Related papers: Covariant Affine Integral Quantization(s)
We develop a general mathematical framework for variational problems where the unknown function assumes values in the space of probability measures on some metric space. We study weak and strong topologies and define a total variation…
We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute…
A `covariant' field that transforms like a relativistic field operator is required to be a linear combination of `canonical' fields that transform like annihilation and creation operators and with invariant coefficients. The Invariant…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of duality: a dual model with inverse Planck constant exists such that the…
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional…
Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often…
Variational hybrid quantum-classical algorithms are some of the most promising workloads for near-term quantum computers without error correction. The aim of these variational algorithms is to guide the quantum system to a target state that…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
Today's quantum field theory (QFT) relies heavenly on canonical quantization (CQ), which fails for $\varphi^4_4$ leading only to a "free" result. Affine quantization (AQ), an alternative quantization procedure, leads to a "non-free" result…
Let $M$ be a smooth manifold equipped with a conformal structure, $E[w]$ the space of densities with the the conformal weight $w$ and $D_{w,w+\de}$ the space of differential operators from $E[w]$ to $E[w+\delta]$. Conformal quantization $Q$…
The integral of the Wigner function of a quantum mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval…
Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…
Building on work of Furstenberg and Tzkoni, we introduce ${\bf r}$-flag affine quermassintegrals and their dual versions. These quantities generalize affine and dual affine quermassintegrals as averages on flag manifolds (where the…
In this paper we define a quantum version of the ``fusion'' tensor product of two representations of an affine Kac-Moody algebra.It is replaced by what we call fusion action of the category of finite-dimensional representations of quantum…
We compare expressions for the atom interferometer phase obtained using the path integral approach and the approach based on the density matrix equation in the Wigner representation. The power series of these expressions over the Planck…
We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is…