The dynamical evolution of 3-space in a higher dimensional steady state universe

We investigate a class of cosmological solutions of Einstein’s field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject to two constraints that (i) the total volume scale factor of the universe is constant and (ii) the effective energy density is constant. We obtain various interesting new dynamics for the external space that yield a time varying deceleration parameter including oscillating cases when the flat/curved external and curved/flat internal spaces are considered. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the extra dimensions.     

The dynamical structure of the Einstein-Cartan-Sciama-Kibble theory of gravity

It is shown that in the SO(3)-covariant Hamiltonian formulation the system of the ECSK equations can be reduced to 7 gravitational constraints, 18 gravitational dynamical equations, and a system of matter field equations. The geometric meaning of the canonical (symplectic) and gauge variables is also explained. Moreover, a general method of how to analyse degenerate matter field lagrangians in the framework of the ECSK theory is discussed. The exposition is given in the language of SO(3)-covariant differential operators on 3-dimensional slices of spacetime.     

The Chern-Simons theory and knot polynomials

The Chern-Simons gauge theory is studied using a functional integral quantization. This leads to a differential equation for expectations of Wilson lines. The solution of this differential equation is shown to be simply related to the two-variable Jones polynomial of the corresponding link, in the case where the gauge group isSU(N). A similar equation has been used before to get the Jones polynomial from a braid representation of the link. The main novelty of our approach is that we get the Jones polynomial from a plat representation of the link.     

QCD axion from a higher dimensional gauge field theory

We point out that a QCD axion solving the strong CP problem can arise naturally from a parity-odd gauge field in five-dimensional (5D) orbifold field theory. The required axion coupling to the QCD anomaly comes from the 5D Chern-Simons coupling, and all other unwanted U(1)PQ breaking axion couplings can be avoided naturally by the 5D gauge symmetry and locality. If the fifth dimension is warped, the resulting axion scale is suppressed by a small warp factor compared to the Planck scale, thereby the model can generate naturally an intermediate axion scale fa = 10(10)-10(12) GeV.     

Witten's identity for Chern-Simons theory

We present a simple heuristic calculational scheme to relate the expectation value of Wilson loops in Chern-Simons theory to the Jones polynomial. We consider the exponential of the generator of homotopy transformations which produces the finite loop deformations that define the crossing change formulas of knot polynomials. Applying this operator to the expectation value of Wilson loops for an unspecified measure, we find a set of conditions on the measure and the regularization such that the Jones polynomial is obtained.     

Chern-Simons theory and fusion algebras

The connection between the Chern-Simons theory and some features of the two-dimensional conformal models is considered. By using the properties of the expectation values of the Wilson line operators, it is shown how the fusion rules emerge in the three-dimensional context. The case G=SU(2) is considered in detail. The fusion algebra is obtained from the tensor algebra of the gauge group by factorizing an appropriate invariant subalgebra generated by a null vector.     

Electronic structure calculations using dynamical mean field theory

The calculation of the electronic properties of materials is an important task of solid-state theory, albeit particularly difficult if electronic correlations are strong, e.g., in transition metals, their oxides and in f-electron systems. The standard approach to material calculations, the density functional theory in its local density approximation (LDA), incorporates electronic correlations only very rudimentarily and fails if the correlations are strong. Encouraged by the success of dynamical mean field theory (DMFT) in dealing with strongly correlated model Hamiltonians, physicists from the bandstructure and the many-body communities have joined forces and developed a combined LDA + DMFT method recently. Depending on the strength of electronic correlations, this new approach yields a weakly correlated metal as in the LDA, a strongly correlated metal or a Mott insulator. This approach is widely regarded as a breakthrough for electronic structure calculations of strongly correlated materials. We review this LDA + DMFT method and also discuss alternative approaches to employ DMFT in electronic structure calculations, e.g., by replacing the LDA part with the so-called GW approximation. Different methods to solve the DMFT equations are introduced with a focus on those that are suitable for realistic calculations with many orbitals. An overview of the successful application of LDA + DMFT to a wide variety of materials, ranging from Pu and Ce, to Fe and Ni, to numerous transition metal oxides, is given.     

Kaluza-Klein theory and Dirac equation in higher dimensional Riemann-Cartan space

The higher dimensional Kaluza-Klein theory in Riemann-Cartan space is discussed. To clarify its implications, we investigate the simplest five-dimensional case of the theory in detail. The Einstein-like, Maxwell, and Dirac equations in four-dimensional space-time are obtained by reducing the corresponding five-dimensional field equations. The effect of spin-spin interaction induced by torsion is revealed by analyzing the Dirac equation in this case.     

Thin shell wormholes in higher dimensional Einstein–Maxwell theory

We construct thin shell Lorentzian wormholes in higher dimensional Einstein–Maxwell theory applying the ‘Cut and Paste’ technique proposed by Visser. The linearized stability is analyzed under radial perturbations around some assumed higher dimensional spherically symmetric static solution of the Einstein field equations in presence of Electromagnetic field. We determine the total amount of exotic matter, which is concentrated at the wormhole throat.