Related papers: Automatically generating Feynman rules for improve…
A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on…
This article builds on Thurston's height functions. His tiling algorithm is reinterpreted using lattice theory and then generalized in order to generate any tiling of a hole-free region. Combined with a natural encoding of tilings by words,…
We provide a new and completely general formalism to compute the effective field theory matching contributions from integrating out massive fields in a manifestly gauge covariant way, at any desired loop order. The formalism is based on old…
FeynRules is a Mathematica-based package which addresses the implementation of particle physics models, which are given in the form of a list of fields, parameters and a Lagrangian, into high-energy physics tools. It calculates the…
We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although…
We consider recent progress in algorithms for generating gauge field configurations that include the dynamical effects of light fermions. We survey what has been achieved in recent state-of-the-art computations, and examine the trade-offs…
We present a simple technique that allows to generate Feynman diagrams for vector models with interactions of order $2n$ and similar models (Gross-Neveu, Thirring model), using a bootstrap equation that uses only the free field value of the…
We provide an algorithm to generate vertices for the Schr\"odinger functional with an abelian background gauge field. The background field has a non-trivial color structure, therefore we mainly focus on a manipulation of the color matrix…
In this paper we present FeynRules, a new Mathematica package that facilitates the implementation of new particle physics models. After the user implements the basic model information (e.g. particle content, parameters and Lagrangian),…
Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and…
Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in…
Applying Feynman diagrammatics to non-fermionic strongly correlated models with local constraints might seem generically impossible for two separate reasons: (i) the necessity to have a Gaussian (non-interacting) limit on top of which the…
The lattice formulation provides a way to regularize, define and compute the Path Integral in a Quantum Field Theory. In this paper we review the theoretical foundations and the most basic algorithms required to implement a typical lattice…
We derive the spherical field formalism for fermions. We find that the spherical field method is free from certain difficulties which complicate lattice calculations, such as fermion doubling, missing axial anomalies, and computational…
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…
We propose a method to improve lattice operators composed of Wilson fermions which allows the removal of all corrections of $O(a)$, including those proportional to the quark mass. It requires off-shell improvement of quark fields and…
We propose a novel, machine-learning-based framework for constructing lattice fermions using Physics-Informed Neural Networks (PINNs). Our approach treats the formulation of the Dirac operator as an optimization problem guided by physical…
I work on a set of Feynman rules that were derived in order to incorporate the constraint of Gauss's law in the perturbation expansion of gauge field theories and calculate the interaction energy of two static sources. The constraint is…
The ability to represent perturbative expansions of interacting quantum field theories in terms of simple diagrammatic rules has revolutionized calculations in particle physics (and elsewhere). Moreover, these rules are readily automated, a…
We propose a lattice field theory formulation which overcomes some fundamental difficulties in realizing exact supersymmetry on the lattice. The Leibniz rule for the difference operator can be recovered by defining a new product on the…