16 research outputs found

    Proper incorporation of self-adjoint extension method to Green's function formalism : one-dimensional δ\delta^{'}-function potential case

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    One-dimensional δ\delta^{'}-function potential is discussed in the framework of Green's function formalism without invoking perturbation expansion. It is shown that the energy-dependent Green's function for this case is crucially dependent on the boundary conditions which are provided by self-adjoint extension method. The most general Green's function which contains four real self-adjoint extension parameters is constructed. Also the relation between the bare coupling constant and self-adjoint extension parameter is derived.Comment: LATEX, 13 page

    A pragmatic approach to the problem of the self-adjoint extension of Hamilton operators with the Aharonov-Bohm potential

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    We consider the problem of self-adjoint extension of Hamilton operators for charged quantum particles in the pure Aharonov-Bohm potential (infinitely thin solenoid). We present a pragmatic approach to the problem based on the orthogonalization of the radial solutions for different quantum numbers. Then we discuss a model of a scalar particle with a magnetic moment which allows to explain why the self-adjoint extension contains arbitrary parameters and give a physical interpretation.Comment: 8 pages, LaTeX, to appear in J. Phys.

    Non-Abelian Geometrical Phase for General Three-Dimensional Quantum Systems

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    Adiabatic U(2)U(2) geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually solving the full eigenvalue problem for the instantaneous Hamiltonian. The parameter space of such systems which has the structure of \xC P^2 is explicitly constructed. The results of this article are applicable for arbitrary multipole interaction Hamiltonians H=Qi1,inJi1JinH=Q^{i_1,\cdots i_n}J_{i_1}\cdots J_{i_n} and their linear combinations for spin j=1j=1 systems. In particular it is shown that the nuclear quadrupole Hamiltonian H=QijJiJjH=Q^{ij}J_iJ_j does actually lead to non-Abelian geometric phases for j=1j=1. This system, being bosonic, is time-reversal-invariant. Therefore it cannot support Abelian adiabatic geometrical phases.Comment: Plain LaTeX, 17 page

    Induced vacuum condensates in the background of a singular magnetic vortex in 2+1-dimensional space-time

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    We show that the vacuum of the quantized massless spinor field in 2+1-dimensional space-time is polarized in the presence of a singular magnetic vortex. Depending on the choice of the boundary condition at the location of the vortex, either chiral symmetry or parity is broken; the formation of the appropriate vacuum condensates is comprehensively studied. In addition, we find that current, energy and other quantum numbers are induced in the vacuum.Comment: LaTeX2e, 27 page

    Euclidean Black Hole Vortices

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    We argue the existence of solutions of the Euclidean Einstein equations that correspond to a vortex sitting at the horizon of a black hole. We find the asymptotic behaviours, at the horizon and at infinity, of vortex solutions for the gauge and scalar fields in an abelian Higgs model on a Euclidean Schwarzschild background and interpolate between them by integrating the equations numerically. Calculating the backreaction shows that the effect of the vortex is to cut a slice out of the Euclidean Schwarzschild geometry. Consequences of these solutions for black hole thermodynamics are discussed.Comment: 24 page

    Bremsstrahlung in the gravitational field of a cosmic string

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    In the framework of QED we investigate the bremsstrahlung process for an electron passing by a straight static cosmic string. This process is precluded in empty Minkowski space-time by energy and momentum conservation laws. It happens in the presence of the cosmic string as a consequence of the conical structure of space, in spite of the flatness of the metric. The cross section and emitted electromagnetic energy are computed and analytic expressions are found for different energies of the incoming electron. The energy interval is divided in three parts depending on whether the energy is just above electron rest mass MM, much larger than MM, or exceeds M/δM/\delta, with δ\delta the string mass per unit length in Planck units. We compare our results with those of scalar QED and classical electrodynamics and also with conic pair production process computed earlier.Comment: 21 pages, to appear in Phys. Rev. D., KONS-RGKU-94-0

    Green functions for generalized point interactions in 1D: A scattering approach

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    Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities which may hide important physical aspects of the problem. In this work we present a new method to calculate the exact Green functions for general point interactions in 1D. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients, RR and TT, to construct GG. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of NN general point interactions; on a line; on a half-line; under periodic boundary conditions; and confined in a box.Comment: Revtex, 9 pages, 3 EPS figures. To be published in PR
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