Related papers: A note on quantization of matrix models
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate…
We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator theory. Given a system in which some components of the state…
It is shown that background fields of a topological character usually introduced as such in compactified string theories correspond to quantum degrees of freedom which parametrise the freedom in choosing a representation of the zero mode…
I discuss a formalism for computing quantum scattering amplitudes using a semiclassical expansion of a functional integral representation for the S-matrix. The classical background for the expansion is determined by solving the equations of…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…
Spontaneous collapse models provide a possible, testable solution to the quantum measurement problem. While experiments are providing increasingly stronger bounds on their parameters, a full-fledged relativistic extension is still missing.…
A new interpretation of quantum mechanics is proposed according to which precedence, freedom and novelty play central roles. This is based on a modification of the postulates for quantum theory given by Masanes and Muller. We argue that…
Inference in graphical models consists of repeatedly multiplying and summing out potentials. It is generally intractable because the derived potentials obtained in this way can be exponentially large. Approximate inference techniques such…
We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
We consider the general free field theory such that system of equations of motion includes a subsystem with a special property. If the subsystem is considered by itself, it would be a topological field theory having no local degrees of…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…
We study the real-time evolution of a self-interacting O(N) scalar field initially prepared in a pure quantum state. We present a complete solution of the nonequilibrium quantum dynamics from a 1/N-expansion of the two-particle-irreducible…
Using the fact that the nonintegrable phase factor can reformulate the gauge theory in terms of path dependent vector potentials, the quantization condition for the nonintegrable phase is investigated. It is shown that the path-dependent…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…