Related papers: Automating Renormalization of Quantum Field Theori…
We compute the beta functions for the three gauge couplings of the Standard Model in the minimal subtraction scheme to three loops. We take into account contributions from all sectors of the Standard Model. The calculation is performed…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
This paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension (=rank) five. We review the perturbative renormalization and the computation of the one loop beta function, confirming the asymptotic…
We study Active Model B+, a scalar field theory extending the paradigmatic Model B for equilibrium coexistence through including terms that do not arise from an underlying free energy functional and thus break detailed balance. In the first…
In the Hopf algebra approach of Connes and Kreimer on renormalization of quantum field theory, the renormalization process is views as a special case of the Algebraic Birkhoff Decomposition. We give a differential algebra variation of this…
We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of…
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field…
We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation encompasses cases where hyperlogarithms have rational…
We extend the method of differential renormalization to massive quantum field theories treating in particular $\ph4$-theory and QED. As in the massless case, the method proves to be simple and powerful, and we are able to find, in…
We discuss how renormalisation group equations can be consistently formulated using the algebraic renormalisation framework, in the context of a dimensionally-renormalised chiral field theory in the BMHV scheme, where the BRST symmetry,…
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…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
We briefly review general concepts of renormalization in quantum field theory and discuss their application to solutions of integral equations with singular potentials in the few-nucleon sector of the low-energy effective field theory of…
Path integral quantization of quantum gauge general relativity is discussed in this paper. First, we deduce the generating functional of green function with external fields. Based on this generating functional, the propagators of…
We decompose renormalized Feynman rules according to the scale and angle dependence of amplitudes. We use parametric representations such that the resulting amplitudes can be studied in algebraic geometry.
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-space integrals, they reveal rich analytic structures and…
In recent years a Hopf algebraic structure underlying the process of renormalization in quantum field theory was found. It led to a Birkhoff factorization for (regularized) Hopf algebra characters, i.e. for Feynman rules. In this work we…
The LanHEP program version 3.0 for Feynman rules generation from the Lagrangian is described. It reads the Lagrangian written in a compact form, close to the one used in publications. It means that Lagrangian terms can be written with…
We discuss the current status of our automatic perturbation theory program as applied to Fermilab Fermions. We give an overview of our methods, a discussion of tree level matching, and one loop results for the coefficients of the higher…