Related papers: Fuzzy Geometries with an Internal Space
We show that the classical equations of motion for a particle on three dimensional fuzzy space and on the fuzzy sphere are underpinned by a natural Lorentz geometry. From this geometric perspective, the equations of motion generally…
The Fuzzy transform is ubiquitous in different research fields and applications, such as image and data compression, data mining, knowledge discovery, and the analysis of linguistic expressions. As a generalisation of the Fuzzy transform,…
We consider a quasi-periodically identified conical spacetime, like the one of a cosmic string or disclination, to investigate nonzero averaged quantum vacuum fluctuations effects on the energy-momentum tensor and induced current density…
Fuzzy tori are finite dimensional C*-algebras endowed with an appropriate notion of noncommutative geometry inherited from an ergodic action of a finite closed subgroup of the torus, which are meant as finite dimensional approximations of…
We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element $ds$. Its unitary representations correspond to Riemannian metrics and Spin…
We clarify a strong link between general nonlinear Fokker-Planck equations with gauge fields associated with nonequilibrium dynamics and the Fisher information of the system. The notion of Abelian gauge theory for the non-equilibrium…
General Relativity formulated with Noncommutative geometry allows one to obtain, via the fluctuation of Dirac operator, an exact equivalence principle: generation of curvature and torsion from flat space. The fluctuation method presented in…
Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary…
In this article we show that a Dirac Hamiltonian in a curved background spacetime can be interpreted, when discretized, as a tight binding Fermi-Hubbard model with non unitary tunnelings. We find the form of the nonunitary tunneling…
We put forward a definition for spectral triples and algebraic backgrounds based on Jordan coordinate algebras. We also propose natural and gauge-invariant bosonic configuration spaces of fluctuated Dirac operators and compute them for…
We study the evolution of quantum fluctuations of a scalar field which is coupled to the geometry, in an exponentially expanding universe. We derive an expression for the spectrum of intrinsic perturbations, and it is shown that the…
Theories defined in higher than four dimensions have been used in various frameworks and have a long and interesting history. Here we review certain attempts, developed over the last years, towards the construction of unified particle…
The quantum space-time and the phase space with fuzzy structure is investigated as the possible quantization formalism. In this theory the state of nonrelativistic particle corresponds to the element of fuzzy ordered set (Foset) - fuzzy…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
We discuss gauge theories for commutative but non-associative algebras related to the $ SO(2k+1)$ covariant finite dimensional fuzzy $2k$-sphere algebras. A consequence of non-associativity is that gauge fields and gauge parameters have to…
We introduce a rotation invariant short distance cut-off in the theory of an ideal fluid in three space dimensions, by requiring momenta to take values in a sphere. This leads to an algebra of functions in position space is non-commutative.…
This manuscript is devoted to introduce a gauge theory of the Lorentz Group based on the ambiguity emerging in dealing with isometric diffeo-morphism-induced Lorentz transformations. The behaviors under local transformations of fermion…
Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor…
In this paper, we discussed about the intuitionistic fuzzy linear transformations (IFLT) and shown that the set of all linear transformations L(V) defined over an intuitionistic fuzzy vector space V does not form an vector space. Here we…
The physical phase space of gauge field theories on a cylindrical spacetime with an arbitrary compact simple gauge group is shown to be the quotient $ {\bf R}^{2r}/W_A, $ $ r $ a rank of the gauge group, $ W_A $ the affine Weyl group. The…