915+105. We find that while the QPO frequency can be explained with the oscillation of shocks in accretion flows, the switching of burst to quiescence states (and vice versa) and their duration can be explained by assuming an outflow from the post-shock region. The duration of the quiescence state is inversely related to the QPO-frequency. We derive this relation. We also find the correlation between the observed low ($\sim 0.001-0.01$Hz) and the intermediate (1-10Hz) QPO frequencies. Our analytical solutions are verified by analyzing several days of public-domain data from RXTE.Comment: Latex, 13 pages with 3 figures; Accepted for Publication in Astrophysical Journal Letter