相关论文: Quantizing the line element field
In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the…
The field of quantum metrology promises measurement devices that are fundamentally superior to conventional technologies. Specifically, when quantum entanglement is harnessed the precision achieved is supposed to scale more favourably with…
In this paper, we define a semi-symmetric metric Killing vector field, then study semi-symmetric metric Killing vector fields on warped and multiply warped products with a semi-symmetric metric connection. We also study Killing and…
We demonstrate, by a simple analysis, that cosmological line elements related by scale factor duality also exhibit a duality with respect to the conservation/violation of the Weak Energy Condition (WEC) by the matter that acts as the source…
A set of observables is described for the topological quantum field theory which describes quantum gravity in three space-time dimensions with positive signature and positive cosmological constant. The simplest examples measure the…
Working over a field ${\mathbb{k}}$ of characteristic $\ne 2$, we study what we call bisector fields, which are arrangements of paired lines in the plane that have the property that each line in the arrangement crosses the paired lines in…
We offer an axiomatic presentation of three-dimensional projective space that adopts the line as its fundamental element and renders automatic the principle of duality.
The canonical analysis and subsequent quantization of the (2+1)-dimensional action of pure gravity plus a cosmological constant term is considered, under the assumption of the existence of one spacelike Killing vector field. The proper…
We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric $\G$ to be scaled by different conformal factors. In particular, we study their…
A signed graph is a graph in which each edge has a positive or negative sign. In this article, first we characterize the distance compatibility in the case of a connected signed graph and discussed the distance compatibility criterion for…
Massive gauge fields whose mass is introduced by hand form very intriguing theories. They depart from their massless counterparts by a straightforward modification. Yet, taking the limit when the same vanishes poses a non-trivial challenge.…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
The electronic structure of heavy elements, when described in a space-time which the metric is affected by the electromagnetic interaction, presents instabilities. These instabilities increase with the atomic number, and above a critical…
In this paper we show that, via an extension of time, some metric structures naturally appear in both classical and quantum mechanics when both are formulated via path integrals. We calculate the various Ricci scalar and curvatures…
A magnetic monopole is placed at the centre of a 3-ball whose surface, S, is tiled by the symmetry group, G, of a regular solid. The quantum mechanics on the two-dimensional quotient, S/G, is developed and the monopole charge is found to be…
Understanding the behavior of quantum systems subject to magnetic fields is of fundamental importance and underpins quantum technologies. However, modeling these systems is a complex task, because of many-body interactions and because…
The identity of classical motion is established for two physically different models, one of which is the relativistic particle with torsion, whose action contains higher derivatives and which is the effective system for the statistically…
What is a vector field on a C*-algebra is defined. Its relation to semigroups of endomorphisms was researched. Some results given about those vector fields and semigroups. There are also various constructions of semigroups including one…
This paper presents a comprehensive perspective of the metric of quantum states with a focus on the background independent metric structures. We also explore the possibilities of geometrical formulations of quantum mechanics beyond the…
We propose an extension of General Relativity with two different metrics. To each metric we define a Levi-Cevita connection and a curvature tensor. We then consider two types of fields, each of which moves according to one of the metrics…