An Algorithmic Approach to Quantum Field Theory
Massimo Di Pierro
TL;DR
This paper reviews the foundational algorithms for lattice quantum field theory computations, focusing on gauge theories with fermions like QCD, and presents typical results from such simulations.
Contribution
It provides a comprehensive overview of key algorithms and their implementation for lattice QFT, especially in the context of gauge theories with fermions.
Findings
Demonstrates typical lattice QCD results for phenomenological quantities
Details algorithms like Metropolis, Gibbs sampling, and inverter methods
Highlights the importance of these algorithms in QFT computations
Abstract
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 computation, including the Metropolis, the Gibbs sampling, the Minimal Residual, and the Stabilized Biconjugate inverters. The main emphasis is on gauge theories with fermions such as QCD. We also provide examples of typical results from lattice QCD computations for quantities of phenomenological interest.
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