Related papers: On Noncommutative Geometric Regularisation
Existence of a minimal measurable length and an upper bound for the momentum fluctuations are the casting reasons for generalization of uncertainty principle and then reformulation of Hilbert space representation of quantum mechanics. In…
Regularity theorems are presented for cosmology and gravitational collapse in non-Riemannian gravitational theories. These theorems establish conditions necessary to allow the existence of timelike and null path complete spacetimes for…
Based on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On other…
We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'')…
The combined action of gravity and quantum mechanics gives rise to a minimum time uncertainty in the lowest order approximation of a perturbative scheme, in which quantum effects are regarded as corrections to the classical spacetime…
Phenomenological approaches to quantum gravity implement a minimum resolvable length-scale but do not link it to an underlying formalism describing geometric superpositions. Here, we introduce an intuitive approach in which points in the…
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such…
We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form…
We examine several zero-range potentials in non-relativistic quantum mechanics. The study of such potentials requires regularization and renormalization. We contrast physical results obtained using dimensional regularization and cutoff…
A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what…
We expect the final theory of gravity to have more symmetries than we suspect and our research points in this direction. To start with, standard general coordinate invariance can be extended to complex holomorphic general coordinate…
We derive generalised uncertainty relations (GURs) for angular momentum and spin in the smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum, and recovers both the generalised…
The no-boundary proposal is a theory of the initial conditions of the universe formulated in semi-classical gravity, and relying on the existence of regular (complex) solutions of the equations of motion. We show by explicit computation…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally)…
In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we…
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…
We derive new space-time uncertainty relations (STUR) at the fundamental Planck length $L_P$ from quantum mechanics and general relativity (GR), both in flat and curved backgrounds. Contrary to claims present in the literature, our approach…
We introduce a geometric realization of noncommutative singularity resolutions. To do this, we first present a new conjectural method of obtaining conventional resolutions using coordinate rings of matrix-valued functions. We verify this…
In black hole physics, inflationary cosmology, and quantum field theories, it is conjectured that the physical laws are subject to radical changes below the Planck length. Such changes are due to effects of quantum gravity believed to…