International Journal of Geometric Methods in Modern Physics

Based on a stringy inspired Gauss–Bonnet (GB) modification of classical gravity, we constructed a model for neutron stars. We derived the modified forms of Tolman–Oppenheimer–Volkoff (TOV) equations for a generic function of f(G) gravity. The hydrostatic equations remained unchanged but the dynamical equations for metric functions are modified due to the effects of GB term.

We present the analytic Lifshitz solutions for a scalar field model minimally coupled with the abelian gauge field in N-dimensions. We also consider the presence of cosmological constant Λ. The Lifshitz parameter z appearing in the solution plays the role of the Lorentz breaking parameter of the model. We investigate the thermodynamical properties of the solutions and discuss the energy issue. Furthermore, we study the hairy black hole solutions in which the abelian gauge field breaks the symmetry near to the horizon. In the holographic picture, it is equivalent to a second-order phase transition. Explicitly we show that there exists a critical temperature which is a function of the Lifshitz parameter z. The system below the critical temperature becomes superconductor, but the critical exponent of the model remains the same of the usual holographic superconductors without the higher-order gravitational corrections, in agreement with Ginzburg–Landau theories.

In this study, we worked on the second kind of relaxed elastic lines on dual spaces which has an important point on kinematic. We also obtained boundary conditions for this type of curves. Moreover, the minimization problem of the energy which occurs with an applied force on an elastic line was discussed. Then, we researched the formed potential energy due to the applied force and derived boundary conditions for that case.

The principal focus of the present work concerns the critical behaviors of a class of three-dimensional (3D) black holes with a scalar field hair. Since the cosmological constant is viewed as a thermodynamic pressure and its conjugate quantity as a volume, we examine such properties in terms of two parameters B and a. The latters are related to the scalar field and the angular momentum, respectively. In particular, we give the equation of state predicting a critical universal number depending on the (B, a) moduli space. In the vanishing limit of the B parameter, we recover the usual perfect gas behavior appearing in the case of the non-rotating BTZ black hole. We point out that in a generic region of the (B, a) moduli space, the model behaves like a Van der Waals system.

We formalize higher-dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type σ-model branes (open brane ending on background brane) are encoded precisely in (super-)L_∞-extension theory and how the resulting "extended (super-)space-times" formalize spacetimes containing σ-model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super-p-brane spectrum of superstring/M-theory is realized this way, including the pure σ-model branes (the "old brane scan") but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional (11D) spacetime with an M2-brane condensate turns out to be the "M-theory super-Lie algebra". We also observe that in this formulation there is a simple formal proof of the fact that type IIA spacetime with a D0-brane condensate is the 11D sugra/M-theory spacetime, and of (prequantum) S-duality for type IIB string theory. Finally we give the non-perturbative description of all this by higher WZW-type σ-models on higher super-orbispaces with higher WZW terms in stacky differential cohomology.

A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla–Selberg series formula, for which an alternative proof is thereby given. In addition, a new proof of the functional determinant on the torus results, which does not use the Kronecker first limit formula nor the functional equation of the non-holomorphic Eisenstein series. As a bonus, several identities involving the Dedekind eta function are obtained as well.

The aim of this paper is to present a relatively complete theory of invariance of global, higher-order integral variational functionals in fibered spaces, as developed during a few past decades. We unify and extend recent results of the geometric invariance theory; new results on deformations of extremals are also included. We show that the theory can be developed by means of the general concept of invariance of a differential form in geometry, which does not require different ad hoc modifications. The concept applies to invariance of Lagrangians, source forms and Euler–Lagrange forms, as well as to extremals of the given variational functional. Equations for generators of invariance transformations of the Lagrangians and the Euler–Lagrange forms are characterized in terms of Lie derivatives. As a consequence of invariance, we derive the global Noether's theorem on existence of conserved currents along extremals, and discuss the meaning of conservation equations. We prove a theorem describing extremals, whose deformations by a vector field are again extremals. The general settings and structures we use admit extension of the global invariance theory to variational principles in physics, especially in field theory.

In this paper, we give a quantum modification of the relative cup product on H*(X, S;ℝ) by using Gromov–Witten invariants when S is a compact codimension 2k symplectic submanifold of the compact symplectic manifold (X, ω).

In this paper, we will demonstrate that like the existence of a minimum measurable length, the existence of a maximum measurable momentum, also influence all quantum mechanical systems. Beyond the simple one-dimensional case, the existence of a maximum momentum will induce non-local corrections to the first quantized Hamiltonian. However, these non-local corrections can be effectively treated as local corrections by using the theory of harmonic extensions of functions. We will also analyze the second quantization of this deformed first quantized theory. Finally, we will analyze the gauge symmetry corresponding to this deformed theory.

The presence of spinor fields is considered in the framework of some extensions of teleparallel gravity, where the Weitzenböck connection is assumed. Some well-known models as the Chaplygin gas and its generalizations are reconstructed in terms of a spinor field in the framework of teleparallel gravity. In addition, the ΛCDM model is also realized with the presence of a spinor field where a simple self-interacting term is considered and the corresponding action is reconstructed. Other cosmological solutions and the reconstruction of the gravitational action in terms of the scalar torsion are studied.

Inter-relation between 1-form of nonmetricity and change of entropy in the course of time is considered in the study. It is shown that change of entropy in expanding universe will be always negative. The obtained result contravenes the second law of thermodynamics, however it explains available ordered macrostructures in the universe.

Studying the geometric flow plays a powerful role in mathematics and physics. We introduce the Yamabe flow on Finsler manifolds and we will prove the existence and uniqueness for solution of Yamabe flow on Berwald manifolds.

We consider gauge models in the causal approach and study one-loop contributions to the chronological products and the anomalies they produce. We prove that in order greater than 4 there are no one-loop anomalies. Next we analyze one-loop anomalies in the second- and third-order of the perturbation theory. We prove that the even parity contributions (with respect to parity) do not produce anomalies; for the odd parity contributions we reobtain the well-known result.