AREA PRESERVING DIFFEOMORPHISM, QUANTUM GROUP AND BERRY PHASE
We study here the relationship between the area preserving diffeomorphism and quantum group with the deformation of symplectic structure and Berry phase in the Landau problem of 2D electron gas in a magnetic field. It is argued that while the area preserving diffeomorphism leads to the quantization of the symmetry , the deformation of the symplectic structure leads to the quantization of the system having the relation Δp. Δ q=2πnℏ, n being an odd integer giving rise to the Berry phase ei2πμ with n=2μ. A possible link between the deformation parameter q of the deformed algebra with the Berry phase factor arising out of the quantization procedure has been suggested. Finally, the latticization of space associated with the quantum group and its connection with the Zp spin system is discussed.

title: QUANTUM HALL SKYRMIONS IN THE FRAMEWORK OF O(4) NONLINEAR SIGMA MODEL
abstract: A new framework for quantum Hall skyrmions in O(4) nonlinear sigma model is studied here. The size and energy of the skyrmions are determined incorporating the quartic stability term in the Lagrangian. Moreover, the introduction of a θ-term determines the spin and statistics of these skyrmions.

title: Stochastic field theory at finite temperature, supersymmetry, and witten index
abstract: Finite temperature supersymmetry is studied here from the point of view of stochastic field theory and the formalism of thermofield dynamics. It is shown that the Witten index can take only the values 1 and ½ in this formalism. It is pointed out that when at a critical temperature T c , below which supersymmetry is spontaneously broken, the zero energy mode is given by a thermal doublet of opposite statistics when the index is 1. However, when the index is ½, the zero energy mode is given by a thermal doublet of the same fermionic statistics.

title: EQUIVALENCE OF STOCHASTIC, KLAUDER AND GEOMETRIC QUANTIZATION
abstract: The relativistic generalization of stochastic quantization helps us to introduce a stochastic-phase-space formulation when a relativistic quantum particle appears as a stochastically extended one. The nonrelativistic quantum mechanics is obtained in the sharp point limit. This also helps us to introduce a gauge-theoretical extension of a relativistic quantum particle when for a fermion the group structure of the gauge field is SU(2). The sharp point limit is obtained when we have a minimal contribution of the residual gauge field retained in the limiting procedure. This is shown to be equivalent to the geometrical approach to the phase-space quantization introduced by Klauder if it is interpreted in terms of a universal magnetic field acting on a free particle moving in a higher-dimensional configuration space when quantization corresponds to freezing the particle to its first Landau level. The geometric quantization then appears as a natural consequence of these two formalisms, since the Hermitian line bundle introduced there finds a physical meaning in terms of the inherent gauge field in stochastic-phase-space formulation or in the interaction with the magnetic field in Klauder quantization.

title: Random fields, ising model and bosson-fermion phase transition
abstract: SummaryIt is here shown that when the stochastic quantization procedure is introduced to a massive Thirring fermion where the latter is described as a bound state of massless oscillators interacting through a gradient term in a linear chain, we find that a boson-fermion phase transition occurs at a critical temperatureT =Tc, and atT >Tc supersymmetry is restored. In this scheme supersymmetry is broken by the generation of mass which arises due to the presence of the gradient term.

title: EXTENDED CONFORMAL GROUP, SUPERSYMMETRY, AND GEOMETRICAL PROPERTIES OF HADRONS
abstract: We have studied the interrelation among conformal symmetry, internal symmetry and super-symmetry and have shown that extended conformal group which includes, apart from conformal transformation, space, time and conformal reflection can give rise to internal symmetry algebra as well as supersymmetry algebra. To achieve this result, we have dealt with conformal spinors which are taken to be the constituents of the hadrons and these split into two Cartan semispinors or Dirac spinors in the Minkowski space, giving rise to the particle and antiparticle configurations. Supersymmetry is broken here just by the mass term and as such no massless hadron can exist in nature. The internal symmetry arises from the discrete symmetry of reflection. The most significant feature of this formalism is that the symmetry structure helps us to explain the meson-baryon mass difference in an elegant way and the role of fictitious superpartners is completely avoided. Again, any baryon number nonconserving process like proton decay is found to be forbidden by the Lorentz invariance. Finally, it is noted that though the discrete symmetry of reflection is taken to be the origin of the internal symmetry, topological nontrivial structures like strings do not appear here and this also avoids the possibility of the nonconservation of global charge.

title: Unusual Higgs boson signal in R-parity violating nonminimal supersymmetric models at the LHC
abstract: We predict an unconventional background free signal of the Higgs boson in $R$-parity violating nonminimal supersymmetric models at the Large Hadron Collider (LHC). The signal comprises dilepton plus four hadronic jets and two large displaced vertices. The displaced leptons and jets are coming from the decay of the lightest supersymmetric particle (LSP), which is predominantly a gauge-singlet neutrino. A pair of such LSPs can couple to a Higgs boson, created via gluon fusion. We have analyzed two cases - one corresponding to the tree-level Higgs boson mass and another with the one-loop corrected mass of the Higgs boson. A reliable Higgs mass reconstruction using this signal can lead to discovery at the LHC with center-of-mass energy $\sqrt{s}=14~\rm{TeV}$ and 5 fb$^{-1}$ of integrated luminosity $(\mathcal{L})$. Even at $\sqrt{s}=7~\rm{TeV}$ and $\mathcal{L}$ = 5 fb$^{-1}$, a reasonable number of events are expected. Besides, mass reconstruction of a gauge-singlet LSP can provide an estimate of the seesaw scale.

title: Associated Higgs production in CP-violating supersymmetry: Probing the 'open hole' at the large hadron collider
abstract: A benchmark CP-violating supersymmetric scenario (known in the literature as 'CPX-scenario') is studied in the context of the Large Hadron Collider (LHC). It is shown that the LHC, with low to moderate accumulated luminosity, will be able to probe the existing 'hole' in the m{sub h{sub 1}}-tan{beta} plane, which cannot be ruled out by the Large Electron Positron Collider data. This can be done through associated production of Higgs bosons with top quark and top squark pairs leading to the signal dilepton+ {<=}5 jets (including 3b-jets)+missing p{sub T}. Efficient discrimination of such a CP-violating supersymmetric scenario from other contending ones is also possible at the LHC with a moderate volume of data.

title: Working group report: Physics at the Large Hadron Collider
abstract: This is a summary of the activities of the Physics at the LHC working group in the XIth Workshop on High Energy Physics Phenomenology (WHEPP-XI) held at the Physical Research Laboratory, Ahmedabad, India in January 2010. We discuss the activities of each sub-working group on physics issues at colliders such as Tevatron and Large Hadron Collider (LHC). The main issues discussed involve (1) results on W mass measurement and associated QCD uncertainties, (2) an attempt to understand the asymmetry measured at Tevatron in the top quark production, and (3) phenomenology of warped space dimension model.

title: Signature of void probability scaling in high energy hadronic interactions
abstract: The rapidity gap probability in the p-AgBr interactions at 2.00 GeV/c and π-AgBr interactions at 200 and 350 GeV/c have been studied in detail. The data indicate scaling behaviour of the void probability in the central rapidity domain, which hints the validity of the linked-pair approximation for the N-particle cumulant correlation function.

title: Probing non-universal gaugino masses via Higgs boson production under SUSY cascades at the LHC: a detailed study
abstract: Cascade decays of Supersymmetric (SUSY) particles are likely to be prolific sources of Higgs bosons at the Large Hadron Collider (LHC). In this work, we explore, with the help of detailed simulation, the role of non-universal gaugino masses in the production of the Higgs bosons under SUSY cascades. The analysis is carried out by choosing an appropriate set of benchmark points with non-universal gaugino masses in the relevant SUSY parameter space and then contrasting the resulting observations with the corresponding cases having universal relationship among the same. It is shown that even of data at an early phase of the LHC-run with 10 fb−1 one would be able to see, under favourable situations, the imprint of non-universal gaugino masses by reconstructing various Higgs boson resonances and comparing their rates. With increased accumulated luminosities, the indications would naturally become distinct over a larger region of the parameter space.