A modified Cayley transform for SU(3) molecular dynamics simulations

2024/06/17 by Kevin Schäfers, Schäfers, Kevin, Mike Peardon +3
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2406.11337

Abstract

We propose a modification to the Cayley transform that defines a suitable local parameterization for the special unitary group SU(3). The new mapping is used to construct splitting methods for separable Hamiltonian systems whose phase space is the cotangent bundle of SU(3) or, more general, SU(3)^N, N ∈ ℕ. Special attention is given to the hybrid Monte Carlo algorithm for gauge field generation in lattice quantum chromodynamics. We show that the use of the modified Cayley transform instead of the matrix exponential neither affects the time-reversibility nor the volume-preservation of the splitting method. Furthermore, the advantages and disadvantages of the Cayley-based algorithms are discussed and illustrated in pure gauge field simulations.

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