Correlations and the relativistic structure of the nucleon self-energy

A key point of Dirac Brueckner Hartree Fock calculations for nuclear matter is to decompose the self energy of the nucleons into Lorentz scalar and vector components. A new method is introduced for this decomposition. It is based on the dependence of the single-particle energy on the small component in the Dirac spinors used to calculate the matrix elements of the underlying NN interaction. The resulting Dirac components of the self-energy depend on the momentum of the nucleons. At densities around and below the nuclear matter saturation density this momentum dependence is dominated by the non-locality of the Brueckner G matrix. At higher densities these correlation effects are suppressed and the momentum dependence due to the Fock exchange terms is getting more important. Differences between symmetric nuclear matter and neutron matter are discussed. Various versions of the Bonn potential are considered.Comment: 18 pages LaTeX, including 6 figure

A second order differential equation for the relativistic description of electrons and photons

A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with a space-time algebra made up of Pauli matrices and hyperbolic numbers. The algebra is used to construct the differential operator of the electron as well as the photon wave equation. The properties of free electron and photon states related to this wave equation are investigated. Interactions are introduced as usual with the minimal substitution of the momentum operators. It can be shown that the new wave equation is equivalent to the quadratic form of the Dirac equation. Furthermore, the Maxwell equations can be derived from the corresponding wave equation for photons.Comment: Reverted preprint to initial version of 1999. Most of the content has been published under the new title "Relativistic quantum physics with hyperbolic numbers". However, interesting parts like the second quantization of fermion fields within a Klein-Gordon theory, which is only possible with the help of hyperbolic or bicomplex numbers, dropped out of the revised versio

Gravitoelectromagnetism in a complex Clifford algebra

A linear vector model of gravitation is introduced in the context of quantum physics as a generalization of electromagnetism. The gravitoelectromagnetic gauge symmetry corresponds to a hyperbolic unitary extension of the usual complex phase symmetry of electromagnetism. The reversed sign for the gravitational coupling is obtained by means of the pseudoscalar of the underlying complex Clifford algebra.Comment: 10 pages Latex2

Spinors in the hyperbolic algebra

The three-dimensional universal complex Clifford algebra is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.Comment: 9 pages Latex2

The Poincare mass operator in terms of a hyperbolic algebra

The Poincare mass operator can be represented in terms of a Cl(3,0) Clifford algebra. With this representation the quadratic Dirac equation and the Maxwell equations can be derived from the same mathematical structure.Comment: 5 pages Latex2