From massive gravity to modified general relativity II

We continue our investigation of massive gravity in the massless limit of vanishing graviton mass. From gauge invariance we derive the most general coupling between scalar matter and gravity. We get further couplings beside the standard coupling to the energy-momentum tensor. On the classical level this leads to a further modification of general relativity.Comment: 12 pages, no figur

Smeared and unsmeared chiral vertex operators

We prove unboundedness and boundedness of the unsmeared and smeared chiral vertex operators, respectively. We use elementary methods in bosonic Fock space, only. Possible applications to conformal two - dimensional quantum field theory, perturbation thereof, and to the perturbative construction of the sine-Gordon model by the Epstein-Glaser method are discussed. From another point of view the results of this paper can be looked at as a first step towards a Hilbert space interpretation of vertex operator algebras.Comment: 18 pages, latex, no figure

Gauge invariance of massless QED

A simple general proof of gauge invariance in QED is given in the framework of causal perturbation theory. It illustrates a method which can also be used in non-abelian gauge theories.Comment: 7 pages, TEX-file, Zuerich University Preprint ZU-TH-33/199

Electron-positron pair production in the external electromagnetic field of colliding relativistic heavy ions

The results concerning the $e^+e^-$ production in peripheral highly relativistic heavy-ion collisions presented in a recent paper by Baltz {\em{et al.}} are rederived in a very straightforward manner. It is shown that the solution of the Dirac equation directly leads to the multiplicity, i.e. to the total number of electron-positron pairs produced by the electromagnetic field of the ions, whereas the calculation of the single pair production probability is much more involved. A critical observation concerns the unsolved problem of seemingly absent Coulomb corrections (Bethe-Maximon corrections) in pair production cross sections. It is shown that neither the inclusion of the vacuum-vacuum amplitude nor the correct interpretation of the solution of the Dirac equation concerning the pair multiplicity is able the explain (from a fundamental point of view) the absence of Coulomb corrections. Therefore the contradiction has to be accounted to the treatment of the high energy limit.Comment: 6 pages, 4 Postscript figures, uses svjour.cls/svepj.cl

Gauge Independence of the S-Matrix in the Causal Approach

The gauge dependence of the time-ordered products for Yang-Mills theories is analysed in perturbation theory by means of the causal method of Epstein and Glaser together with perturbative gauge invariance. This approach allows a simple inductive proof of the gauge independence of the physical S-matrix.Comment: 19 pages, latex, 1 figur