Related papers: On $\varepsilon$-factorised bases and pure Feynman…
We study generalised core partitions arising from affine Grassmannian elements in arbitrary Dynkin type. The corresponding notion of size is given by the atomic length in the sense of [CLG22]. In this paper, we first develop the theory for…
Suppose we have two nonequivalent but s-equivalent Lagrange functions, the question arises: are they both equally well fitted for the Feynman quantization procedure or do they lead to two different quantization schemes.
A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable…
Suppose that a transcendental meromorphic function in the plane has finitely many critical values, while its multiple points have bounded multiplicities, and its inverse function has finitely many transcendental singularities. Using the…
We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…
Feynman integrals are very often computed from their differential equations. It is not uncommon that the $\varepsilon$-factorised differential equation contains only dlog-forms with algebraic arguments, where the algebraic part is given by…
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However,…
We argue that the notion of pure sate within Standard Quantum Mechanics is presently applied within the specialized literature in relation to two mutually inconsistent definitions. While the first (operational purity) provides a…
We elucidate the vector space (twisted relative cohomology) that is Poincar\'e dual to the vector space of Feynman integrals (twisted cohomology) in general spacetime dimension. The pairing between these spaces - an algebraic invariant…
We extend the classical Bernstein technique to the setting of integro-differential operators. As a consequence, we provide first and one-sided second derivative estimates for solutions to fractional equations, including some convex fully…
In this talk we discuss the interplay of two elliptic curves, which occur in different sub-sectors of Feynman integrals. We analyse a particular Feynman integral depending on two elliptic curves and derive an associated differential…
Since Feynman integrals (FIs) at higher spacetime dimensions are free of infrared and collinear divergence--and their ultraviolet divergences can be systematically subtracted--this allows us to construct a wide range of locally finite…
Partition- and moment functions for a general (not necessarily Gaussian) functional measure that is perturbed by a Gibbs factor are calculated using generalized Feynman graphs. From the graphical calculus, a new notion of Wick ordering…
The investigation of quantum gravity effects in order to avoid the big bang singularity is a requisite, so that the idea of oscillating universes is introduced as an alternative for standard cosmological model. Therefore, the Friedmann…
Complex-valued Feynman integrals in the imaginary time formalism and zero-temperature limit suffer from particular types of infrared divergences that can not be regulated by integration dimension alone. Related problems leading to…
The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a…
Although axial QED suffers from a gauge anomaly, gauge invariance may be maintained by the addition of a nonlocal counterterm. Such nonlocal conterterms, however, are expected to ruin unitarity of the theory. We explicitly investigate some…
We focus on numerical techniques for expanding 3-loop Feynman integrals with respect to the dimensional regularization parameter $\varepsilon,$ which is related to the space-time dimension as $\nu = 4-2\varepsilon,$ and describes underlying…
Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the…
In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier…