Frölicher-smooth geometries,quantum jet bundles and BRST symmetry

We attempt a clarification of geometric aspects of quantum field theory by using the notion of smoothness introduced by Frölicher and exploited by several authors in the study of functional bundles. A discussion of momentum and position representations in curved spacetime, in terms of generalized semi-densities, leads to a definition of quantum configuration bundle which is suitable for a treatment of that kind. A consistent approach to Lagrangian field theories, vertical infinitesimal symmetries and related currents is then developed, and applied to a formulation of BRST symmetry in a gauge theory of the Yang–Mills type.     

Noether symmetry for Gauss–Bonnet dilatonic gravity

Noether symmetry for Gauss–Bonnet Dilatonic interaction exists for a constant dilatonic scalar potential and a linear functional dependence of the coupling parameter on the scalar field. The symmetry with the same form of the potential and coupling parameter exists all in the vacuum, radiation and matter dominated era. The late time acceleration is driven by the effective cosmological constant rather than the Gauss–Bonnet term, while the later compensates for the large value of the effective cosmological constant giving a plausible answer to the well-known coincidence problem.     

A BRST gauge-fixing procedure for Yang–Mills theory on sphere

A gauge-fixing procedure for the Yang–Mills theory on an n  -dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler's gauge-fixing condition used in massless Euclidean QED on a hypersphere is not conventional because of the presence of an extra free index, and hence is unfavorable for the gauge-fixing procedure based on the BRST invariance principle (or simply BRST gauge-fixing procedure). Choosing a suitable gauge condition, which is proved to be equivalent to a generalization of Adler's condition, we apply the BRST gauge-fixing procedure to the Yang–Mills theory on a hypersphere to obtain consistent results. Field equations for the Yang–Mills field and associated fields are derived in manifestly O(n+1)$\mathrm{O}(n+1)$ covariant or invariant forms. In the large radius limit, these equations reproduce the corresponding field equations defined on the n-dimensional flat space.     

Quantum modified Regge–Teitelboim cosmology

In this paper we study the late evolution of Relic Gravitational Waves in coupled dark energy models, where dark energy interacts with cold dark matter. Relic Gravitational Waves are second tensorial order perturbations of the Lemaitre–Friedman–Robertson–Walker metric and experiment an evolution ruled by the scale factor of the metric. We find that the amplitude of Relic Gravitational Waves is smaller in coupled dark energy models than in models with non interacting dark energy. We also find that the amplitude of the waves predicted by the models with coupling term proportional to the dark energy density is smaller than those of the models with coupling term proportional to dark matter density.     

Maximal invariants for Lorentz–Wishart models

In this paper we consider two statistical hypotheses for the families of Wishart type distributions. These distributions are analogs of the Wishart distributions defined and parametrized over a Lorentz cone. We test these hypotheses by means of maximal invariant statistics which are explicitly derived in the paper. The testing problems, respectively, concern the hypothesis that parameters are in a sub-Lorentz-cone and the hypothesis that two observations have the same parameter.     

Field-theoretical formulation of Regge–Teitelboim gravity

Theory of gravity is considered in the Regge–Teitelboim approach in which the pseudo-Rimannian space is treated as a surface isometrically embedded in an ambient Minkowski space of higher dimension. This approach is formulated in terms of a field theory in which the original pseudo-Rimannian space is defined by the field constant-value surfaces. The symmetry properties of the proposed theory are investigated, and possible structure of the field-theoretical Lagrangian is discussed.     

The symmetry energy γ parameter of relativistic mean-field models

The relativistic mean-field models tested in previous works against nuclear matter experimental values,critical parameters and macroscopic stellar properties are revisited and used in the evaluation of the symmetry energyγ parameter obtained in three different ways. We have checked that, independent of the choice made to calculate theγ values, a trend of linear correlation is observed between γ and the symmetry energy(S_0) and a more clear linear relationship is established between γ and the slope of the symmetry energy(L_0). These results directly contribute to the arising of other linear correlations between γ and the neutron star radii of R_(1.0) and R_(1.4), in agreement with recent findings. Finally, we have found that short-range correlations induce two specific parametrizations, namely,IU-FSU and DD-MEδ, simultaneously compatible with the neutron star mass constraint of 1.93≤M_(max)/M_☉≤2.05 and with the overlap band for the L_0 ×S_0 region, to present γ in the range of γ=0.25±0.05.     

Separation of variables for integrable spin–boson models

We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang–Baxter algebra. The main deviation from the standard approach consists in a half infinite Sklyanin lattice made of the eigenvalues of the operator zeros of the Bethe annihilation operator. By a separation of variables, functional TQ-equations are obtained for this half infinite lattice. They provide valuable information about the spectrum of a given Hamiltonian model. We apply this procedure to integrable spin–boson models subject to both twisted and open boundary conditions. In the case of general twisted and certain open boundary conditions polynomial solutions to these TQ-equations are found and we compute the spectrum of both the full transfer matrix and its quasi-classical limit. For generic open boundaries we present a two-parameter family of Bethe equations, derived from TQ-equations that are compatible with polynomial solutions for Q. A connection of these parameters to the boundary fields is still missing.     

The Ponzano–Regge Model and Parametric Representation

We give a parametric representation of the effective noncommutative field theory derived from a ${\kappa}$ -deformation of the Ponzano–Regge model and define a generalized Kirchhoff polynomial with ${\kappa}$ -correction terms, obtained in a ${\kappa}$ -linear approximation. We then consider the corresponding graph hypersurfaces and the question of how the presence of the correction term affects their motivic nature. We look in particular at the tetrahedron graph, which is the basic case of relevance to quantum gravity. With the help of computer calculations, we verify that the number of points over finite fields of the corresponding hypersurface does not fit polynomials with integer coefficients, hence the hypersurface of the tetrahedron is not polynomially countable. This shows that the correction term can change significantly the motivic properties of the hypersurfaces, with respect to the classical case.     

Quantum Regge Calculus of Einstein–Cartan theory

We study the Quantum Regge Calculus of Einstein–Cartan theory to describe quantum dynamics of Euclidean space–time discretized as a 4-simplices complex. Tetrad field eμ(x)$e_{\mu }(x)$ and spin-connection field ωμ(x)${\omega }_{\mu }(x)$ are assigned to each 1-simplex. Applying the torsion-free Cartan structure equation to each 2-simplex, we discuss parallel transports and construct a diffeomorphism and local   gauge-invariant Einstein–Cartan action. Invariant holonomies of tetrad and spin-connection fields along large loops are also given. Quantization is defined by a bounded partition function with the measure of SO(4)$\mathit{SO}(4)$-group valued ωμ(x)${\omega }_{\mu }(x)$ fields and Dirac-matrix valued eμ(x)$e_{\mu }(x)$ fields over 4-simplices complex.     

Painlevé analysis,infinite dimensional symmetry group and symmetry reductions for the(2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

The(2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani(KdVSKR) equation is studied by the singularity structure analysis. It is proven that it admits the Painlevé property. The Lie algebras which depend on three arbitrary functions of time t are obtained by the Lie point symmetry method. It is shown that the KdVSKR equation possesses an infinite-dimensional Kac–Moody–Virasoro symmetry algebra. By selecting first-order polynomials in t, a finitedimensional subalgebra of physical transformati...     

Vibrational energy flow models for the Rayleigh–Love and Rayleigh–Bishop rods

Energy Flow Analysis (EFA) has been developed to predict the vibrational energy density of the system structures in the medium-to-high frequency range. The elementary longitudinal wave theory is often used to describe the longitudinal vibration of a slender rod. However, for relatively large diameter rods or high frequency ranges, the elementary longitudinal wave theory is inaccurate because the lateral motions are not taken into account. In this paper, vibrational energy flow models are developed to analyze the longitudinally vibrating Rayleigh–Love rod considering the effect of lateral inertia, and the Rayleigh–Bishop rod considering the effect not only of the lateral inertia but also of the shear stiffness. The derived energy governing equations are second-order differential equations which predict the time and space averaged energy density and active intensity distributions in a rod. To verify the accuracy of the developed energy flow models, various numerical analyses are performed for a rod and coupled rods. Also, the EFA results for the Rayleigh–Love and Rayleigh–Bishop rods are compared with the analytical solutions for these models, the traditional energy flow solutions, and the analytical solutions for the classical rod.     

Prandtl–Ishlinskii hysteresis models for complex time dependent hysteresis nonlinearities

We introduce a new class of time dependent hysteresis models by combining the time dependent Prandtl–Ishlinskii model with functional nonlinearities. This combination improves the capability of the time dependent Prandtl–Ishlinskii model to characterize a class of complex time dependent hysteresis nonlinearities in smart actuators. The analytical inversion for the proposed time dependent hysteresis model is also presented in order to extend the inversion algorithm of the inverse time dependent Prandtl–Ishlinskii model for a class of complex time dependent hysteresis nonlinearities.     

Opinion evolution analysis for short-range and long-range Deffuant–Weisbuch models

In this paper, we propose and then analyze two generalized Deffuant–Weisbuch (DW) models. The generalized models extend the conventional DW model by taking multiple choices in two different ways. First, we demonstrate the almost sure convergence of the agent opinions for the short-range multi-choice DW dynamics when only the opinions within confidence regions may be count in. Then we analyze dynamical behavior about the long-range multi-choice DW model when some opinions out of the confidence ranges are considered with a weighted combination. Moreover, both theoretical and simulation results show that the dynamical behaviors of the two models are totally different.     

Newton–Hooke-type symmetry of anisotropic oscillators

Rotation-less Newton–Hooke-type symmetry, found recently in the Hill problem, and instrumental for explaining the center-of-mass decomposition, is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton–Hooke symmetry is recovered in the isotropic case. Star escape from a galaxy is studied as an application.