Profile: Martin Schaden

Associate Professor

Faculty
Department of Physics

Research:My research in quantum field theory and atomic physics ranges from non-perturbative aspects of QuantumChromoDynamics (QCD) and semiclassical studies of Casimir effects to the quantitative theoretical description of magnetic resonance experiments in atomic physics. My current research is at the interface of classical and quantum physics with particular emphasis on the following topics.

  • Gauge-fixing as a Topological Quantum Field Theory.
    I proved that the Neuberger- and Gribov- Problems in the gauge fixing of non-abelian gauge theories are related to the Euler characteristic of the gauge group manifold[31,32]. One can partially gauge fix a non-abelian lattice gauge theory to a physically equivalent abelian LGT with the Cartan subgroup as structure group by an equivariant Topological (Lattice) Field Theory of Witten type[37]. Recent progress suggests that one can also localize the remaining compact abelian group up to singular points. It is unclear whether these singularities give important non-perturbative effects.
  • Perturbation theory of SU(N) gauge theory near the Hagedorn transition for large N.
    It was shown that planar diagrams give subleading contributions to the free energy of an SU(N)-gauge theory at large N if one perturbs about a center-symmetric ground state[51]. The confining phase of SU(N) gauge theory may be superheated beyond the first order deconfinement temperature up to a Hagedorn temperature[52,55]. I am investigating a perturbative expansion that is valid on the confining side of this second order Hagedorn transition.
  • Semiclassical and numerical calculation of Casimir effects.
    Progress in the understanding of the renormalization of vacuum energies[53,60] has allowed us to study Casimir effects numerically[62] and in semiclassical approximation[35,40,45,53]. Extensions of the scalar methods to the physically more interesting electromagnetic case[56,67] with realistic materials are currently being investigated. I recently proved [68,69] finiteness of irreducible N-body Casimir energies. With the graduate student Hua Yao Wu I developed a field-theoretic approach to roughness corrections. This research is supported by the National Science Foundation with Grant No: PHY-09-02054. The Grant also supports the postdoctoral work of Dr. K.V. Shajesh.
  • Semiclassical vacuum effects due to black holes and the size of the universe.
    The formation of a black hole from an unstable dust cloud changes the spectrum of the Laplace-Beltrami operator and, in the absence of supersymmetry, changes the quantum vacuum energy of massless fields. This semiclassical contribution to the total mass is significant for miniature black holes of approximately Planck mass and may even stabilize them. Similarly, changes in the vacuum energy due to changes in the size of the universe cannot be absorbed in a (constant) cosmological constant and may have been significant just after the Big-Bang.
  • Edge enhancement and surface effects in magnetic resonance response.
    This is recent theoretical work in conjunction with experiments performed at Rutgers/Newark by the magnetometer group. The observed paramagnetic electron resonance lines of spin polarized Rb-vapor depend sensitively on a number of properties of the enclosing coated glass cells -- in particular on their dimensions and on gross properties of the coating. We developed a quantitative theoretical description [57, 58, 59, 63, 65] that allows the determination of important surface interaction parameters from the observed line shapes.