Related papers: The Feynman Legacy
Quantum theory has shown its superiority in enhancing machine learning. However, facilitating quantum theory to enhance graph learning is in its infancy. This survey investigates the current advances in quantum graph learning (QGL) from…
Presented is a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a superbraid. The crossing of world lines is purely quantum in nature,…
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. We provide a…
We prove a neat factorization property of Feynman graphs in covariant perturbation theory. The contribution of the graph to the effective action is written as a product of a massless scalar momentum integral that only depends on the basic…
Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for constructing multivariate intersection numbers relevant to Feynman integrals,…
In this paper, I consider the issue of how two mathematical models of modern physics, the variational principles and the quantum path integral formalism, relate to reality. I assume that the observed phenomena are consistent with the…
As an alternative but unified and more fundamental description for quantum physics, Feynman path integrals generalize the classical action principle to a probabilistic perspective, under which the physical observables' estimation translates…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational/operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity.…
This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I start from a rigorous treatment of a…
Some formal aspects of the Semantic Spacetime graph model are presented, with reference to its use for directed knowledge representations and process modelling. A finite $\gamma(3,4)$ representation is defined to form a closed set of…
Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of…
By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved…
Strongly simulating a quantum circuit, that is, computing an output amplitude, amounts to summing the circuit's Feynman paths, a weighted count over assignments to the Boolean ``path'' variables. The circuit's gates induce correlations…
An analog of Kreimer's coproduct from renormalization of Feynman integrals in quantum field theory, endows an analog of Kontsevich's graph complex with a dg-coalgebra structure. The graph complex is generated by orientation classes of…
The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees…
It is first pointed out that there is a common mathematical model for the universe and the quantum computer. The former is called the histories approach to quantum mechanics and the latter is called measurement based quantum computation.…
In perturbative QED, the approximation is improved by summing more Feynman graphs; in non-perturbative QCD, by refining the lattice. Here we observe that in quantum gravity the two procedures may well be the same. We outline the…
Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…