Related papers: New Classical Limits of Quantum Theories
Quantum matrix models in the large-N limit arise in many physical systems like Yang-Mills theory with or without supersymmetry, quantum gravity, string-bit models, various low energy effective models of string theory, M(atrix) theory,…
We shall show that the abstract and formal rules which govern the quantum kinematic and dynamics can be derived from a law of change of the information content or the degree of uncertainty that the system has a certain configuration in a…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
This article examines the consequences of the existence of an upper particle momentum limit in quantum electrodynamics, where this momentum limit is the Planck momentum. The method used is Fourier analysis as developed already by Fermi in…
It is widely believed that mean-field theory is exact for a wide-range of classical long-range interacting systems. Is this also true once quantum fluctuations have been accounted for? As a test case we study the Hamiltonian Mean Field…
The theory of quantum fields propagating on an isotropic cosmological quantum spacetime is reexamined by generalizing the scalar test field to an electromagnetic (EM) vector field. For any given polarization of the EM field on the classical…
The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is…
Many quantum systems may have the same classical limit. We argue that in the classical limit their traces do not necessarily converge one to another. The trace formula allows to express quantum traces by means of classical quantities as…
Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit…
A classical solution to the Yang-Mills theory is given a new semiclassical interpretation. The boundary value problem on a complex time contour which arises from the semiclassical approximation to multiparticle scattering amplitudes is…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{quantum} geometries. We initiate the development of a quantum theory of test scalar fields on these…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
A non-perturbative and mathematically rigorous quantum Yang-Mills theory on 4-dimensional Minkowski spacetime is set up in the functional framework of a complex nuclear Kree-Gelfand triple. It involves a symbolic calculus of operators with…
Recently, there appeared results of lattice measurements in Yang-Mills theories which indicate non-trivial dependences on the lattice spacing of many observables. In particular, volume occupied by fermionic zero modes shrinks to zero in the…
This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
We first give a rigorous mathematical proof that classical mathematics (involving such notions as infinitely small/large, continuity etc.) is a special degenerate case of finite one in the formal limit when the characteristic $p$ of the…
Optomechanical systems can exhibit self-sustained limit cycles where the quantum state of the mechanical resonator possesses nonclassical characteristics such as a strongly negative Wigner density, as was shown recently in a numerical study…
We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite…