A robust generalization of the Legendre transform for QFT
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 …
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
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 …
stochastic dynamics for correlation splitting, that is, for evaluating the mean value of the …
Efficient method to create superoscillations with generic target behavior
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 …
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 …
homogeneous PDE of the second order in time and infinite order in spatial variable in the …
Integration by differentiation: new proofs, methods and examples
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 …
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 …
\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 …
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 …
to demonstrate that the modern Hopf-algebraic formulation is entirely natural and compatible …
Towards a more algebraic footing for quantum field theory
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 …
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
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 …
time for a homogeneous differential equation which is second-order in time and has …