Compression algorithm for discrete light-cone quantization

TL;DR

This paper adapts a compression algorithm to eigenvectors of light-front Hamiltonians, enabling efficient representation and computation in discrete light-cone quantization for quantum field theories.

Contribution

It introduces a novel application of tensor decomposition and singular value truncation to compress eigenvectors in light-front quantum field theory calculations.

Findings

Efficient eigenvector compression via tensor decomposition.

Application to a model theory demonstrates effectiveness.

Potential for reducing computational complexity in light-cone quantization.

Abstract

We adapt the compression algorithm of Weinstein, Auerbach, and Chandra from eigenvectors of spin lattice Hamiltonians to eigenvectors of light-front field-theoretic Hamiltonians. The latter are approximated by the standard discrete light-cone quantization technique, which provides a matrix representation of the Hamiltonian eigenvalue problem. The eigenvectors are represented as singular value decompositions of two-dimensional arrays, indexed by transverse and longitudinal momenta, and compressed by truncation of the decomposition. The Hamiltonian is represented by a rank-four tensor that is decomposed as a sum of contributions factorized into direct products of separate matrices for transverse and longitudinal interactions. The algorithm is applied to a model theory, to illustrate its use.