Related papers: From operads and PROPs to Feynman Processes
A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined.…
In the theory of operads we consider functors of generalized symmetric powers defined by sums of coinvariant modules under actions of symmetric groups. One observes classically that the construction of symmetric functors provides an…
In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's…
The quantum Dirac-like equation and the QED vertex operator for a composite particle are suggested. The vertex operator and the fermionic propagator are connected by the QED Ward identity. It is shown that all of the Feynman QED-integrals…
In the present paper we introduce positive flows and processes, which generalize the ordinary dynamical systems and stochastic processes. We develop a branch of theory of positive operators based on the concepts of phase and positive…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
Quantum information and computation may serve as a source of useful axioms and ideas for the quantum logic/quantum structures project of characterizing and classifying types of physical theories, including quantum mechanics and classical…
Operads were originally defined by May to have right actions of the symmetric groups, but later formulations have also used no groups actions at all or group actions by such families as the braid groups. We call such families action…
In this article we give a short and informal overview of some aspects of the theory of C*- and von Neumann algebras. We also mention some classical results and applications of these families of operator algebras.
Wall-crossing phenomena are ubiquitous in many problems of algebraic geometry and theoretical physics. Various ways to encode the relevant information and the need to track the changes under the variation of parameters lead to rather…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
These notes provide an explanation of the type classification of von Neumann algebras, which has made many appearances in recent work on entanglement in quantum field theory and quantum gravity. The goal is to bridge a gap in the literature…
It is shown that Feynman's formulation of quantum mechanics can be reproduced as a description of the set of intermediate cardinality. Properties of the set follow directly from the independence of the continuum hypothesis. Six referee…
The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase…
We investigate the relationship between symmetric functions and the representation theory of operads, relative operads, and props. We extend the classical character map for symmetric sequences to relative bisymmetric sequences and symmetric…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
Quantum operations are the most widely used tool in the theory of quantum information processing, representing elementary transformations of quantum states that are composed to form complex quantum circuits. The class of quantum…
We introduce and study the notion of a dual Feynman transform of a modular operad. This generalizes and gives a conceptual explanation of Kontsevich's dual construction producing graph cohomology classes from a contractible differential…
We present a derivation of the Feynman-Vernon approach to open quantum systems in the language of super-operators. We show that this gives a new and more direct derivation of the generating function of energy changes in a bath, or baths.…
The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of…