Quantum Theory of Unstable Elementary Particles

Werner Karl Heisenberg

Victor F. Weisskopf

Eliahu Comay

The paper emphasizes the significance of density of an elementary massive quantum particle.In quantum field theory, a quantum function of an elementary particle takes the form of ( ) ,t ψ r .This kind of function is used for putting the inner product of the corresponding Hilbert space in the form of an appropriate integral, and the inner product of a function with itself depends on the particle's density.Density also affects the multi-particle Fock space, because this space relies on single-particle Hilbert space.This work shows a new reason where a coherent theoretical expression for the density of an elementary particle is required: A theoretical description of experiments that measure the transition of unstable states and the decay of an elementary quantum particle.This new aspect of density strengthens its meaning in quantum theories.The usefulness of this outcome is shown in its application to the decay of the muon and the electroweak's , W Z ± particles.It turns out that the Dirac theory provides a consistent description of the muon decay.In contrast, the electroweak theory fails to explain the decay of the , W Z ± particles.

S. Ali, Luciano Fonda, G. C. Ghirardi

Bent E. Sørensen

Ulf Leonhardt, T. Kiss, Patrik Öhberg

Like classical fluids, quantum gases may suffer from hydrodynamic instabilities. Our paper develops a quantum version of the classical stability analysis in fluids, the Bogoliubov theory of elementary excitations in unstable Bose-Einstein condensates. In unstable condensates the excitation modes have complex frequencies. We derive the normalization conditions for unstable modes such that they can serve in a mode decomposition of the non-condensed component. Furthermore, we develop approximative techniques to determine the spectrum and the mode functions. Finally, we apply our theory to a sonic white hole and find that the spectrum of unstable modes is intrinsically discrete.