Related papers: The Vector Equivalence Technique
Leveraging the decomposability of the fast Fourier transform, I propose a new class of tensor network that is efficiently contractible and able to represent many-body systems with local entanglement that is greater than the area law.…
In this paper, we present an algorithm to generate the collider events of the GeV-scale oscillating sterile neutrinos with the ready-made event generation tools in the case that the crossing-widths among the nearly-degenerate fermionic…
We develop Wigner - Weyl formalism for the lattice models. For the definiteness we consider Wilson fermions in the presence of $U(1)$ gauge field. The given technique reduces calculation of the two point fermionic Green function to solution…
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…
We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element…
By adopting a methodology proposed by R.J. Adler \etl, we study the interesting analogy between the fermion-gravity and the fermion-electromagnetic interactions in the presence of the minimal Lorentz-violating (LV) fermion coefficients. The…
jQuery.Feyn is a tool for drawing Feynman diagrams with Scalable Vector Graphics (SVG), written in JavaScript and runs in modern browsers. It features predefined propagator styles, vertex types, and symbols. Math formulae can be included as…
Parallel tempering simulates at many quark masses simultaneously, by changing the mass during the simulation while remaining in equilibrium. The algorithm is faster than pure HMC if more than one mass is needed, and works better the smaller…
We discuss a progress in calculation of Feynman integrals which has been done with help of the Differential Equation Method and demonstrate the results for a class of two-point two-loop diagrams.
We present a general formalism for simplifying manipulations of spin indices of massless and massive spinors and vectors in Feynman diagrams. The formalism is based on covariantly reducing the number of field components in the action in…
In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…
We present STR (Star-Triangle Relations), a Mathematica package designed to solve Feynman diagrams by means of the method of uniqueness in any Euclidean spacetime dimension. The method of uniqueness is a powerful technique to solve…
It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…
We study fermionic one-matrix, two-matrix and $D$-dimensional gauge invariant matrix models. In all cases we derive loop equations which unambiguously determine the large-$N$ solution. For the one-matrix case the solution is obtained for an…
In quantum electrodynamics, optical processes are theoretically described by double-sided Feynman diagrams. This formalism is powerful in the case of molecules but proves inappropriate to account for light-matter interactions within complex…
A T-dualized selfdual inspired formulation of massive vector fields coupled to arbitrary matter is generated; subsequently its perturbative series modeling a spontaneously broken gauge theory is analyzed. The new Feynman rules and external…
Using dispersive techniques, it is possible to avoid ultraviolet divergences in the calculation of Feynman diagrams, making subsequent regularization of divergent diagrams unnecessary. We give a simple introduction to the most important…
The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present two different conforming virtual element formulations for the numerical approximation…
The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master…