Related papers: Quantization of classical curves
Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…
We analyse the classical and quantum theory of a scalar field interacting with gravitation in two dimensions. We describe a class of analytic solutions to the Wheeler-DeWitt equation from which we are able to synthesise states that give…
These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…
In this article we review some results obtained from a generalization of quantum mechanics obtained from modification of the canonical commutation relation $[q,p]={\rm i}\hbar$. We present some new results concerning relativistic…
Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
It is well known that classical and quantum theories carry distinct types of representations, each type of representation corresponding to possible values of generalized charges in the classical or quantum context. This paper demonstrates a…
We apply QED theory to quantum gravity and find it leads to general relativity in the classical limit. We discuss the implications of the result for the quantum-classical divide. This enables us to relate our result to M-theory.
Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum…
In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum…
We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume…
Canonical quantization (CQ) is built around $[Q,P]=i\hbar1\!\!1$, while affine quantization (AQ) is built around $[Q,D]=i\hbar\,Q$, where $D\equiv(PQ+QP)/2$. The basic CQ operators must fit $-\infty< P, Q <\infty$, while the basic AQ…
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
The p - q duality is a relation between the (p,q) model and the (q,p) model of two-dimensional quantum gravity. Geometrically this duality corresponds to a relation between the two relevant points of the Sato Grassmannian. Kharchev and…
We demonstrate that, in certain cases, quantization and the classical limit provide functors that are "almost inverse" to each other. These functors map between categories of algebraic structures for classical and quantum physics,…
This is a survey article describing the relationship between quantum curves and topological recursion. A quantum curve is a Schr\"odinger operator-like noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants…
Coherent states path integral formalism for the simplest quantum algebras, q-oscillator, SU_q(2) and SU_q(1,1) is introduced. In the classical limit canonical structure is derived with modified symplectic and Riemannian metric. Non-constant…
We consider classical theories described by Hamiltonians $H(p,q)$ that have a non-degenerate minimum at the point where generalized momenta $p$ and generalized coordinates $q$ vanish. We assume that the sum of squares of generalized momenta…