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Low-energy spectrum of SU(3) Yang-Mills Quantum Mechanics of spatially constant gluon fields
Wednesday, 13 November, 2019 - 11:00
The SU(3) Yang-Mills Quantum Mechanics of spatially constant gluon fields is considered in the unconstrained Hamiltonian approach. The exact implementation of the non-Abelian Gauss-law constraints is carried out in a new algebraic gauge with a simple but non-trivial Faddeev-Popov operator. The low-energy eigensystem of the obtained physical Hamiltonian can be calculated (in principle with arbitrary high precision) using the orthonormal basis of eigenstates of the corresponding harmonic oscillator problem with the same non-trivial Jacobian (only replacing the magnetic potential by the multidimensional harmonic oscillator potential). This turns out to be integrable and its eigenstates to be made out of orthogonal polynomials of the 35 components of seven elementary spatial tensors. The calculations in this work have been carried out in all sectors JPC up to spin J=11, and up to polynomial order 10 for even and 11 for odd parity. The low-energy eigensystem of the physical Hamiltonian of SU(3) Yang-Mills Quantum Mechanics is found to converge nicely when truncating at higher and higher polynomial order (equivalent to increasing the resolution in functional space). Our results are in good agreement with the results of Weisz and Zieman (1986) using the constrained Hamiltonian approach. We find excellent agreement in the 0++ and 2++ sectors, much more accurate values in other sectors considered by them, e.g. in the 1-- and 3-- sectors, and quite accurate "new results" for the sectors not considered by them, e.g. 2--, 4--, 5--, 3++.