Jörn Boehnke

 

About Me

I am a postdoctoral fellow at the Center of Mathematical Sciences and Applications at Harvard University, and a Research Affiliate at the Labor and Worklife Program of the Harvard Law School. My research focuses on topics in applied microeconomics, particularly quantitative marketing and empirical industrial organization. I received my Ph.D. in economics from the University of Chicago in 2015.

 

Contact Information

Center of Mathematical Sciences and Applications
Harvard University
20 Garden Street
Cambridge, MA 02138

boehnke@cmsa.fas.harvard.edu
312-985-6376

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Mathematical Physics

  • The Costratified Hilbert Space Structure of an SU(3) Lattice Gauge Model    Abstract
  • The weak and strong interactions are modelled by non-abelian gauge field theory. Perturbation methods are the usual approach in dealing with the corresponding gauge fields. For some fundamental phenomena of gauge theory, however, only non-perturbative methods are applicable. In this work, we analyse a toy model of classical SU(3) lattice gauge theory on a single plaquette.
    At first, we give an introduction of the mathematical foundations and the model is analysed. In order to reduce the gauge symmetry, we subsequently apply the singular Marsden-Weinstein reduction to the phase space of our system, a Hamiltonian G-manifold. This procedure yields the reduced phase space, a symplectic stratified space.
    The reduced phase space is a singular object which is composed of seven different connected components: three zero-dimensional strata, three two-dimensional strata and one four-dimensional stratum. The physical Hilbert space of our system arises by geometric quantisation. We characterise and analyse the Hilbert spaces associated with the singular strata of the SU(3) toy model. The set of these single Hilbert spaces amounts to the structure of a costratified Hilbert space. The results obtained may be regarded as a contribution to non-perturbative quantisation procedures in lattice gauge theory.

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