Related papers: The Feynman Legacy
We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It…
Our previous work on quantum mechanics in Hilbert spaces of finite dimensions N is applied to elucidate the deep meaning of Feynman's path integral pointed out by G. Svetlichny. He speculated that the secret of the Feynman path integral may…
Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a…
Expander graphs are fundamental in both computer science and mathematics, with a wide array of applications. With quantum technology reshaping our world, quantum expanders have emerged, finding numerous uses in quantum information theory,…
We consider how vectorial aspects (polarization) of light propagation can be implemented, and its origin, within a Feynman path integral approach. A key part of this scheme is in generalising the standard optical path length integral from a…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
The paper develops the idea that the dynamics of both classical and quantum processes is time reversible. It is shown how this classical analogy allows one to define the measure for the path integral in quantum mechanics.
The Lie algebra of Feynman graphs gives rise to two natural representations, acting as derivations on the commutative Hopf algebra of Feynman graphs, by creating or eliminating subgraphs. Insertions and eliminations do not commute, but…
It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast…
Quantum Graph Neural Networks (QGNNs) represent a novel fusion of quantum computing and Graph Neural Networks (GNNs), aimed at overcoming the computational and scalability challenges inherent in classical GNNs that are powerful tools for…
Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual…
This model is one of the possible geometrical interpretations of Quantum Mechanics where found to every image Path correspondence the geodesic trajectory of classical test particles in the random geometry of the stochastic fields…
In perturbative calculations of quantum mechanical path integrals in curvilinear coordinates, Feynman diagrams involve multiple temporal integrals over products of distributions, which are mathematically undefined. We derive simple rules…
The worldline path integral approach to the Bern-Kosower formalism is reviewed, which offers an alternative to Feynman diagram calculations in quantum field theory. Recent progress in constructing a multiloop generalization of this…
We reformulate quantum computation in terms of Lagrangian (sum-over-path) formalism, in contrast to the widely used Hamiltonian (unitary gate) formulation. We exemplify this formalism with some widely-studied models, including the standard…
Feynman path integrals provide an elegant, classically inspired representation for the quantum propagator and the quantum dynamics, through summing over a huge manifold of all possible paths. From computational and simulational…
In this paper we reformulate in a simpler way the combinatoric core of constructive quantum field theory We define universal rational combinatoric weights for pairs made of a graph and one of its spanning trees. These weights are nothing…
In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much…
Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…