Showing papers by "Harald Grosse published in 1992"
TL;DR: In this paper, a non-commutative generalization of the Schwinger model has been proposed in which at scales less than a certain length ϰ the notion of a point does not exist.
117 citations
TL;DR: The integrability of R2•gravity with torsion in two dimensions is traced to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian phase space.
Abstract: The integrability of R2‐gravity with torsion in two dimensions is traced to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian phase space. It may be interpreted as a quadratically deformed iso(2,1)‐algebra with the deformation consisting of the Casimir operators of the undeformed algebra. The locally conserved quantity encountered in the explicit solution is identified as an element of the center of this algebra. Specific contractions of the algebra are related to specific limits of the explicit solutions of this model.
55 citations
TL;DR: In this article, a formalism comprising and extending quasifree second quantization of charged bosons and fermions is presented, and representations of Lie superalgebras are given which are semidirect products of extensions of affine Kac-Moody algesha and the Virasoro algebra.
Abstract: A formalism comprising and extending quasifree second quantization of charged bosons and fermions is presented. The second quantization of one‐particle observables leads to current superalgebras, and a super‐Schwinger term shows up. Anticommuting parameters are introduced in order to construct super‐Bogoliubov transformations mixing bosons and fermions. As an application, representations of Lie superalgebras are given which are semidirect products of extensions of affine Kac–Moody algebras and the Virasoro algebra, and of the super‐Virasoro algebra.
32 citations
TL;DR: In this paper, the quantization of fermions interacting with external fields is discussed and the occurrence of equivalent as well as inequivalent representations of the canonical anticommutation relations is observed.
Abstract: We discuss the quantization of fermions interacting with external fields and observe the occurrence of equivalent as well as inequivalent representations of the canonical anticommutation relations. Implementability of gauge and axial gauge transformations leads to generators which fulfil an algebra of current with a Schwinger term. This term can be written as a cocycle and leads to the boson-fermion correspondence. Transport of a quantum-mechanical system along a closed loop of parameter space may yield a geometric phase. We discuss models for which nonintegrable phase factors are obtained from the adiabatic parallel transport. After second quantization, one obtains, in addition, a Schwinger term. Depending on the type of transformation, a subtle relationship between these two obstructions can occur. We indicate finally how we may transport density matrices along closed loops in parameter space.
12 citations
TL;DR: In this paper, it was shown that if a particle satisfying the Dirac equation is submitted to a potential composed of a pure Coulomb part and of a vector-like perturbation with negative laplacian, the energy levels belonging to a Coulomb multiplet are completely ordered.
6 citations
TL;DR: In this paper, the integrability of gravity with torsion in two dimensions is traced to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian phase space.
Abstract: The integrability of $R^2$-gravity with torsion in two dimensions is traced to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian phase space. It may be interpreted as a quadratically deformed $iso(2,1)$-algebra with the deformation consisting of the Casimir operators of the undeformed algebra. The locally conserved quantity encountered in the explicit solution is identified as an element of the centre of this algebra. Specific contractions of the algebra are related to specific limits of the explicit solutions of this model.
2 citations
TL;DR: In this paper, the dynamical symmetry of R2-gravity with torsion in two dimensions is investigated within Hamiltonian approach, and the symmetry may be interpreted as quadratically deformed iso(2,1)-gauge algebra with the deformation given by the Casimir operators of the undeformed algebra.
Abstract: The dynamical symmetry ofR2-gravity with torsion in two dimensions is investigated within Hamiltonian approach. The symmetry may be interpreted as quadratically deformed iso(2,1)-gauge algebra with the deformation given by the Casimir operators of the undeformed algebra.
1 citations