Related papers: Foundations for Relativistic Quantum Theory I: Fey…
We determine closed and compact expressions for the epsilon-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations. This epsilon-expansion is…
We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
A novel functorial relationship in perturbative quantum field theory is pointed out that associates Feynman diagrams (FD) having no external line in one theory ${\bf Th}_1$ with singlet operators in another one ${\bf Th}_2$ having an…
The circular $\beta$ ensemble for $\beta =1,2$ and 4 corresponds to circular orthogonal, unitary and symplectic ensemble respectively as introduced by Dyson. The statistical state of the eigenvalues is then a determinantal point process…
Many interesting physical theories have analytic classical actions. We show how Feynman's path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. We start by introducing a class of…
We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic $L^2$ transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time…
This paper combines the post-Minkowskian expansion of general relativity with the language of intersection theory. Because of the nature of the soft limit inherent to the post-Minkowskian expansion, the intersection-based approach is of…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
By extending Lv-Xin-Zhou's first layer formulas of the $q$-Dyson product, we prove Kadell's conjecture for the Dyson product and show the error of his $q$-analogous conjecture. With the extended formulas we establish a $q$-analog of…
We argue that the variational calculus leading to Euler's equations and Noether's theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in…
A modification of the Fokker action is proposed, which allows one to formulate the covariant quantum theory of the charge system, in which the proper time of each particle serves as the evolution parameter and the particles themselves…
We establish a Wiman-Valiron theory of a polynomial series based on the Askey-Wilson operator $\mathcal{D}_q$, where $q\in(0,1)$. For an entire function $f$ of log-order smaller than $2$, this theory includes (i) an estimate which shows…
We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and…
The Feynman path integral plays a crucial role in quantum mechanics, offering significant insights into the interaction between classical action and propagators, and linking quantum electrodynamics (QED) with Feynman diagrams. However, the…
In this short note we resort to the well known Hellmann-Feynman theorem to prove that some non-relativistic Hamiltonian operators support an infinite number of bound states.
Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of…