SU(2) Yang-Mills quantum mechanics of spatially constant fields

Abstract

As a first step towards a strong coupling expansion of Yang-Mills theory, the SU(2) Yang-Mills quantum mechanics of spatially constant gauge fields is investigated in the symmetric gauge, with the six physical fields represented in terms of a positive definite symmetric (3 x 3) matrix S. Representing the eigenvalues of S in terms of elementary symmetric polynomials, the eigenstates of the corresponding harmonic oscillator problem can be calculated analytically and used as orthonormal basis of trial states for a variational calculation of the Yang-Mills quantum mechanics. In this way high precision results are obtained in a very effective way for the lowest eigenstates in the spin-0 sector as well as for higher spin. Furthermore I find, that practically all excitation energy of the eigenstates, independently of whether it is a vibrational or a rotational excitation, leads to an increase of the expectation value of the largest eigenvalue <ϕ_3>, whereas the expectation values of the other two eigenvalues, <ϕ_1> and <ϕ_2>, and also the component <B_3> = g<ϕ_1ϕ_2> of the magnetic field, remain at their vacuum values.

7 pages, 4 figures

References in corpus (6)

• Hamiltonian reduction of SU(2) Dirac-Yang-Mills mechanics
• Unconstrained Hamiltonian Formulation of SU(2) Gluodynamics
• Unconstrained SU(2) Yang-Mills Theory with Topological Term in the Long-Wavelength Approximation
• On the Groundstate of Yang-Mills Quantum Mechanics
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Cited by in corpus (4)

• Expansion of the Yang-Mills Hamiltonian in spatial derivatives and glueball spectrum
• SU(2) Dirac-Yang-Mills quantum mechanics of spatially constant quark and gluon fields
• Unconstrained Hamiltonian formulation of low energy QCD
• A novel strong coupling expansion of the QCD Hamiltonian