arXiv subjects
Publications and source records attributed to Maciej Trzetrzelewski.
The hamiltonian formulation of Supersymmetric Yang-Mills quantum mechanics (SYMQM) is discussed. We focus on the Fock space formulation of the models since it is convenient for the numerical analysis, however some novel analytical results are also pointed out.
We construct all vacuum states of $\mathcal{N}=2$ supersymmetric Yang-Mills quantum mechanics (for SU(N) group) and discuss their origin from the SU(N) real cohomology.
We analyze the $N \to \infty $ limit of supersymmetric Yang-Mills quantum mechanics (SYMQM) in two spacetime dimensions. To do so we introduce a particular class of SU(N) invariant polynomials and give the solutions of 2D SYMQM in terms of them. We conclude that in this limit the system is not fully described by the single trace operators $Tr({a^{\dagger}}^n)$ since there are other, bilinear operators $Tr^n(a^{\dagger}a^{\dagger})$ that play a crucial role when the hamiltonian is free.
We present the hamiltonian study of super Yang-Mills quantum mechanics (SYMQM). The recently introduced method based on Fock space representation allows to analyze SYMQM numerically. The detailed analysis for SYMQM in two dimensions for SU(3) group is given.
We present a systematic method to express all $su(N)$ invariant tensors in terms of forests i.e. products of tree tensors.
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between discrete and continuous spectrum is stressed. In particular a new scaling low for nonlocalized states is obtained. Exact solutions for several cases as well as general properties of the method are given.