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

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 3×3 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 〈ϕ3〉 of S, whereas the expectation values of the other two eigenvalues, 〈ϕ1〉 and 〈ϕ2〉, and also the component 〈B3〉=g〈ϕ1ϕ2〉 of the magnetic field, remain at their vacuum values.