Self-Dual Chiral Boson: Augmented Superfield Approach

We exploit the standard tools and techniques of the augmented version of Bonora-Tonin (BT) superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST and (anti-)co-BRST symmetry transformations for the Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density of a self-dual bosonic system. In the derivation of the full set of the above transformations, we invoke the (dual-)horizontality conditions, (anti-)BRST and (anti-)co-BRST invariant restrictions on the superfields that are defined on the (2, 2)-dimensional supermanifold. The latter is parameterized by the bosonic variable x^\mu\,(\mu = 0,\, 1) and a pair of Grassmanian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0 and \theta\bar\theta + \bar\theta\theta = 0). The dynamics of this system is such that, instead of the full (2, 2) dimensional superspace coordinates (x^\mu, \theta, \bar\theta), we require only the specific (1, 2)-dimensional super-subspace variables (t, \theta, \bar\theta) for its description. This is a novel observation in the context of superfield approach to BRST formalism. The application of the dual-horizontality condition, in the derivation of a set of proper (anti-)co-BRST symmetries, is also one of the new ingredients of our present endeavor where we have exploited the augmented version of superfield formalism which is geometrically very intuitive.Comment: LaTeX file, 27 pages, minor modifications, Journal reference is give

Superspace Unitary Operator in QED with Dirac and Complex Scalar Fields: Superfield Approach

We exploit the strength of the superspace (SUSP) unitary operator to obtain the results of the application of the horizontality condition (HC) within the framework of augmented version of superfield formalism that is applied to the interacting systems of Abelian 1-form gauge theories where the U(1) Abelian 1-form gauge field couples to the Dirac and complex scalar fields in the physical four (3 + 1)-dimensions of spacetime. These interacting theories are generalized onto a (4, 2)-dimensional supermanifold that is parametrized by the four (3 + 1)-dimensional (4D) spacetime variables and a pair of Grassmannian variables. To derive the (anti-)BRST symmetries for the matter fields, we impose the gauge invariant restrictions (GIRs) on the superfields defined on the (4, 2)-dimensional supermanifold. We discuss various outcomes that emerge out from our knowledge of the SUSP unitary operator and its hermitian conjugate. The latter operator is derived without imposing any operation of hermitian conjugation on the parameters and fields of our theory from outside. This is an interesting observation in our present investigation.Comment: LaTeX file, 11 pages, journal versio

Curci-Ferrari Type Condition in Hamiltonian Formalism: A Free Spinning Relativistic Particle

The Curci-Ferrari (CF)-type of restriction emerges in the description of a free spinning relativistic particle within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism when the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations for this system are derived from the application of horizontality condition (HC) and its supersymmetric generalization (SUSY-HC) within the framework of superfield formalism. We show that the above CF-condition, which turns out to be the secondary constraint of our present theory, remains time-evolution invariant within the framework of Hamiltonian formalism. This time-evolution invariance (i) physically justifies the imposition of the (anti-)BRST invariant CF-type condition on this system, and (ii) mathematically implies the linear independence of BRST and anti-BRST symmetries of our present theory.Comment: LaTeX file, 11 Pages, journal versio

Quantum Trivelpiece-Gould waves in a magnetized dense plasma

The dispersion relation for the electrostatic waves below the electron plasma frequency in a dense quantum plasma is derived by using the magnetohydrodynamic model. It is shown that in the classical case the dispersion relation reduces to the expression obtained for the well-known Trivelpiece-Gould (TG) modes. Attention is also devoted to the case of solitary waves associated with the nonlinear TG modes.Comment: 8 pages, 0 figure

Attractive Potential around a Thermionically Emitting Microparticle

We present a simulation study of the charging of a dust grain immersed in a plasma, considering the effect of electron emission from the grain (thermionic effect). It is shown that the OML theory is no longer reliable when electron emission becomes large: screening can no longer be treated within the Debye-Huckel approach and an attractive potential well forms, leading to the possibility of attractive forces on other grains with the same polarity. We suggest to perform laboratory experiments where emitting dust grains could be used to create non-conventional dust crystals or macro-molecules.Comment: 3 figures. To appear on Physical Review Letter

Modulational instability of spatially broadband nonlinear optical pulses in four-state atomic systems

The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schr\"odinger equation, a wave-kinetic equation is derived. A comparison between coherent and random phase wave states is made. It is found that the spatial spectral broadening can contribute to the nonlinear stability of ultra-short optical pulses. In practical terms, this could be achieved by using random phase plate techniques.Comment: 9 pages, 3 figures, to appear in Phys. Rev.

Stabilisation of BGK modes by relativistic effects

Context. We examine plasma thermalisation processes in the foreshock region of astrophysical shocks within a fully kinetic and self-consistent treatment. We concentrate on proton beam driven electrostatic processes, which are thought to play a key role in the beam relaxation and the particle acceleration. Our results have implications for the effectiveness of electron surfing acceleration and the creation of the required energetic seed population for first order Fermi acceleration at the shock front. Aims. We investigate the acceleration of electrons via their interaction with electrostatic waves, driven by the relativistic Buneman instability, in a system dominated by counter-propagating proton beams. Methods. We adopt a kinetic Vlasov-Poisson description of the plasma on a fixed Eulerian grid and observe the growth and saturation of electrostatic waves for a range of proton beam velocities, from 0.15c to 0.9c. Results. We can report a reduced stability of the electrostatic wave (ESW) with increasing non-relativistic beam velocities and an improved wave stability for increasing relativistic beam velocities, both in accordance with previous findings. At the highest beam speeds, we find the system to be stable again for a period of ≈160 plasma periods. Furthermore, the high phase space resolution of the Eulerian Vlasov approach reveals processes that could not be seen previously with PIC simulations. We observe a, to our knowledge, previously unreported secondary electron acceleration mechanism at low beam speeds. We believe that it is the result of parametric couplings to produce high phase velocity ESW’s which then trap electrons, accelerating them to higher energies. This allows electrons in our simulation study to achieve the injection energy required for Fermi acceleration, for beam speeds as low as 0.15c in unmagnetised plasma

Novel symmetries in the modified version of two dimensional Proca theory

By exploiting Stueckelberg's approach, we obtain a gauge theory for the two (1+1)-dimensional (2D) Proca theory and demonstrate that this theory is endowed with, in addition to the usual Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries, the on-shell nilpotent (anti-)co-BRST symmetries, under which the total gauge-fixing term remains invariant. The anticommutator of the BRST and co-BRST (as well as anti-BRST and anti-co-BRST) symmetries define a unique bosonic symmetry in the theory, under which the ghost part of the Lagrangian density remains invariant. To establish connections of the above symmetries with the Hodge theory, we invoke a pseudo-scalar field in the theory. Ultimately, we demonstrate that the full theory provides a field theoretic example for the Hodge theory where the continuous symmetry transformations provide a physical realization of the de Rham cohomological operators and discrete symmetries of the theory lead to the physical realization of the Hodge duality operation of differential geometry. We also mention the physical implications and utility of our present investigation.Comment: LaTeX file, 21 pages, journal referenc

Supervariable Approach to the Nilpotent Symmetries for a Toy Model of the Hodge Theory

We exploit the standard techniques of the supervariable approach to derive the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a toy model of the Hodge theory (i.e., a rigid rotor) and provide the geometrical meaning and interpretation to them. Furthermore, we also derive the nilpotent (anti-)co-BRST symmetry transformations for this theory within the framework of the above supervariable approach. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian of our present theory within the framework of augmented supervariable formalism. We also express the (anti-)BRST and (anti-)co-BRST charges in terms of the supervariables (obtained after the application of the (dual-)horizontality conditions and (anti-)BRST and (anti-)co-BRST invariant restrictions) to provide the geometrical interpretations for their nilpotency and anticommutativity properties. The application of the dual-horizontality condition and ensuing proper (i.e., nilpotent and absolutely anticommuting) fermionic (anti-)co-BRST symmetries are completely novel results in our present investigation

Nonlinear excitation of zonal flows by rossby wave turbulence

We apply the wave-kinetic approach to study nonlinearly coupled Rossby wave-zonal flow fluid turbulence in a two-dimensional rotating fluid. Specifically, we consider for the first time nonlinear excitations of zonal flows by a broad spectrum of Rossby wave turbulence. Short-wavelength Rossby waves are described here as a fluid of quasi-particles, and are referred to as the 'Rossbyons'. It is shown that Reynolds stresses of Rossbyons can generate large-scale zonal flows. The result should be useful in understanding the origin of large-scale planetary and near-Earth atmospheric circulations. It also provides an example of a turbulent wave background driving a coherent structure