相关论文: Ricci flow, quantum mechanics and gravity
We obtain Schroedinger quantum mechanics from Perelman's functional and from the Ricci flow equations of a conformally flat Riemannian metric on a closed 2-dimensional configuration space. We explore links with the recently discussed…
We introduce $*$-structures on braided groups and braided matrices. Using this, we show that the quantum double $D(U_q(su_2))$ can be viewed as the quantum algebra of observables of a quantum particle moving on a hyperboloid in q-Minkowski…
This paper introduces a novel abstraction for programming quantum operations, specifically projective Cliffords, as functions over the qudit Pauli group. Generalizing the idea behind Pauli tableaux, we introduce a type system and lambda…
We develop a perturbative formulation of the Ricci flow in gravity. Following steps analogous to the gradient flow in QCD, we supplement the usual Feynman rules for perturbative gravity by flowed propagators and vertices as well as graviton…
We describe a few elementary aspects of the circle of ideas associated with a quantum field theory (QFT) approach to Riemannian Geometry, a theme related to how Riemannian structures are generated out of the spectrum of (random or quantum)…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature,…
Holographic RG flows dual to QFTs on maximally symmetric curved manifolds (dS$_d$, AdS$_d$, and $S^d$) are considered in the framework of Einstein-dilaton gravity in $d+1$ dimensions. A general dilaton potential is used and the flows are…
Motivated by group-theoretical questions that arise in the context of asymptotic symmetries in gravity, we study model spaces and their quantization from the viewpoint of constrained Hamiltonian systems. More precisely, we propose that a…
We study two classes of quantum spheres and hyperboloids which are $*$-quantum spaces for the quantum orthogonal group $\mathcal{O}(SO_q(3))$. We construct line bundles over the quantum homogeneous space of invariant elements for the…
A coarse graining operation of spatially homogeneous quantum states based on an SU(1,1) Lie group structure has recently been proposed in [1] and used in [2] to compute an explicit renormalisation group flow in the context of loop quantum…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation…
Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are…
We study geodesics flows on curved quantum Riemannian geometries using a recent formulation in terms of bimodule connections and completely positive maps. We complete this formalism with a canonical $*$ operation on noncommutative vector…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
We consider Ricci flow on two classes of nilpotent Lie groups that generalize the three-dimensional Heisenberg group: the higher-dimensional classical Heisenberg groups, and the groups of real unitriangular matrices. Each group is known to…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…
For a Dirac theory of quantum gravity obtained from the refined algebraic quantization procedure, we propose a quantum notion of Cauchy surfaces. In such a theory, there is a kernel projector for the quantized scalar and momentum…
Loop Quantum Gravity heavily relies on a connection formulation of General Relativity such that 1. the connection Poisson commutes with itself and 2. the corresponding gauge group is compact. This can be achieved starting from the Palatini…