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We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the considered systems to higher dimensions and more complicated potentials.
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to define Clifford algebras with scalars in arbitrary rings and provides new suggestions for an infinite-dimensional… (More)
A certain SO(7) × U (1) invariant Hamiltonian arising from the standard membrane matrix model via conjugating any of the super-charges by a cubic, octonionic, exponential is proven to have a spectrum covering the whole half-axis R +. The model could be useful in determining a normalizable zero-energy state in the original SO(9) invariant SU (N) matrix model.
We reveal a dynamical SU(2) symmetry in the asymptotic description of supersymmetric matrix models. We also consider a recursive approach for determining the ground state, and point out some additional properties of the model(s).
Simple recursion relations for zero energy states of supersymmetric matrix models are derived by using an unconventional reducible representation for the fermionic degrees of freedom.
A weighted Hilbert space approach to the study of zero-energy states of supersymmetric matrix models is introduced. Applied to a related but technically simpler model, it is shown that the spectrum of the corresponding weighted Hamiltonian simplifies to become purely discrete for sufficient weights. This follows from a bound for the number of negative… (More)
We explicitly construct a (unique) Spin(9)×SU (2) singlet state, φ, involving only the fermionic degrees of freedom of the supersymmetric matrix-model corresponding to reduced 10-dimensional super Yang-Mills theory, resp. supermembranes in 11-dimensional Minkowski space. Any non-singular wavefunction annihilated by the 16 super-charges of SU (2) matrix… (More)
We reveal a dynamical SU(2) symmetry in the asymp-totic description of supersymmetric matrix models. We also consider a recursive approach for determining the ground state, and point out some additional properties of the model(s).
We apply a method of group averaging to states and operators appearing in (truncations of) the Spin(9) × SU(N) invariant matrix models. We find that there is an exact correspondence between the standard supersymmetric Hamiltonian and the Spin(9) average of a relatively simple lower-dimensional model.
In this report for the course " Lie algebras and quantum groups " at KTH I discuss the origin of the Virasoro algebra, give the physical motivation for studying its unitary irreducible highest weight representations, and examine the necessary and sufficient conditions for such representations to exist.