Related papers: Geodesic nature and quantization of shift vector
The study of quantum geometry effects in materials has been one of the most important research directions in recent decades. The quantum geometry of a material is characterized by the quantum geometry tensor of the Bloch states. The…
Any metric theory of gravity whose interaction with quantum particles is described by a covariant wave equation is equivalent to a vector theory that satisfies Maxwell-type equations identically. This result does not depend on any…
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a…
We introduce the notion of a monodromy for gauge fields with vanishing curvature on the noncommutative torus. Similar to the ordinary gauge theory, traces of the monodromies define noncommutative Wilson lines. Our main result is that these…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
We consider a quantum test particle in the background of a Newtonian gravitational field in the framework of Cartan's formulation of nonrelativistic spacetimes. We have proposed a novel quantization of a point particle which amounts to…
Shape Dynamics is a gauge theory based on spatial diffeomorphism- and Weyl-invariance which is locally indistinguishable form classical General Relativity. If taken seriously, it suggests that the spacetime--geometry picture that underlies…
Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analytical scheme for calculating the curvature of the quantum…
The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under…
This is the second paper in the series to introduce a graphical method to loop quantum gravity. We employ the graphical method as a powerful tool to calculate the actions of the Euclidean Hamiltonian constraint operator and the so-called…
We present and analyze a gauge-invariant quantum theory of the Friedmann-Robertson-Walker universe with dust. We construct the reduced phase space spanned by gauge-invariant quantities by using the so-called relational formalism at the…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…
We analyze parallel transport of a vector field around an equatorial orbit in Kerr and stationary axisymmetric spacetimes that are reflection symmetric about their equatorial planes. As in Schwarzschild spacetime, there is a band structure…
The identity of quantum matter can be effectively altered by means of gauge fields. In two spatial dimensions this is illustrated by the Chern-Simons flux-attachment mechanism, but such a mechanism is not possible in lower dimensions. Here,…
This model is one of the possible geometrical interpretations of Quantum Mechanics where found to every image Path correspondence the geodesic trajectory of classical test particles in the random geometry of the stochastic fields…
The role of gauge invariance is reconsidered by "deriving it without assuming it" within an autonomous approach to interactions of Standard Model particles. In this approach, the renormalizable interactions are purely constrained by quantum…
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality…
The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a…
A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their…