Kumar S. Gupta

κ-Minkowski spacetime and the star product realizations

We investigate a Lie algebra-type κ-deformed Minkowski spacetime with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of κ-Minkowski space. The coproduct and the star product corresponding to each of them are found. An explicit connection between realizations and orderings is established and the relation between the coproduct and the star product, provided through an exponential map, is proved. Utilizing the properties of the natural realization, we construct a scalar field theory on κ-deformed Minkowski space and show that it is equivalent to the scalar, nonlocal, relativistically invariant field theory on the ordinary Minkowski space. This result is universal and does not depend on the realizations, i.e. the orderings, used.

Twisted statistics in kappa-Minkowski spacetime

We consider the issue of statistics for identical particles or fields in {kappa}-deformed spaces, where the system admits a symmetry group G. We obtain the twisted flip operator compatible with the action of the symmetry group, which is relevant for describing particle statistics in the presence of the noncommutativity. It is shown that for a special class of realizations, the twisted flip operator is independent of the ordering prescription.

Near-horizon conformal structure of black holes

The near-horizon properties of a black hole are studied within an algebraic framework, using a scalar field as a simple probe to analyze the geometry. The operator H governing the near-horizon dynamics of the scalar field contains an inverse square interaction term. It is shown that the operators appearing in the corresponding algebraic description belong to the representation space of the Virasoro algebra. The operator H is studied using the representation theory of the Virasoro algebra. We observe that the wave functions exhibit scaling behaviour in a band-like region near the horizon of the black hole.

Further evidence for the conformal structure of a Schwarzschild black hole in an algebraic approach

We study the excitations of a massive Schwarzschild black hole of mass M resulting from the capture of infalling matter described by a massless scalar field. The near-horizon dynamics of this system is governed by a Hamiltonian which is related to the Virasoro algebra and admits a one-parameter family of self-adjoint extensions described by a parameter z∈R. The density of states of the black hole can be expressed equivalently in terms of z or M, leading to a consistent relation between these two parameters. The corresponding black hole entropy is obtained as S=S(0)−32 logS(0)+C, where S(0) is the Bekenstein–Hawking entropy, C is a constant with other subleading corrections exponentially suppressed. The appearance of this precise form for the black hole entropy within our formalism, which is expected on general grounds in any conformal field theoretic description, provides strong evidence for the near-horizon conformal structure in this system.

Twisted statistics inκ-Minkowski spacetime

We consider the issue of statistics for identical particles or fields in {kappa}-deformed spaces, where the system admits a symmetry group G. We obtain the twisted flip operator compatible with the action of the symmetry group, which is relevant for describing particle statistics in the presence of the noncommutativity. It is shown that for a special class of realizations, the twisted flip operator is independent of the ordering prescription.

Inequivalent quantizations of the rational Calogero model

We show that the rational Calogero model with suitable boundary condition admits quantum states with non-equispaced energy levels. Such a spectrum generically consists of infinitely many positive energy states and a single negative energy state. The new states appear for arbitrary number of particles and for specific ranges of the coupling constant. These states owe their existence to the self-adjoint extensions of the corresponding Hamiltonian, which are labelled by a real parameter z. Each value of z corresponds to a particular spectrum, leading to inequivalent quantizations of the model.

Constraints on the quantum gravity scale from κ-Minkowski spacetime

We compare two versions of deformed dispersion relations (energy vs. momenta and momenta vs. energy) and the corresponding time delay up to the second-order accuracy in the quantum gravity scale (deformation parameter). A general framework describing modified dispersion relations and time delay with respect to different noncommutative κ-Minkowski spacetime realizations is firstly proposed here and it covers all the cases introduced in the literature. It is shown that some of the realizations provide certain bounds on quadratic corrections, i.e. on quantum gravity scale, but it is not excluded in our framework that the quantum gravity scale is the Planck scale. We also show how the coefficients in the dispersion relations can be obtained through a multiparameter fit of the gamma-ray burst (GRB) data.

Electron capture and scaling anomaly in polar molecules

Abstract We present a new analysis of the electron capture mechanism in polar molecules, based on von Neumanns theory of self-adjoint extensions. Our analysis suggests that it is theoretically possible for polar molecules to form bound states with electrons, even with dipole moments smaller than the critical value D 0 = 1.63 × 10 −18 esu cm . We argue that the quantum mechanical scaling anomaly is responsible for the formation of these bound states.

Noncommutative BTZ black hole and discrete time

We search for all Poisson brackets for the BTZ black hole which are consistent with the geometry of the commutative solution and are of lowest order in the embedding coordinates. For arbitrary values of the angular momentum we obtain two two-parameter families of contact structures. We obtain the symplectic leaves, which characterize the irreducible representations of the corresponding noncommutative theory. The requirement that they be invariant under the action of the isometry group restricts to symplectic leaves which are topologically , where is associated with the Schwarzschild time. Quantization may then lead to a discrete spectrum for the time operator.

Bound states in one-dimensional quantum N-body systems with inverse square interaction

Abstract We investigate the existence of bound states in N-body Calogero model without the confining term. The effective Hamiltonian of this system admits a one-parameter family of self-adjoint extensions and the bound states occur when most general boundary conditions are considered. Such states are found to exist only when N=3,4 and for certain values of the system parameters.