Related papers: Time-dependent metrics and connections

A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer's topological degree for the solution of functional equations. It is shown to be very useful for…

A possibility to represent the standard model of fundamental particles covariant derivatives by means of approximate generalized fractional Riemann-Liouville derivatives of multifractal time and space model is shown.

We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…

We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…

We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we…

Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one--dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of…

We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…

The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. For many complex systems, however, it is useful to develop continuous-time models of…

Reference frames are crucial for describing local observers in general relativity. In quantum gravity, different proposals exist for how to treat reference frames. There are models with either classical or quantum reference frames.…

The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…

We address classical and quantum mechanics in a general setting of arbitrary time-dependent transformations. Classical non-relativistic mechanics is formulated as a particular field theory on smooth fibre bundles over a time axis.…

The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…

In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. Starting with the Covariant Force Law, we first develop autonomous…

In this series of papers I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable manifold, and their dimension is one unit…

Time-dependent quantities are calculated in the linear response limit for a correlated one dimensional model atom driven by an external quadrupolar time-dependent field. Besides the analysis of the time-evolving energy change in the…

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.

This paper is devoted to a systematic study and classification of invariant affine or metric connections on certain classes of naturally reductive spaces. For any non-symmetric, effective, strongly isotropy irreducible homogeneous…

We propose an approach to use the state covariance of linear systems to track time-varying covariance matrices of non-stationary time series. Following concepts from Riemmanian geometry, we investigate three types of covariance paths…

Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…

In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport…