Lattice Perturbation Theory
By Stefano Capitani. 2002
135 citations recorded by the source corpus.
Abstract The consideration of quantum fields defined on a spacetime lattice provides computational techniques which are invaluable for studying gauge theories nonperturbatively from first principles. Perturbation theory is an essential aspect of computations on the lattice, especially for investigating the behavior of lattice theories near the continuum limit. Particularly important is its role in connecting the outcome of Monte Carlo simulations to continuum physical results. For these matchings the calculation of the renormalization factors of lattice matrix elements is required. In this review we explain the main methods and techniques of lattice perturbation theory, focusing on the cases of Wilson and Ginsparg–Wilson fermions. We will illustrate, among other topics, the peculiarities of perturbative techniques on the lattice, the use of computer codes for the analytic calculations and the computation of lattice integrals. Methods for the computation of 1-loop integrals with very high precision are also discussed. The review presents in a pedagogical fashion also some of the recent developments in this kind of calculations. The coordinate method of Luscher and Weisz is explained in detail. Also discussed are the novelties that Ginsparg–Wilson fermions have brought from the point of view of perturbation theory. Particular emphasis is given throughout the paper to the role of chiral symmetry on the lattice and to the mixing of lattice operators under renormalization. The construction of chiral gauge theories regularized on the lattice, made possible by the recent advances in the understanding of chiral symmetry, is also discussed. Finally, a few detailed examples of lattice perturbative calculations are presented.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/ab31e55cbdaea25982dc2546dad31bb671e4c948
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In Nuclear and High Energy Physics
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Citations in the corpus
- theta dependence of SU(N) gauge theories in the presence of a topological term (2007, background): “absence of mixing among operators in different chiral representations. Thus, the pattern of lattice renormalization becomes greatly simplified with respect to lattice fermions violating chiral symmetry [16,126,304]. Lattice gauge theories with GW fermions have been proved to be renormalizable to all o”
- Transport properties of the quark-gluon plasma (2011, methodology): “alculations of thermal spectral functions and Euclidean correlators are reviewed in section (3.5). Here we describe the results of free field calculations performed in lattice perturbation theory (see [138] for a general review of this subject). The motivation is to quantify the size of discretizatio”
- Extracting parton distribution functions from lattice QCD calculations (2014, unknown): “(1) outlines three necessary steps to identify a good lattice “cross section”: (1) demonstrate that σ̃E(x̃, μ̃ (2), Pz) is UV and IR safe, and the matching coefficients Z’s are calculable in lattice QCD perturbation theory [12], (2) verify that σ̃E(x̃, μ̃ (2), Pz) = σ̃M(x̃, μ̃ (2), Pz), and (3) show”
- Light Hadron Masses from Lattice QCD (2012, background): “While both strong (Wilson, 1974) and weak (see e.g.(Capitani, 2003)) coupling expansions are possible, neither allows for a detailed quantitative understanding of the nonperturbative dynamics of the system.”