International Journal of Geometric Methods in Modern Physics

We use the theory of Cartan connections to analyze the geometrical structures underpinning the gauge-theoretical descriptions of the gravitational interaction. According to the theory of Cartan connections, the spin connection ω and the soldering form θ that define the fundamental variables of the Palatini formulation of general relativity can be understood as different components of a single field, namely a Cartan connection A = ω + θ. In order to stress both the similarities and the differences between the notions of Ehresmann connection and Cartan connection, we explain in detail how a Cartan geometry (P_H → M, A) can be obtained from a G-principal bundle P_G → M endowed with an Ehresmann connection (being the Lorentz group H a subgroup of G) by means of a bundle reduction mechanism. We claim that this reduction must be understood as a partial gauge fixing of the local gauge symmetries of P_G, i.e. as a gauge fixing that leaves "unbroken" the local Lorentz invariance. We then argue that the "broken" part of the symmetry — that is the internal local translational invariance — is implicitly preserved by the invariance under the external diffeomorphisms of M.

A detailed Hamiltonian analysis for a 5D Kalb–Ramond, massive Kalb–Ramond and Stüeckelberg Kalb–Ramond theories with an extra compact dimension is performed. We develop a complete constraint program, then we quantize the theory by constructing the Dirac brackets. From the gauge transformations of the theories, we fix a particular gauge and we find pseudo-Goldstone bosons in Kalb–Ramond and Stüeckelberg Kalb–Ramond systems. Finally we discuss some remarks and prospects.

There are several approaches to extend General Relativity in order to explain the phenomena related to the Dark Matter and Dark Energy. These theories, generally called Extended Theories of Gravity, can be tested using observations coming from relativistic binary systems as PSR J0348 + 0432. Using a class of analytical f(R)-theories, one can construct the first time derivative of orbital period of the binary systems starting from a quadrupolar gravitational emission. Our aim is to set boundaries on the parameters of the theory in order to understand if they are ruled out, or not, by the observations on PSR J0348 + 0432. Finally, we have computed an upper limit on the graviton mass showing that agree with constraint coming from other observations.

String structures in degree 4 are associated with cancelation of anomalies of string theory in 10 dimensions. Fivebrane structures in degree 8 have recently been shown to be associated with cancelation of anomalies associated to fivebranes in string theory and M-theory. We introduce and describe Ninebrane structures in degree 12 and demonstrate how they capture some anomaly cancelation phenomena in M-theory. Along the way we also define certain variants, considered as intermediate cases in degrees 9 and 10, which we call 2-Orientation and 2-Spin structures, respectively. As in the lower degree cases, we also discuss the natural twists of these structures and characterize the corresponding topological groups associated to each of the structures, which likewise admit refinements to differential cohomology.

The Schwarzschild approach is applied to solve the field equations describing a Nexus graviton field. The resulting solutions are free from singularities which have been a problem in general relativity since its inception. Findings from this work also demonstrate that at the Hubble radius, the metric signature of space-time changes generating short-lived but intense bursts of energy during the transition process. The solutions in this paper also provide an explanation to the enigma of late time cosmic acceleration, the galaxy rotation curve problem and the coincidence problem.

Here, a nonlinear analysis method is applied rather than classical one to study projective changes of Finsler metrics. More intuitively, a projectively invariant pseudo-distance is introduced and characterized with respect to the Ricci tensor and its covariant derivatives.

We review the definition by Perlick of standard clocks in a Weyl geometry and show how a congruence of clocks can be used to fix the conformal gauge in the EPS framework. Examples are discussed in detail.

Using the Einstein, Bergmann–Thomson, Landau–Lifshitz, Møller, Papapetrou and Tolman energy–momentum complexes in general relativity (GR) and teleparallel gravity (TG), we calculate the total energy–momentum distributions associated with N-dimensional Bianchi type V universe. While the solutions of Einstein, Bergmann–Thomson and Tolman energy and momentum densities are the same as each other, the solutions of Landau–Lifshitz, Møller and Papapetrou energy–momentum densities are different for N-dimensional Bianchi type V space-time in GR and TG. Obtained results for Einstein, Bergmann–Thomson and Landau–Lifshitz definitions we could say that GR and TG are in the same class. Because different energy–momentum distributions provide same results. However we have discussed N-dimensional Bianchi type I solutions and then we obtained all energy–momentum solutions are vanish in GR and TG theories. These results agree with Banerjee–Sen, Xulu, Aydoḡdu–Saltı and Radinschi in four dimensions.

In this paper we show that the Thomas precession of the spinning bodies, which is in general case constrained in all rigid bodies, induces magnetic field of the spinning bodies. This is one of the main reasons for the magnetic field of the spinning bodies. The general formula for this magnetic field is deduced and if it is applied to the Earth, its magnetic field changes between 0.295 G at the equator and 0.59 G at the poles, assuming that the density inside the Earth is uniform.

The operators with large scaling dimensions can be labeled by Young diagrams. Among other bases, the operators using restricted Schur polynomials have been known to have a large N but nonplanar limit under which they map to states of a system of harmonic oscillators. We analyze the oscillator algebra acting on pairs of long rows or long columns in the Young diagrams of the operators. The oscillator algebra can be reached by a Inonu–Wigner contraction of the u(2) algebra inside of the u(p) algebra of p giant gravitons. We present evidences that integrability in this case can persist at higher loops due to the presence of the oscillator algebra which is expected to be robust under loop corrections in the nonplanar large N limit.

We analytically study the critical phase of a mixed system of the U(2) gauge fields and global symmetry on the boundary using gauge/gravity. A variational minimization problem has been formulated. The numerical results pertinently show that there exists a minimum chemical potential in which both scalar (s-wave) and vector (p-wave) condensates exist in a mixture, as well as in the distinct s- and p-phases. This result is obtained by breaking the symmetry into U(1) symmetry and rotational symmetry. While the analytical solutions of condensates and charge densities are achieved in both cases: the balanced and unbalanced holographic superconductors. This is the first analytical study of the coexistence of two modes of the superconductivity with different order parameters. The realistic model consists of two different phases of the superfluidity in helium.

A new formulation of relativistic classical mechanics allows a reconsideration of old unsolved problems in relativistic kinetic theory and in relativistic statistical mechanics. In particular a definition of the relativistic micro-canonical partition function is given strictly in terms of the Poincaré generators of an interacting N-particle system both in the inertial and non-inertial rest frames. The non-relativistic limit allows a definition of both the inertial and non-inertial micro-canonical ensemble in terms of the Galilei generators.

In this paper, the Wheeler–DeWitt equation in full superspace formalism will be written in a matrix-valued first-order formalism. We will also analyze the Wheeler–DeWitt equation in minisuperspace approximation using this matrix-valued first-order formalism. We will note that this Wheeler–DeWitt equation, in this minisuperspace approximation, can be expressed as an eigenvalue equation. We will use this fact to analyze the spacetime foam in this formalism. This will be done by constructing a statistical mechanical partition function for the Wheeler–DeWitt equation in this matrix-valued first-order formalism. This will lead to a possible solution for the cosmological constant problem.

In this paper, we investigate lightlike hypersurfaces which are Chaki type pseudo-symmetric, Chaki type pseudo-Ricci symmetric and Chaki type pseudo-projective symmetric in a semi-Euclidean space. We also give some physical interpretations of Chaki type pseudo-symmetry condition.