Related papers: On $\varepsilon$-factorised bases and pure Feynman…
A sketch of the affine quantum gravity program illustrates a different perspective on several difficult issues of principle: metric positivity; quantum anomalies; and nonrenormalizability.
The paper concerns the fictitious entanglement of the so-called ``singularities'' in problems, pertaining to quantum gravity, due, in point of fact, to the way we try to employ, in that context, differential geometry, the latter being…
We remark on pseudo-elliptic integrals and on exceptional function fields, namely function fields defined over an infinite base field but nonetheless containing non-trivial units. Our emphasis is on some elementary criteria that must be…
This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future…
In canonical quantum gravity, the formal functional integral includes an integration over the local conformal factor, and we propose to perform the functional integral over this factor before doing any of the other functional integrals. By…
We discuss the notion of causality in Quantum Gravity in the context of sum-over-histories approaches, in the absence therefore of any background time parameter. In the spin foam formulation of Quantum Gravity, we identify the appropriate…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
We explore a new route toward a non-perturbative quantization of gravity based on a purely affine formulation, where the affine connection is the fundamental field and the metric, when it exists, emerges as a derived quantity. Starting from…
The celebrated variational path integral approach to the polaron problem shows remarkable discrepancies with diagrammatic Monte Carlo for the Bogoliubov-Fr\"{o}hlich Hamiltonian which describes an impurity weakly coupled to a Bose condensed…
We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.
The quantum singular value transformation has revolutionised quantum algorithms. By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms. However, polynomials are restricted to definite parity…
It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
We demonstrate that the recently introduced linear equation, reformulating the first Friedmann equation, is the first-order WKB expansion of a quantum cosmological equation. This result shows a deeper underlying connection between General…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can evaluate almost all forms of computation using various…
We study the partition function of N=1 supersymmetric De Rham quantum mechanics on a Riemannian manifold, with a nontrivial chemical potential $\mu$ for the fermions. General arguments suggest that when $\mu \to \infty$ we should get the…
The article is devoted to approximate, global and along curves differentiability of functions over non-archimedean infinite fields with non-trivial valuations. Fields with zero and non-zero characteristics are considered. Spaces of…
We introduce a universality theorem for functionals of measures on partitions which "behave like" the Ewens measure. Various limit theorems for the Ewens measure, most notably the Poisson-Dirichlet limit for the longest parts, the…
In this article, we consider the conjectured relationship between F-purity and log canonicity for polynomials over the complex numbers. We associate to a collection M of n monomials a rational polytope P contained in [0,1]^n. Using P and…