Volume 46, Issue 5, May 2005
 RELATIVISTIC QUANTUM MECHANICS, FIELD THEORY, BRANE THEORY (INCLUDING STRINGS)


Phase space properties and the short distance structure in quantum field theory
View Description Hide DescriptionThe paper investigates relations between the phase space structure of a quantum field theory (“nuclearity”) and the concept of pointlike localized fields. Given a net of local observable algebras, a phase space condition is introduced that allows a very detailed description of the theory’s field content. An appendix discusses noninteracting models as examples.

Wilson polynomials and the Lorentz transformation properties of the parity operator
View Description Hide DescriptionThe parity operator for a paritysymmetric quantum field theory transforms as an infinite sum of irreducible representations of the homogeneous Lorentz group. These representations are connected with Wilson polynomials.

Cauchy problems of the gauged sigma model
View Description Hide DescriptionWe study the gauged sigma model. In the existence of the global smooth solution will be proved. Furthermore we show that the global weak solutions exist in .

The symmetries of the Dirac–Pauli equation in two and three dimensions
View Description Hide DescriptionWe calculate all symmetries of the Dirac–Pauli equation in twodimensional and threedimensional Euclidean space. Further, we use our results for an investigation of the issue of zero mode degeneracy. We construct explicitly a class of multiple zero modes with their gauge potentials.

The Kähler potential of Abelian Higgs vortices
View Description Hide DescriptionWe calculate the Kähler potential for the Samols metric on the moduli space of Abelian Higgs vortices on , in two different ways. The first uses a scaling argument. The second depends on a variant of the relationship between accessory parameters and the regularized action in Liouville field theory. The Kähler potential on the moduli space of vortices on is also derived, and we are led to a geometrical reinterpretation of these vortices.

Spectral properties of a Dirac operator in the chiral quark soliton model
View Description Hide DescriptionWe consider a Dirac operator acting in the Hilbert space, which describes a Hamiltonian of the chiralquark soliton model in nuclear physics. The mass term of is a matrixvalued function formed out of a function , called a profile function, and a vector field on , which fixes pointwise a direction in the isospin space of the pion. We first show that, under suitable conditions, may be regarded as a generator of a supersymmetry. In this case, the spectra of are symmetric with respect to the origin of . We then identify the essential spectrum of under some condition for . For a class of profile functions , we derive an upper bound for the number of discrete eigenvalues of . Under suitable conditions, we show the existence of a positive energy ground state or a negative energy ground state for a family of scaled deformations of . A symmetry reduction of is also discussed. Finally a unitary transformation of is given, which may have a physical interpretation.

The large Behavior of pseudorelativistic atoms
View Description Hide DescriptionIn this paper we study the large behavior of the ground state energy of atoms with electrons having relativistic kinetic energy . We prove that to leading order in the energy is the same as in the nonrelativistic case, given by (nonrelativistic) Thomas–Fermi theory. For the problem to make sense, we keep the product fixed (here is Sommerfeld’s fine structure constant), and smaller than, or equal to, , which means that as tends to infinity, tends to zero.
