相关论文: The Uncanny Precision of the Spectral Action

A phase-space approach to quantum-deformed gravity is developed. Following its reduction to an effective four-dimensional spacetime structure, we utilize it in reanalyzing the cosmic inflationary dynamics and quantum gravity. The…

We derive the exact form of the spectral interaction of two strings mediated by a constant scalar field using methods derived from noncommutative geometry. This is achieved by considering a non-product modification of the Connes-Lott model…

Inspired by the similarity between the fractal Weierstrass function and quantum systems with discrete scaling symmetry, we establish general conditions under which the dynamics of a quantum system will exhibit fractal structure in the time…

This work concerns a new reformulation of quantum geometrodynamics, which allows to overcome a fundamental ambiguity contained in the canonical approach to quantum gravity: the possibility of performing a (3+1)-slicing of space-time, when…

We establish a quantum dynamics framework for curved submanifolds embedded in higher-dimensional spaces. Through rigorous dimensional reduction, we derive the first complete Schr\"{o}dinger and Klein-Gordon equations incorporating…

Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…

The principles of noncommutative geometry impose severe restrictions on the structure of (almost) commutative field theories. The Standard Model fits surprisingly well into the noncommutative framework. Here we overview some universal…

We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In…

We show how the bosonic spectral action emerges from the fermionic action by the renormalization group flow in the presence of a dilaton and the Weyl anomaly. The induced action comes out to be basically the Chamseddine-Connes spectral…

We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…

Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…

We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative…

The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…

At high temperature the infrared modes of a weakly coupled quantum field theory can be treated nonperturbatively in real time using the classical field approximation. We use this to introduce a nonperturbative approach to the calculation of…

The effective action for quantum fields on a $d$-dimensional spacetime can be computed using a non local expansion in powers of the curvature. We show explicitly that, for conformal fields and up to quadratic order in the curvature, the non…

At mesoscopic scales, the quantum corrected field equations of gravity should arise from extremizing, $\Omega$, the number of microscopic configurations of pre-geometric variables consistent with a given geometry. This $\Omega$, in turn, is…

With approaching quantum/noncommutative models for the deep microscopic spacetime in mind, and inspired by our recent picture of the (projective) Hilbert space as the model of physical space behind basic quantum mechanics, we reformulate…

An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape…

We introduce a new family of metrics, called functional metrics, on noncommutative tori and study their spectral geometry. We define a class of Laplace type operators for these metrics and study their spectral invariants obtained from the…

Noncommutative geometry is a mathematical framework that expresses the structure of space-time in terms of operator algebras. By using the tools of quantum mechanics to describe the geometry, noncommutative space-times are expected to give…