Related papers: Gordon Metric Revisited

Area metric manifolds emerge as effective classical backgrounds in quantum string theory and quantum gauge theory, and present a true generalization of metric geometry. Here, we consider area metric manifolds in their own right, and develop…

We have recently introduced a new and very simple action for three-dimensional massive gravity. This action is written in a first order formulation where the triad and the connection play a manifestly symmetric role, but where internal…

Geometric momentum is the appropriate momentum for a particle constrained to move on a curved surface, which depends on the extrinsic curvature and leads to observable effects, and curvature-induced quantum potentials appear for a…

Light is the richest information retriever for most physical systems, particularly so for astronomy and cosmology, in which gravitation is of paramount importance, and also for solid state defects and metamaterials, in which some effects…

Transportation distances have been used for more than a decade now in machine learning to compare histograms of features. They have one parameter: the ground metric, which can be any metric between the features themselves. As is the case…

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…

In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…

We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the…

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16(1), (1975)] provides a sense in which the geodesic principle has the status of a theorem in General Relativity (GR).…

Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…

We reveal a fundamental geometric structure of momentum space arising from the nonadiabatic evolution of Bloch electrons. By extending semiclassical wave packet theory to incorporate nonadiabatic effects, we introduce a momentum-space…

A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely defines…

For a contravariant 4-metric which changes signature from Lorentzian to Riemannian across a spatial hypersurface, the mixed Einstein tensor is manifestly non-singular. In Gaussian normal coordinates, the metric contains a step function and…

We complete the program of spectral geometry, in the sense that we show that a manifold's shape, i.e., its metric, can be reconstructed from its resonant sound when tapped lightly, i.e., from its spectrum, -- if in addition we also record…

This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…

Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…

Area metrics and area metric backgrounds provide a unified framework for quantum gravity. They encode physical degrees of freedom beyond those of a metric. These non-metric degrees of freedom must be suppressed by a potential at…

The interplay between quantum geometry and electron correlation has emerged as a compelling paradigm in quantum many-body physics. Recent studies have highlighted the diagnostic utility of quantum geometry in identifying magnetic…

Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…

We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…