Douglas Lundholm

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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)
We consider a thought experiment where two distinct species of 2D particles in a perpendicular magnetic field interact via repulsive potentials. If the magnetic field and the interactions are strong enough, one type of particles forms a Laughlin state and the other type couples to Laughlin quasiholes. We show that, in this situation, the motion of the(More)
Anyons are 2D or 1D quantum particles with intermediate statistics, interpolating between bosons and fermions. We study the ground state of a large number N of 2D anyons, in a scaling limit where the statistics parameter α is proportional to N when N → ∞. This means that the statistics is seen as a “perturbation from the bosonic end”. We model this(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 YangMills theory, resp. supermembranes in 11-dimensional Minkowski space. Any non-singular wavefunction annihilated by the 16 supercharges of SU(2) matrix theory(More)
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)