Related papers: Automatic generation of Feynman rules in the Schro…
A set of programs is presented for automatically generating and calculating Feynman diagrams. Diagrams are generated with FeynArts, then algebraically simplified using a combination of Mathematica and FORM implemented in the package…
We propose a new symbolic algorithm and a C++ program for generating and calculating supersymmetric Feynman diagrams for ${\cal N}=1$ supersymmetric electrodynamics regularized by higher derivatives in four dimensions. According to standard…
The current algebra generated by fermions coupled to external gauge potentials and metrics on a manifold with boundary is discussed. It is shown that the previous methods, based on index theory arguments and used in the case without…
In this work we make use of proper-time method to evaluate Schwinger effect in the presence of Lorentz-violating background fields. Specifically, we evaluate the one-loop effective Lagrangian in the presence of Lorentz-violating time-like…
Resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods. A general theory is developed, with new and weaker conditions, allowing for perturbations of threshold eigenvalues and relaxed Fermi…
The Feynman integral for the Schroedinger propagator is constructed as a generalized function of white noise, for a linear space of potentials spanned by measures and Laplace transforms of measures, i.e., locally singular as well as rapidly…
Feynman diagrams are calculated by means of their Taylor series expansion in terms of external momenta squared. It is demonstrated in various examples that by the application of conformal mapping and Pad\'{e} approximants, it is possible to…
We derive a counting formula for the eigenvalues of Schr\"odinger operators with self-adjoint boundary conditions on quantum star graphs. More specifically, we develop techniques using Evans functions to reduce full quantum graph eigenvalue…
The paper presents an automatic generator of approximate nonreflecting boundary conditions, analytical and numerical, for scalar wave equations. This generator has two main ingredients. The first one is a set of local Trefftz functions --…
We present the Vector Equivalence technique. This technique allows a simple and systematic calculating of Feynman diagrams involving massive fermions at the matrix element level. As its name suggests, the technique allows two Lorentz…
We introduce a learning method for recovering action parameters in lattice field theories. Our method is based on the minimization of a convex loss function constructed using the Schwinger-Dyson relations. We show that score matching, a…
The dynamically assisted Schwinger effect, the generation of fermion-antifermion pairs in vacuum under a strong, slow-varying field and a weak, high-frequency field, has become a promising avenue to probe the vacuum structure and the…
We present a method for a recursive graphical construction of Feynman diagrams with their correct multiplicities in quantum electrodynamics. The method is first applied to find all diagrams contributing to the vacuum energy from which all…
Landscape functions are a popular tool used to provide upper bounds for eigenvectors of Schr\"odinger operators on domains. We review some known results obtained in the last ten years, unify several approaches used to achieve such bounds,…
We develop a systematic approach to the calculation of scattering cross sections in theories with violation of the Lorentz invariance taking into account the whole information about the theory Lagrangian. As an illustration we derive the…
In this paper we will present very recent results obtained in the ambit of quantum electrodynamics in curved spacetime. We utilize a newly developed non-perturbative heat kernel asymptotic expansion on homogeneous Abelian bundles over…
The present paper provides a method for finding partial differential equations satisfied by the Feynman integrals for diagrams of various types, using the Griffiths theorem on the reduction of poles of rational differential forms. As an…
We derive the (matrix-valued) Feynman rules of the mass perturbation theory and use it for the resummation of the $n$-point functions with the help of the Dyson-Schwinger equations. We use these results for a short review of the complete…
We construct the spectrum generating algebra (SGA) for a free particle in the three dimensional sphere $S^3$ for both, classical and quantum descriptions. In the classical approach, the SGA supplies time-dependent constants of motion that…
Recently we introduced the chirality-flow formalism, a method which builds on the spinor-helicity formalism and is inspired by the color-flow idea in QCD. With this formalism, Feynman rules and diagrams are simplified to the extent that it…