Pseudo-Complex Field Theory

Abstract

A new formulation of field theory is presented, based on a pseudo-complex description. An extended group structure is introduced, implying a minimal scalar length, rendering the theory regularized a la Pauli-Villars. Cross sections are calculated for the scattering of an electron at an external Coulomb field and the Compton scattering. Deviations due to a smallest scalar length are determined. The theory also permits a modification of the minimal coupling scheme, resulting in a generalized dispersion relation. A shift of the Greisen-Zatsepin-Kuzmin-limit (GZK) of the cosmic ray spectrum is the consequence.

21 pages, 1 figure

References in corpus (16)

• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• High-Energy Tests of Lorentz Invariance
• Extension of the Cosmic-Ray Energy Spectrum Beyond the Predicted Greisen-Zatsepin-Kuz'min Cutoff
• Cosmic Ray and Neutrino Tests of Special Relativity
• Planck-scale deformation of Lorentz symmetry as a solution to the UHECR and the TeV-$\gamma$ paradoxes
• The geometry of quantum spin networks
• Finslerian spaces possessing local relativistic symmetry
• On a Possibility of Phase Transitions in the Geometric Structure of Space-Time
• Born-Infeld Kinematics
• Constraints on Lorentz Invariance Violating Quantum Gravity and Large Extra Dimensions Models using High Energy Gamma Ray Observations
• Representations of the Canonical group, (the semi-direct product of the Unitary and Weyl-Heisenberg groups), acting as a dynamical group on noncommuting extended phase space
• A class of anisotropic (Finsler-) space-time geometries
• Pauli-Villars regularisation and Born-Infeld kinematics
• Canonically Relativistic Quantum Mechanics: Representations of the Unitary Semidirect Heisenberg Group, U(1,3) *s H(1,3)
• Born-Infeld Kinematics and Correction to the Thomas Precession
• Almost product manifolds as the low energy geometry of Dirichlet branes

Cited by in corpus (9)

• Pseudo-complex General Relativity
• Pseudo-Complex General Relativity: Schwarzschild, Reissner-Nordström and Kerr Solutions
• Axial gravity: a non-perturbative approach to split anomalies
• Geometrical Origin of the Cosmological Constant
• The Robertson-Walker Metric in a Pseudo-Complex General Relativity
• Quintessence and phantom emerging from the split-complex field and the split-quaternion field
• Die Kerr-Metrik in pseudokomplexer Allgemeiner Relativitätstheorie
• Die Reissner-Nordström-Metrik in der Pseudokomplexen Allgemeinen Relativitätstheorie
• Consequences of a minimal length in a pseudo-complex extension of General Relativity