A robust generalization of the Legendre transform for QFT

DM Jackson, A Kempf, AH Morales - Journal of Physics A …, 2017 - iopscience.iop.org
Although perturbative quantum field theory is highly successful, it possesses a number of
well-known analytic problems, from ultraviolet and infrared divergencies to the divergence of …

Extensions of the Novikov–Furutsu theorem, obtained by using Volterra functional calculus

GA Athanassoulis, KI Mamis - Physica Scripta, 2019 - iopscience.iop.org
Abstract The Novikov–Furutsu (NF) theorem is a well-known mathematical tool, used in
stochastic dynamics for correlation splitting, that is, for evaluating the mean value of the …

Efficient method to create superoscillations with generic target behavior

B Šoda, A Kempf - Quantum Studies: Mathematics and Foundations, 2020 - Springer
We introduce a new numerically stable method for constructing superoscillatory wave forms
in an arbitrary number of dimensions. The method allows the construction of superoscillatory …

The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem

Z Nytrebych, O Malanchuk - Demonstratio Mathematica, 2019 - degruyter.com
The solvability of the problem with local nonhomogeneous two-point in time conditions for a
homogeneous PDE of the second order in time and infinite order in spatial variable in the …

Integration by differentiation: new proofs, methods and examples

D Jia, E Tang, A Kempf - Journal of Physics A: Mathematical and …, 2017 - iopscience.iop.org
Recently, new methods were introduced which allow one to solve ordinary integrals by
performing only derivatives. These studies were originally motivated by the difficulties of the …

Evaluating improper integrals using Laplace transforms

RA Gordon, SM Stewart - 2023 - projecteuclid.org
We discuss and verify an interesting method for evaluating certain integrals of the form
\int_0^∞f(t)\,dt using Laplace transforms. Careful proofs are given to justify the method and …

Probabilistic responses of dynamical systems subjected to Gaussian coloured noise excitation. Foundations of a non-Markovian theory

KI Mamis - arxiv preprint arxiv:2006.04773, 2020 - arxiv.org
The topic of this PhD thesis is the derivation of evolution equations for probability density
functions (pdfs) describing the non-Markovian response to dynamical systems under …

Hopf Algebra Theory of Renormalization

PH Balduf - … Equations, Renormalization Conditions, and the Hopf …, 2024 - Springer
The second chapter is a detailed account of renormalization theory. The goal is, in particular,
to demonstrate that the modern Hopf-algebraic formulation is entirely natural and compatible …

Towards a more algebraic footing for quantum field theory

DM Jackson, A Kempf, AH Morales - Journal of Physics A …, 2021 - iopscience.iop.org
The predictions of the standard model of particle physics are highly successful in spite of the
fact that several parts of the underlying quantum field theoretical framework are analytically …

Differential-symbol method of constructing the quasipolynomial solutions of a two-point problem for a partial differential equation

ZM Nytrebych, VS Il'kiv, PY Pukach… - Journal of Mathematical …, 2019 - Springer
We studied the solvability of a problem with local inhomogeneous conditions two-point in
time for a homogeneous differential equation which is second-order in time and has …