S. Wickramasekara

Galilean and dynamical invariance of entanglement in particle scattering.

Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs are defined and various notions of entanglement are considered for scattering states.

Relativistic dynamics of quasistable states. I. Perturbation theory for the Poincaré group

We propose a theory of resonances by combining the S-matrix approach with the Bakamjian–Thomas (BT) construction. Characterization of resonances by the poles of the S-matrix has many advantages. Foremost among them is perhaps the gauge invariance of the definitions of resonance mass and width, a problem with which some definitions based on field theoretical approaches suffer. The BT construction provides a general framework for constructing Poincare generators for an interacting quantum system. While much of what we develop here can be cast in the language of quantum field theory, in the spirit of BT construction, which does not assume the existence of local field mediating interactions, we will work at the fundamental level of an interacting Poincare algebra. Our construction shows that a subset of this Poincare algebra integrates to a representation of the semigroup of causal transformations of relativistic space-time. These representations are characterized by the spin and S-matrix complex pole positio...

Relativistic dynamics of quasistable states. II. Differentiable representations of the causal Poincaré semigroup

We construct two rigged Hilbert spaces that furnish differentiable representations of the causal Poincare semigroup. These rigged Hilbert spaces provide the mathematical foundation for a theory of relativistic quasistable states that synthesizes the S-matrix description of resonance scattering with the Bakamjian–Thomas construction for interacting relativistic quantum systems.

Quantum mechanics in noninertial reference frames: Violations of the nonrelativistic equivalence principle

Abstract In previous work we have developed a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group that includes transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as is the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. A special feature of these previously constructed representations is that they all respect the non-relativistic equivalence principle, wherein the fictitious forces associated with linear acceleration can equivalently be described by gravitational forces. In this paper we exhibit a large class of cocycle representations of the Galilean line group that violate the equivalence principle. Nevertheless the classical mechanics analogue of these cocycle representations all respect the equivalence principle.

Near-extremal black hole thermodynamics from AdS 2 =CFT 1 correspondence in the low energy limit of 4D heterotic string theory

A bstractWe compute the full asymptotic symmetry group of the four dimensional near-extremal Kerr-Sen black hole within an AdS2/CFT1 correspondence. We do this by performing a Robinson-Wilczek two dimensional reduction and construct an effective quantum theory of the remaining field content. The resulting energy momentum tensor generates an asymptotic Virasoro algebra, to s-wave, with a calculable central extension. This center in conjunction with the proper regularized lowest Virasoro eigen-mode yields the near-extremal Kerr-Sen entropy via the statistical Cardy formula. Finally we analyze quantum holomorphic fluxes of the dual CFT giving rise to a finite Hawking temperature weighted by the central charge of the near-extremal Kerr-Sen metric.

Comment on 'On the inconsistency of the Bohm-Gadella theory with quantum mechanics'

Rigged Hilbert spaces of Hardy functions lead to a consistent theory of resonance scattering and decay. Contrary to the claims of a recent article [8], the theory holds for a wide range of potentials and rigorously describes the asymmetric time evolution of resonances.

Point-form dynamics of quasistable states

We present a field theoretical model of point-form dynamics which exhibits resonance scattering. In particular, we construct point-form Poincare generators explicitly from field operators and show that in the vector spaces for the in-states and out-states (endowed with certain analyticity and topological properties suggested by the structure of the S-matrix) these operators integrate to furnish differentiable representations of the causal Poincare semigroup, the semidirect product of the semigroup of spacetime translations into the forward lightcone and the group of Lorentz transformations. We also show that there exists a class of irreducible representations of the Poincare semigroup defined by a complex mass and a half-integer spin. The complex mass characterizing the representation naturally appears in the construction as the square root of the pole position of the propagator. These representations provide a description of resonances in the same vein as Wigners unitary irreducible representations of the Poincare group provide a description of stable particles.

Quantum mechanics in non-inertial reference frames: Time-dependent rotations and loop prolongations

Abstract This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group , the generalization of the Galilei group to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of the Galilean line group that uphold the non-relativistic equivalence principle as well as representations that violate the equivalence principle. In these previous studies, the focus was on linear accelerations. In this paper, we undertake an extension of the formulation to include rotational accelerations. We show that the incorporation of rotational accelerations requires a class of loop prolongations of the Galilean line group and their unitary cocycle representations. We recover the centrifugal and Coriolis force effects from these loop representations. Loops are more general than groups in that their multiplication law need not be associative. Hence, our broad theoretical claim is that a Galilean quantum theory that holds in arbitrary non-inertial reference frames requires going beyond groups and group representations, the well-established framework for implementing symmetry transformations in quantum mechanics.

Hardy class functions for potential scattering and decay

We construct a general procedure for obtaining rigged Hilbert spaces in the radial representation for a class of potentials such that these rigged Hilbert spaces are unitarily equivalent to rigged Hilbert spaces of Hardy class functions in the energy representation. We apply the procedure to the spherical shell potential and show that the Hardy hypothesis is consistent with all the physical requirements of potential scattering.

On Quantum Microstates in the Near Extremal, Near Horizon Kerr Geometry

We study the thermodynamics of near horizon near extremal Kerr (NHNEK) geometry within the framework of