Related papers: BV Quantization
Based on the wavelet-defined multiscale random noise proposed in [Doklady Physics 2003, v.48, 478], a multiscale version of the stochastic quantization procedure is considered. A new type of the commutation relations emerging from the…
Gauge-invariant systems of a general form with higher order derivatives of gauge parameters are investigated within the framework of the BFV formalism. Higher order terms of the BRST charge and BRST-invariant Hamiltonian are obtained. It is…
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions.…
This note documents the specification of normal forms in cubical type theory. The definition is already present in the proof of normalization for cubical type theory, but we present it in a more traditional style explicitly for reference.
We survey various origins and expressions for the quantum potential with some new observations.
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions…
A generally covariant system can be deparametrized by means of an ``extrinsic'' time, provided that the metric has a conformal ``temporal'' Killing vector and the potential exhibits a suitable behavior with respect to it. The quantization…
Quantum computing has recently appeared in the headlines of many scientific and popular publications. In the context of quantitative finance, we provide here an overview of its potential.
The third quantization formalism of quantum cosmology adds simplicity and conceptual insight into the quantum description of the multiverse. Within such a formalism, the existence of squeezed and entangled states raises the question of…
Valuation-Based~System can represent knowledge in different domains including probability theory, Dempster-Shafer theory and possibility theory. More recent studies show that the framework of VBS is also appropriate for representing and…
The basic formalism of a novel scale invarinat nonlinear analysis is presented. A few analytic number theoretic results are derived independent of standard approaches.
We obtain simple proofs of certain inequalites for bivariate means.
This is a didactical review on the canonical BV Laplacian on half-densities.
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
Different formalisms for unintegrated parton densities are discussed, and some results and applications are presented.
Quantum characterization, verification, and validation (QCVV) is a set of techniques to probe, describe, and assess the behavior of quantum bits (qubits), quantum information-processing registers, and quantum computers. QCVV protocols probe…
An introduction to total positivity (TP), with the emphasis on efficient TP criteria and parametrizations of TP matrices. Intended for general mathematical audience.
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
This article reviews the extraordinary features of quantum information predicted by the quantum formalism, which, combined with the development of modern quantum technologies, have opened new horizons in quantum physics that can potentially…
This note gives a brief and `crash' introduction to the method of Homogenization with the use of wave equation and diffusion equation with periodic in space coefficients as instructive examples. We expose the method with the use of an…