### Abstract

The states (Schrödinger picture) and observables (Heisenberg picture) in the standard quantum theory evolve symmetrically in time, given by the unitary group with time extending over - < t < +. This time evolution is a mathematical consequence of the Hilbert space boundary condition for the dynamical differential equations. However, this unitary group evolution violates causality. Moreover, it does not solve an old puzzle of Wigner: How does one describe excited states of atoms which decay exponentially, and how is their lifetime τ related to the Lorentzian width Γ? These question can be answered if one replaces the Hilbert space boundary condition by new, Hardy space boundary conditions. These Hardy space boundary conditions allow for a distinction between states (prepared by a preparation apparatus) and observables (detected by a registration apparatus). The new Hardy space quantum theory is time asymmetric, i.e, the time evolution is given by the semigroup with t0 ≤ t < +, which predicts a finite «beginning of time» t0, where t0 is the ensemble of time at which each individual system has been prepared. The Hardy space axiom also leads to the new prediction: the width Γ and the lifetime τ are exactly related by τ/γ.

Original language | English (US) |
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Article number | 012016 |

Journal | Journal of Physics: Conference Series |

Volume | 428 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2013 |

Externally published | Yes |

Event | 21st International Symposium on the Jahn-Teller Effect 2012 - Tsukuba, Japan Duration: Aug 26 2012 → Aug 31 2012 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Journal of Physics: Conference Series*,

*428*(1), [012016]. https://doi.org/10.1088/1742-6596/428/1/012016