On the SU(3) parametrization of qutrits
Parametrization of qutrits on the complex projective plane CP^2 = SU(3)/U(2) is given explicitly. A set of constraints that characterize mixed state density matrices is found.
quant-ph↗
arXiv subjects
T. Dereli
Publications and source records attributed to T. Dereli.
Solutions of the Gaudin Equation and Gaudin Algebras
Three well-known solutions of the Gaudin equation are obtained under a set of standard assumptions. By relaxing one of these assumptions we introduce a class of mutually commuting Hamiltonians based on a different solution of the Gaudin equation. Application of the algebraic Bethe ansatz technique to diagonalize these Hamiltonians reveals a new infinite dimensional complex Lie algebra.
math-ph↗
Exactly Solvable Pairing Model Using an Extension of Richardson-Gaudin Approach
We introduce a new class of exactly solvable boson pairing models using the technique of Richardson and Gaudin. Analytical expressions for all energy eigenvalues and first few energy eigenstates are given. In addition, another solution to Gaudin's equation is also mentioned. A relation with the Calogero-Sutherland model is suggested.
nucl-th↗
Possible effects of spacetime non-metricity on neutrino oscillations
The contribution of gravitational neutrino oscillations to the solar neutrino problem is studied by constructing the Dirac Hamiltonian and calculating the corresponding dynamical phase in the vicinity of the Sun in a non-Riemann background Kerr space-time with torsion and non-metricity. We show that certain components of non-metricity and the axial as well as non-axial components of torsion may contribute to neutrino oscillations. We also note that the rotation of the Sun may cause a suppression of transitions among neutrinos. However, the observed solar neutrino deficit could not be explained by any of these effects because they are of the order of Planck scales.
gr-qc↗
An Exactly Solvable Model of Interacting Bosons
We introduce a class of exactly solvable boson models. We give explicit analytic expressions for energy eigenvalues and eigenvectors for an sd-boson Hamiltonian, which is related to the SO(6) chain of the Interacting Boson Model Hamiltonian.
nucl-th↗
Axi-Dilaton Gravity in D \geq 4 Dimensional Space-Times with Torsion
We study models of axi-dilaton gravity in space-time geometries with torsion. We discuss conformal re-scaling rules in both Riemannian and non-Riemannian formulations. We give static, spherically symmetric solutions and examine their singularity structure.
gr-qc↗
Spinor couplings to dilaton gravity induced by the dimensional reduction of topologically massive gravity
A Dirac spinor is coupled to topologically massive gravity and the D=3 dimensional action is reduced to D=2 dimensions with a metric that includes both the electromagnetic potential 1-form A and a dilaton scalar ϕ. The dimensionnaly reduced spinor is made a mass eigenstate with a (local) chiral rotation. The non-trivial interactions thus induced are discussed.
gr-qc↗
Newton-Cartan connections with torsion
We re-formulate the notion of a Newton-Cartan manifold and clarify the compatibility conditions of a connection with torsion with the Newton-Cartan structure.
gr-qc↗
On the Energy-Momentum Density of Gravitational Plane Waves
By embedding Einstein's original formulation of GR into a broader context we show that a dynamic covariant description of gravitational stress-energy emerges naturally from a variational principle. A tensor $T^G$ is constructed from a contraction of the Bel tensor with a symmetric covariant second degree tensor field $Φ$ and has a form analogous to the stress-energy tensor of the Maxwell field in an arbitrary space-time. For plane-fronted gravitational waves helicity-2 polarised (graviton) states can be identified carrying non-zero energy and momentum.
hep-th↗
Autoparallel orbits in Kerr Brans-Dicke spacetimes
The bounded orbital motion of a massive spinless test particle in the background of a Kerr Brans-Dicke geometry is analysed in terms of worldlines that are auto-parallels of different metric compatible spacetime connections. In one case the connection is that of Levi-Civita with zero-torsion. In the second case the connection has torsion determined by the gradient of the Brans-Dicke background scalar field. The calculations permit in principle to discriminate between these possibilities.
gr-qc↗
Seiberg-Witten type monopole equations on 8-manifolds with Spin(7) holonomy as minimizers of a quadratic action
We obtain an elliptic system of monopole equations on 8-manifolds with Spin(7) holonomy by minimizing an action involving negative spinors coupled to an Abelian gauge fields.
hep-th↗
Dirac equation in spacetimes with torsion and non-metricity
Dirac equation is written in a non-Riemannian spacetime with torsion and non-metricity by lifting the connection from the tangent bundle to the spinor bundle over spacetime. Foldy-Wouthuysen transformation of the Dirac equation in a Schwarzschild background spacetime is considered and it is shown that both the torsion and non-metricity couples to the momentum and spin of a massive, spinning particle. However, the effects are small to be observationally significant.
gr-qc↗
A Broken Gauge Approach to Gravitational Mass and Charge
We argue that a spontaneous breakdown of local Weyl invariance offers a mechanism in which gravitational interactions contribute to the generation of particle masses and their electric charge. The theory is formulated in terms of a spacetime geometry whose natural connection has both dynamic torsion and non-metricity. Its structure illuminates the role of dynamic scales used to determine measurable aspects of particle interactions and it predicts an additional neutral vector boson with electroweak properties.
hep-th↗
Conformal Black Hole Solutions of Axi-Dilaton Gravity in D-dimensions
Static, spherically symmetric solutions of axi-dilaton gravity in $D$ dimensions is given in the Brans-Dicke frame for arbitrary values of the Brans-Dicke constant $ω$ and an axion-dilaton coupling parameter $k$. The mass and the dilaton and axion charges are determined and a BPS bound is derived. There exists a one parameter family of black hole solutions in the scale invariant limit.
gr-qc↗
On the Motion of Matter in Spacetime
We argue that the geodesic hypothesis based on auto-parallels of the Levi-Civita connection may need refinement in theories of gravity with additional scalar fields. This argument is illustrated with a re-formulation of the Brans-Dicke theory in terms of a spacetime connection with torsion determined dynamically in terms of the gradient of the Brans-Dicke scalar field. The perihelion shift in the orbit of Mercury is calculated on the alternative hypothesis that its world-line is an auto-parallel of such a connection. If scalar fields couple significantly to matter and spinless test particles move on such world-lines, current time keeping methods based on the conventional geodesic hypothesis may need refinement.
gr-qc↗
On the Detection of Scalar Field Induced Spacetime Torsion
We argue that the geodesic hypothesis based on the autoparalllels of the Levi-Civita connection may need refinement in the scalar- tensor theories of gravity. Based on a reformulation of the Brans- Dicke theory in terms of a connection with torsion determined dynamically in terms of the gradient of the Brans-Dicke scalar field, we compute the perihelion shift in the orbit of Mercury on the alternative hypothesis that its worldline is an autoparallel of a connection with torsion. If the Brans-Dicke scalar field couples significantly to matter and test particles move on such worldlines, the current time keeping methods based on the conventional geodesic hypothesis may need refinement.
gr-qc↗
Neutrino Oscillations Induced by Space-Time Torsion
The gravitational neutrino oscillation problem is studied by considering the Dirac Hamiltonian in a Riemann-Cartan space-time and calculating the dynamical phase. Torsion contributions which depend on the spin direction of the mass eigenstates are found. These effects are of the order of Planck scales.
gr-qc↗
Electroweak Theory and Noncommutative Geometry
The noncommutative generalisation of the standard electroweak model due to Balakrishna, Gursey and Wali is formulated in terms of the derivations Der_2(M_3) of a three dimensional representation of the su(2) Lie algebra of weak isospin. A light Higgs boson of mass about 130 GeV, together with four very heavy scalar bosons are predicted.
hep-th↗