相关论文: The Uncanny Precision of the Spectral Action

We study a three dimensional non-commutative space emerging in the context of three dimensional Euclidean quantum gravity. Our starting point is the assumption that the isometry group is deformed to the Drinfeld double D(SU(2)). We…

Noncommutative geometry, in its many incarnations, appears at the crossroad of various researches in theoretical and mathematical physics: from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and…

The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of $N$th order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and…

A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides…

We develop a Heisenberg-picture \emph{kinematical} framework in which (i) time is treated as a quantum observable, admitting both a relational POVM construction for semibounded spectra and a fully self-adjoint realization on an enlarged…

It has been observed earlier that, in principle, it is possible to obtain a quantum mechanical interpretation of higher order quantum cosmological models in the spatially homogeneous and isotropic background, if auxiliary variable required…

Functional geometry is a framework using concepts from geometry to understand the invariance of amplitudes in quantum field theory under a large class of field redefinitions, including those involving derivatives. It is inspired by…

After an introduction to some basic issues in non-commutative geometry (Gel'fand duality, spectral triples), we present a "panoramic view" of the status of our current research program on the use of categorical methods in the setting of…

In the noncommutative geometry approach to the standard model we discuss the possibility to derive the extra scalar field sv- initially suggested by particle physicist to stabilize the electroweak vacuum - from a "grand algebra" that…

In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs…

We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states…

These lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate…

A finite non-commutative geometry consists of a fuzzy space together with a Dirac operator satisfying the axioms of a real spectral triple. This paper addreses the question of how to extract information about these geometries from the…

We study the canonical quantization of the theory given by Chamseddine-Connes spectral action on a particular finite spectral triple with algebra $M_2(\Cset)\oplus\Cset$. We define a quantization of the natural distance associated with this…

The object of this work is the numerical investigation of a non-commutative field theory defined via the spectral action principle. The Starting point is a spectral triple (A,H,D) referred to as harmonic. The construction of these data…

This research establishes an operational measurement way to express the quantum field theory in a geometrical form. In four-dimensional spacetime continuum, the orthogonal rotation is defined. It forms two sets of equations: one set is…

We consider K\"ahler toric manifolds $N$ that are torifications of statistical manifolds $\mathcal{E}$ in the sense of [M. Molitor, "K\"ahler toric manifolds from dually flat spaces", arXiv:2109.04839], and prove a geometric analogue of the…

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…

Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…

We show that, apart from the usual area operator of non-perturbative quantum gravity, there exists another, closely related, operator that measures areas of surfaces. Both corresponding classical expressions yield the area. Quantum…