The molecular Hamiltonian with two-rotational-angle embedding

Our approach for the derivation of the exact (non-relativistic) translational–rovibronic Hamiltonian, based on the Hamiltonian operator in tensor form, is now extended to cases in which a body-fixed frame is defined via the introduction of two Euler angles (two-rotational-angle embedding). Diatomic molecules and diatom–diatom systems are considered as examples for this general formulation. For comparison, the three-rotational-angle embedding version of the diatom–diatom Hamiltonian is also derived.     

Induced Chern-Simons term of a paired electron state in the quantum Hall system

The induced Chern-Simons term for a paired electron state is calculated in the quantum Hall system by using a field theory on the von Neumann lattice. The coefficient of the Chern-Simons term, which is the Hall conductance, has not only the usual term proportional to a filling factor due to P (parity) & T (time reversal) symmetry breaking but also correction terms due to P & T & U(1) symmetry breaking. The correction term essentially comes from the Nambu-Goldstone mode and depends on an infrared limit. It is shown that the correction term is related to a topological number of a gap function in the momentum space.     

Abelian Higgs model with a Chern-Simons term in 3-dimensional gravitation

We consider the Abelian Higgs model with a Chern-Simons term coupled to the Einstein theory of gravitation in 3-dimensional space-time. We seek a finite solution, regular everywhere, having a stationary, cylindrically symmetric metric. We analyze these field equations and we suggest that such a solution exists. We find that the asymptotic metric of this solution corresponds to that which describes gravitationally a massive particle with spin. We obtain explicitly the expression of the spin. We give only the expression of the mass in the first order with respect to the gravitational coupling constant.     

Combinatorial quantization of the Hamiltonian Chern-Simons theory II

This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [1]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observablesA _CS of the Chern Simons model. It is a *-algebra of functions on the quantum moduli space of flat connections and comes equipped with a positive functional (integration). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly [2], the algebraA _CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group.Supported by Swedish Natural Science Research Council (NFR) under the contract F-FU 06821304 and by the Federal Ministry of Science and Research, Austria.Part of project P8916-PHY of the Fonds zur Förderung der wissenschaftlichen Forschung in ÖsterreichSupported in part by DOE Grant No DE-FG02-88ER25065     

Combinatorial quantization of the Hamiltonian Chern-Simons theory I

Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *- operation and a positive inner product.Supported by Swedish Natural Science Research Council (NFR) under the contract F-FU 06821-304 and by the Federal Ministry of Science and Research, AustriaPart of project P8916-PHY of the Fonds zur Förderung der wissenschaftlichen Forschung in ÖsterreichSupported in part by DOE Grant No DE-FG02-88ER25065;     

Charged vortices in an abelian Higgs model with Chern-Simons term

The existence is shown of charged vortices of finite energy in a (2+1)-dimensional abelian Higgs model with Chern-Simons (C-S) term. Further, lower bounds on the energy and angular momentum of these vortices are obtained. Finally it is shown that the “glueballs” are absent in (2+1)-dimensional QED or QCD with C-S term for any compact gauge group.     

Abelian Chern-Simons term in superfluid 3He-A

We show in this paper that an Abelian Chern-Simons term is induced in (2 + 1)- and (3 + 1)-dimensional rotating superfluid ³He-A and that it plays an important role in its dynamics. Because U(1) symmetry is spontaneously broken in ³He-A, a Goldstone mode appears and contributes to the induced Chern-Simons term. We found that the coefficient of the Chern-Simons term, which is equivalent to Hall conductance, depends on an infra-red cut-off of the Goldstone mode, and that the orbital angular momentum of ³He-A in a cylinder geometry is derived from the Chern-Simons term.     

Some supersymmetric counterparts of the Lorentz Chern-Simons term

We determine some of the terms that must be added to the action of N = 1 supergravity coupled to N = 1 Yang-Mills theory in ten dimensions, if the Lorentz Chern-Simons term is included in the definition of the H_mnp field strength, and supersymmetry is to be preserved. Amongst the new terms, we find that one has squares of the curvature tensors appearing in precisely the linear combinations suggested by other authors. We rewrite the theory in a geometrically suggestive form suitable for interpreting H_mnp as a torsion tensor. We also comment on the relevance of this work to compactification on Calabi-Yau spaces.     

Dimensionally reduced gravitational Chern-Simons term and its kink

When the gravitational Chern-Simons term is reduced from 3 to 2 dimensions, the lower dimensional theory supports a symmetry breaking solution and an associated kink. Kinks in general relativity bear a close relation to flat-space kinks, governed by identical potentials.