Related papers: Non-Perturbative Quantum Geometry
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the…
We demonstrate the feasibility of a nonperturbative analysis of quantum field theory in the worldline formalism with the help of an efficient numerical algorithm. In particular, we compute the effective action for a super-renormalizable…
On the occasion of this ArkadyFest, celebrating Arkady Vainshtein's 60th birthday, I review some selected aspects of the connection between perturbative and nonperturbative physics, a subject to which Arkady has made many important…
The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave…
The thermodynamics of gauge theories on the noncommutative plane is studied in perturbation theory. For U(1) noncommutative Yang-Mills we compute the first quantum correction to the ideal gas free energy density and study their behavior in…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
A nonperturbative quantization procedure based on a nonassociative decomposition of quantum field operators on nonassociative constituents is considered. It is shown that such approach gives rise to quantum corrections by calculations of…
We derive a new perturbative quantum master equation for the reduced density matrix of a system interacting with an environment (with a dense spectrum of energy levels). The total system energy (system plus environment) is constant and…
By means of the Ehrenfest's Theorem inside the context of a noncommutative Quantum Mechanics it is obtained the Newton's Second Law in noncommutative space. Considering discrete systems with infinite degrees of freedom whose dynamical…
The free scalar field is studied on the Y-junction of three semi infinite axes which is the simplest example of a non-manifold space. It is shown that under an assumption that the junction point can not gain a macroscopic amount of energy…
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…
Quantum field theory in curved spacetime is perhaps the most reliable framework in which one can investigate quantum effects in the presence of strong gravitational fields. Nevertheless, it is often studied by means of perturbative…
The concept of effective particles as degrees of freedom in a relativistic quantum field theory is defined using a non-perturbative renormalization group procedure for Hamiltonians. However, every candidate for a basic physical theory…
In this work we have shown precisely that the curvature of a 2-sphere introduces quantum features in the system through the introduction of the noncommutative (NC) parameter that appeared naturally via equations of motion. To obtain this…
In this paper we study the quantum dynamics of an electron/hole in a two-dimensional quantum ring within a spherical space. For this geometry, we consider a harmonic confining potential. Suggesting that the quantum ring is affected by the…
We calculate the excitation spectrum of a one-dimensional self-bound quantum droplet in a two-component bosonic mixture described by the Gross-Pitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from…
Quantum-mechanical wave equation for a particle with spin 1 is investigated in presence of external magnetic field in spaces with non-Euclidean geometry with constant positive curvature. Separation of the variable is performed; differential…
We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density…
We show that perturbative quantum gravity based on the Einstein-Hilbert action, has a novel continuum limit. The renormalized trajectory emanates from the Gaussian fixed point along (marginally) relevant directions but enters the…
We consider quantum mechanics on the noncommutative plane in the presence of magnetic field $B$. We show, that the model has two essentially different phases separated by the point $B\theta=c\hbar^2/e$, where $\theta$ is a parameter of…