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2003•arXiv (Cornell University)Open access

SU(N) Lattice Gauge Theory on a Single Cube

Jesse Carlsson, Bruce H. J. McKellar

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Abstract

In this paper we study the viability of persuing analytic variational techniques for the calculation of glueball masses in 3+1 dimensional Hamiltonian lattice gauge theory (LGT) in the pure gauge sector. We discuss the major problems presented by a move from 2+1 to 3+1 dimensions and develop analytic techniques to approximate the integrals appearing in 3+1 dimensional variational glueball mass calculations. We calculate $0^{++}$ and $1^{+-}$ glueball masses on a lattice consisting of a single cube. Despite the use of a very simplistic model, promising signs of an approach to asymptotic scaling is displayed by the SU(N) $1^{+-}$ glueball mass as N is increased.

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What this paper is about

In this paper we study the viability of persuing analytic variational techniques for the calculation of glueball masses in 3+1 dimensional Hamiltonian lattice gauge theory (LGT) in the pure gauge sector. We discuss the major problems presented by a move from 2+1 to 3+1 dimensions and develop analytic techniques to approximate the integrals appearing in 3+1 dimensional variational glueball mass calculations. We calculate $0^{++}$ and $1^{+-}$ glueball masses on a lattice consisting of a single cube. Despite the use of a very simplistic model, promising signs of an approach to asymptotic scaling is displayed by the SU(N) $1^{+-}$ glueball mass as N is increased.

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Available abstract

In this paper we study the viability of persuing analytic variational techniques for the calculation of glueball masses in 3+1 dimensional Hamiltonian lattice gauge theory (LGT) in the pure gauge sector. We discuss the major problems presented by a move from 2+1 to 3+1 dimensions and develop analytic techniques to approximate the integrals appearing in 3+1 dimensional variational glueball mass calculations. We calculate $0^{++}$ and $1^{+-}$ glueball masses on a lattice consisting of a single cube. Despite the use of a very simplistic model, promising signs of an approach to asymptotic scaling is displayed by the SU(N) $1^{+-}$ glueball mass as N is increased.

Key concepts: Glueball, Hamiltonian (control theory), Lattice (music), Gauge theory, Hamiltonian lattice gauge theory, Cube (algebra), Lattice gauge theory, Lattice field theory

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