Related papers: Automating Renormalization of Quantum Field Theori…
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the…
We introduce the multi-scale entanglement renormalization ansatz (MERA), an efficient representation of certain quantum many-body states on a D-dimensional lattice. Equivalent to a quantum circuit with logarithmic depth and distinctive…
We compute the two-loop $\beta$-function of scalar and spinorial quantum electrodynamics as well as pure Yang-Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using Implicit…
Using an infinitesimal approach, this work addresses the renormalization problem to deal with the ultraviolet divergences arising in quantum field theory. Under the assumption that the action has already been renormalized to yield an…
A method to calculate two-loop self-energy diagrams of the Standard Model is demonstrated. A direct physical application is the calculation of the two-loop electroweak contribution to the anomalous magnetic moment of the muon…
The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making…
We present a new Mathematica package that provides a platform to perform multi-loop computations. ANATAR integrates several existing tools designed for higher-order computations. In particular, it uses QGRAF to generate Feynman diagrams and…
We present a method to evaluate numerically Feynman diagrams directly from their Feynman parameters representation. We first disentangle overlapping singularities using sector decomposition. Threshold singularities are treated with an…
We consider the perturbative renormalisation of the $\Phi^4_d$ model from Euclidean Quantum Field Theory for any, possibly non-integer dimension $d<4$. The so-called BPHZ renormalisation, named after Bogoliubov, Parasiuk, Hepp and…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
We generalize the concept of Borel resummability and renormalons to a quantum field theory with an arbitrary number of fields and couplings, starting from the known notion based on the running coupling constants. An approach to identify the…
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…
We consider one-loop tensor and scalar integrals, which occur in a massless quantum field theory and we report on the implementation into a numerical program of an algorithm for the automated computation of these one-loop integrals. The…
We summarize recent results connecting multiloop Feynman diagram calculations to different parts of mathematics, with special attention given to the Hopf algebra structure of renormalization.
In this work, we employ a field-theoretic renormalization group approach to study a paradigmatic model of directed percolation. We focus on the perturbative calculation of the equation of state, extending the analysis to the three-loop…
Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with…
Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory. They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically…
In the very near future the first data from LHC will be available. The searches for the Higgs boson and for new physics will require precise predictions both for the signal and the background processes. Tree level calculations typically…