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We present a field theoretical model of point-form dynamics which exhibits resonance scattering. In particular, we construct point-form Poincare generators explicitly from field operators and show that in the vector spaces for the in-states and out-states (endowed with certain analyticity and topological properties suggested by the structure of the $S$-matrix) these operators integrate to furnish differentiable representations of the causal Poincare semigroup, the semidirect product of the semigroup of spacetime translations into the forward lightcone and the group of Lorentz transformations. We also show that there exists a class of emph{irreducible} representations of the Poincare semigroup defined by a complex mass and a half-integer spin. The complex mass characterizing the representation naturally appears in the construction as the square root of the pole position of the propagator. These representations provide a description of resonances in the same vein as Wigners unitary irreducible representations of the Poincare group provide a description of stable particles.
We deal with the reversible dynamics of coupled quantum and classical systems. Based on a recent proposal by the authors, we exploit the theory of hybrid quantum-classical wavefunctions to devise a closure model for the coupled dynamics in which both
We consider normal forms in `magnetic bottle type Hamiltonians of the form $H=frac{1}{2}(rho^2_rho+omega^2_1rho^2) +frac{1}{2}p^2_z+hot$ (second frequency $omega_2$ equal to zero in the lowest order). Our main results are: i) a novel method to constr
Sinkhorn proved that every entry-wise positive matrix can be made doubly stochastic by multiplying with two diagonal matrices. In this note we prove a recently conjectured analogue for unitary matrices: every unitary can be decomposed into two diagon
When atoms are exposed to intense laser or microwave pulses ~10% of the atoms are found in Rydberg states subsequent to the pulse, even if it is far more intense than required for static field ionization. The optical spectra of the surviving Li atoms
We extend the new perturbation formula of equilibrium states by Hastings to KMS states of general $W^*$-dynamical systems.