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Resonances, Gamow Vectors and Time Asymmetric Quantum Theory
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Decaying states can be represented by Gamow vectors with an exponential, asymmetric time evolution. This asymmetric evolution is a manifestation of irreversibility on the microphysical level. The Rigged Hilbert Space provides a mathematical theory.
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Operator-frame geometry of non-compact quantum systems with frame-vacuum phase transitions
An operator-frame principal bundle with an Ehresmann connection yields a quantum geometric tensor that remains analytic across vacuum-instability phase transitions where conventional state-space geometry fails.
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