Space-time resolved quantum field theory

Matthias Lienert, Sören Petrat, Roderich Tumulka

Piotr Krekora, Qichang C. Su, R. Grobe

Using space-time resolved solutions in relativistic quantum field theory we analyze the electron-positron pair creation process from vacuum and resolve the Klein-paradox. We show that there are in principle no limitations to the localization length of an electron and demonstrate that its spatial probability density can be much narrower than the Compton wavelength. We also argue that quantum field theory prohibits the occurrence of Zitterbewegung for an electron in contrast to claims found in textbooks.

CHRISTOF WETTERICH

C. Syros, C. Schulz-Mirbach

A quantum time topological space is developed and applied to solve some problems about quantum theory. It is disconnected and satifies specific separation axioms. The degree of disconnectedness of the time-space is a decreasing function of the number of simultaneous or almost simultaneous fundamental interactions. In this topology the U+R Penrose dynamics is implemented by means of a time evolution operator in QFT. This operator is unitary or non-unitary, depending on the type of quantization of the field action-integral. The time evolution operator allows to find the Boltzmann factor in QFT in the above space-time. From an elementary solution of the Liouville equation the quantization of the time follows and the Planck constant has been calculated. Compatibility between time-reversal and irreversibility is spontaneously obtained. The renormalization of the field action-integral follows from quantization. The solution of the measurement problem and the wave function reduction have been deduced in the framework of the Schroedinger theory. The Schroedinger cat's paradoxon and the paradoxon of the wave packet decay have been resolved.

Meinard Kuhlmann, Manfred Stöckler

Piotr Krekora, Qichang C. Su, R. Grobe

Based on space-time-resolved solutions to relativistic quantum field theory we illustrate interpretational difficulties in associating field-theoretical quantities with properties of particles. These difficulties are related to the fact that the definition of the spatial probability density of particles depends on the choice of the Hilbert subspace on which the field operator is projected. We illustrate these problems by analyzing pair-production probabilities and spatial densities for the electron-positron dynamics associated with a spatially localized subcritical potential that is turned on and off in time.