Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-09-17
Phys.Lett.B550:121-127,2002
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, 1 figure
Scientific paper
10.1016/S0370-2693(02)02969-6
A new, recursive method of calculating matrix elements of polynomial hamiltonians is proposed. It is particularly suitable for the recent algebraic studies of the supersymmetric Yang-Mills quantum mechanics in any dimensions. For the D=2 system with the SU(2) gauge group, considered here, the technique gives exact, closed expressions for arbitrary matrix elements of the hamiltonian and of the supersymmetric charge, in the occupation number representation. Subsequent numerical diagonalization provides the spectrum and restricted Witten index of the system with very high precision (taking into account up to $10^5$ quanta). Independently, the exact value of the restricted Witten index is derived analytically for the first time.
Campostrini Massimo
Wosiek Jacek
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