Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory

Hartung, Tobias; Nuyens, Dirk; Kuo, Frances Y.; Sloan, Ian H.; Jansen, Karl; Leövey, Hernan

Preprint

PUBDB-2021-04262

Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory

Hartung, T.Extern* ; Jansen, K.DESY* ; Kuo, F. Y. ; Leövey, H. ; Nuyens, D. (Corresponding author) ; Sloan, I. H.

2020

[10.3204/PUBDB-2021-04262]

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Report No.: DESY-20-209; arXiv:2011.05451

Abstract: •Recursive integration strategies independent of the number of integration variables are proposed.•We show lattice based cubature methods that can improve certain integrals occurring in physics.•We show FFT based methods to efficiently calculate certain integrals occurring in physics. High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product structure with low order couplings, motivated by models in lattice gauge theory from quantum field theory. A novel element of this work is the potential benefit in using lattice cubature rules. The group structure within lattice rules combined with the special structure in the physics integrands may allow efficient computations based on Fast Fourier Transforms. Applications to the quantum mechanical rotor and compact U(1) lattice gauge theory in two and three dimensions are considered.

Keyword(s): dimension: 3 ; lattice ; lattice field theory ; Fourier transformation ; field theory ; quantum mechanics ; U(1) ; Lattice cubature ; Quasi-Monte Carlo ; Recursive integration ; Lattice gauge theory ; Quantum physics