Spin and Rotation in General Relativity

Rapporteur's Introduction to the GT8 session of the Ninth Marcel Grossmann Meeting (Rome, 2000); to appear in the Proceedings.Comment: LaTeX file, no figures, 15 page

A Gauge field Induced by the Global Gauge Invariance of Action Integral

As a general rule, it is considered that the global gauge invariance of an action integral does not cause the occurrence of gauge field. However, in this paper we demonstrate that when the so-called localized assumption is excluded, the gauge field will be induced by the global gauge invariance of the action integral. An example is given to support this conclusion.Comment: 13 pages. Some typing errors are corrected and the format is update

Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations

Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group. This paper extends the geometrical foundation for Pandres' theory by developing an appropriate covariant derivative which is covariant under all local Lorentz (frame) transformations, including complex Lorentz transformations, as well as conservative transformations. After defining this extended covariant derivative, an appropriate Lagrangian and its resulting field equations are derived. As in Pandres' theory, these field equations result in a stress-energy tensor that has terms which may automatically represent the electroweak field. Finally, the theory is extended to include 2-spinors and 4-spinors.Comment: Aug 25 replacement has corrected margin width

An assessment of Evans' unified field theory II

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans' theory and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve it with respect to the torsion. It turns out that for all physical cases the torsion vanishes and the first field equation, together with Evans' unified field theory, collapses to an ordinary Einstein equation.Comment: 11 pages of late

A Perspective on Regularization and Curvature

A global connection on the Connes Marcolli renormalization bundle relates $\beta$-functions of a class of regularization schemes by gauge transformations, as well as local solutions to $\beta$-functions over curved space-time.Comment: As publishe

Multiple electromagnetic electron positron pair production in relativistic heavy ion collisions

We calculate the cross sections for the production of one and more electron-positron pairs due to the strong electromagnetic fields in relativistic heavy ion collisions. Using the generating functional of fermions in an external field we derive the N-pair amplitude. Neglecting the antisymmetrisation in the final state we find that the total probability to produce N pairs is a Poisson distribution. We calculate total cross sections for the production of one pair in lowest order and also include higher-order corrections from the Poisson distribution up to third order. Furthermore we calculate cross sections for the production of up to five pairs including corrections from the Poisson distribution.Comment: 13 pages REVTeX, 4 Postscript figures, This and related papers may also be obtained from http://www.phys.washington.edu/~hencken

Exactly solvable path integral for open cavities in terms of quasinormal modes

We evaluate the finite-temperature Euclidean phase-space path integral for the generating functional of a scalar field inside a leaky cavity. Provided the source is confined to the cavity, one can first of all integrate out the fields on the outside to obtain an effective action for the cavity alone. Subsequently, one uses an expansion of the cavity field in terms of its quasinormal modes (QNMs)-the exact, exponentially damped eigenstates of the classical evolution operator, which previously have been shown to be complete for a large class of models. Dissipation causes the effective cavity action to be nondiagonal in the QNM basis. The inversion of this action matrix inherent in the Gaussian path integral to obtain the generating functional is therefore nontrivial, but can be accomplished by invoking a novel QNM sum rule. The results are consistent with those obtained previously using canonical quantization.Comment: REVTeX, 26 pages, submitted to Phys. Rev.

Particle and Antiparticle sectors in DSR1 and kappa-Minkowski space-time

In this paper we explore the problem of antiparticles in DSR1 and $\kappa$-Minkowski space-time following three different approaches inspired by the Lorentz invariant case: a) the dispersion relation, b) the Dirac equation in space-time and c) the Dirac equation in momentum space. We find that it is possible to define a map $S_{dsr}$ which gives the antiparticle sector from the negative frequency solutions of the wave equation. In $\kappa$-Poincar\'e, the corresponding map $S_{kp}$ is the antipodal mapping, which is different from $S_{dsr}$. The difference is related to the composition law, which is crucial to define the multiparticle sector of the theory. This discussion permits to show that the energy of the antiparticle in DSR is the positive root of the dispersion relation, which is consistent with phenomenological approaches.Comment: 15 pages, no figures, some references added, typos correcte

Dynamically avoiding fine-tuning the cosmological constant: the "Relaxed Universe"

We demonstrate that there exists a large class of action functionals of the scalar curvature and of the Gauss-Bonnet invariant which are able to relax dynamically a large cosmological constant (CC), whatever it be its starting value in the early universe. Hence, it is possible to understand, without fine-tuning, the very small current value of the CC as compared to its theoretically expected large value in quantum field theory and string theory. In our framework, this relaxation appears as a pure gravitational effect, where no ad hoc scalar fields are needed. The action involves a positive power of a characteristic mass parameter, M, whose value can be, interestingly enough, of the order of a typical particle physics mass of the Standard Model of the strong and electroweak interactions or extensions thereof, including the neutrino mass. The model universe emerging from this scenario (the "Relaxed Universe") falls within the class of the so-called LXCDM models of the cosmic evolution. Therefore, there is a "cosmon" entity X (represented by an effective object, not a field), which in this case is generated by the effective functional and is responsible for the dynamical adjustment of the cosmological constant. This model universe successfully mimics the essential past epochs of the standard (or "concordance") cosmological model (LCDM). Furthermore, it provides interesting clues to the coincidence problem and it may even connect naturally with primordial inflation.Comment: LaTeX, 63 pp, 8 figures. Extended discussion. Version accepted in JCA