Related papers: Galilean Geometry in Condensed Matter Systems
We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with…
An effective U(1) gauge invariant theory is constructed for a non-commutative Schrodinger field coupled to a background U(1)_{\star} gauge field in 2+1-dimensions using first order Seiberg-Witten map. We show that this effective theory can…
While the equations of general relativity take the same form in any coordinate system, choosing a suitable set of coordinates is essential in any practical application. This poses a challenge in background-independent quantum gravity, where…
We analyze the problem of general covariance for quantum gravity theories in the background field formalism with respect to gauge fixing procedure. We prove that the background effective action is not invariant under general coordinate…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
The aim of this series of papers is to generalise the ambient approach of Duval et al. regarding the embedding of Galilean and Carrollian geometries inside gravitational waves with parallel rays. In this first part, we propose a…
We analyze some features of the entanglement entropy for an integer quantum Hall state ($\nu =1 $) in comparison with ideas from relativistic field theory and noncommutative geometry. The spectrum of the modular operator, for a restricted…
We generalize the scale invariant gravity by allowing a negative kinetic energy term for the classical scalar field. This gives birth to a new scalar-tensor theory of gravity, in which the scalar field is in fact an auxiliary field. For a…
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum…
The theory of the intrinsic Hall effect, both linear and nonlinear, is rooted in a geometry which is defined in the Bloch-vector parameter space; the formal expressions are mostly derived from semiclassical concepts. When disorder and…
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…
A system's invariance under Galilean transformation implies three locally conserved densities. Including them as variables, the thermodynamics is rendered explicitly frame independent, dissipative mass currents are shown to vanish, and…
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…
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
Besides the two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the one-way velocity of light in all inertial frames of reference, the special theory of relativity employs another assumption. This…
It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken.…
As a natural application of the {\it theory of geometric averaging} in Finsler geometry and generalized Finsler geometry, a new approach to investigate {\it generalized Finsler geometry}, based on a convex invariance of the average…
The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall…
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…
The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as…