Superstring theoryをめぐって(放談室)

Exact interior and exterior solutions to Einstein's field equations are derived for vacuum strings. The exterior solution for a uniform density vacuum string corresponds to a conical space while the interior solution is that of a spherical cap. For Mu equals 0-1/4 the external metric is ds-squared = -dt-squared + dr-squared + (1-4 Mu)-squared r-squared dphi-squared + dz-squared, where Mu is the mass per unit length in the string in Planck masses per Planck length. A maximum mass per unit length for a string is 6.73 x 10 to the 27th g/cm. It is shown that strings cause temperature fluctuations in the cosmic microwave background and produce equal brightness double QSO images separated by up to several minutes of arc. Formulae for lensing probabilities, image splittings, and time delays are derived for strings in a realistic cosmological setting. String searches using ST, the VLA, and the COBE satellite are discussed.

Gravitational Lensing Effects of Vacuum Strings: Exact Solutions

The theoretical description of fermions in the presence of Lorentz and $CPT$ violation is developed. We classify all Lorentz- and $CPT$-violating and invariant terms in the quadratic Lagrange density for a Dirac fermion, including operators of arbitrary mass dimension. The exact dispersion relation is obtained in closed and compact form, and projection operators for the spinors are derived. The Pauli Hamiltonians for particles and antiparticles are extracted, and observable combinations of operators are identified. We characterize and enumerate the coefficients for Lorentz violation for any operator mass dimension via a decomposition using spin-weighted spherical harmonics. The restriction of the general theory to various special cases is presented, including isotropic models, the nonrelativistic and ultrarelativistic limits, and the minimal Standard-Model Extension. Expressions are derived in several limits for the fermion dispersion relation, the associated fermion group velocity, and the fermion spin-precession frequency. We connect the analysis to some other formalisms and use the results to extract constraints from astrophysical observations on isotropic ultrarelativistic spherical coefficients for Lorentz violation.

Neutrinos with Lorentz-violating operators of arbitrary dimension

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.

Quantum Dynamics in Open Quantum-Classical Systems

The aharonov-bohm effect

On the Klein–Gordon oscillator subject to a Coulomb-type potential

On the interaction of the Dirac oscillator with the Aharonov-Casher system in topological defect backgrounds

In this contribution, we study the Dirac oscillator under the influence of noninertial effects of a rotating frame in the cosmic string spacetime. We show that both noninertial effects and the topology of the cosmic string spacetime restrict the physical region of the spacetime where the quantum particle can be placed, and discuss two different cases of bound states solutions of the Dirac equation by analysing the behaviour of the Dirac oscillator frequency.

Rotating effects on the Dirac oscillator in the cosmic string spacetime

On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential

We investigate the analog effect of the Aharonov–Bohm effect for bound states in two relativistic quantum systems in a spacetime with a spacelike dislocation. We assume that the topological defect has an internal magnetic flux. Then, we analyze the interaction of a charged particle with a uniform magnetic field in this topological defect spacetime, and thus, we extend this analysis to the confinement of a hard-wall potential and a linear scalar potential. Later, the interaction of the Klein–Gordon oscillator with a uniform magnetic field is analyzed. We first focus on the effects of torsion that stem from the spacetime with a spacelike dislocation and the geometric quantum phase. Then, we analyze the effects of torsion and the geometric quantum phase under the presence of a hard-wall potential and a linear scalar potential.

Knut Bakke

Papers

On the Klein–Gordon oscillator subject to a Coulomb-type potential

On the interaction of the Dirac oscillator with the Aharonov-Casher system in topological defect backgrounds

Rotating effects on the Dirac oscillator in the cosmic string spacetime

On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential

Aharonov–Bohm effect for bound states in relativistic scalar particle systems in a spacetime with a spacelike dislocation