Complex symmetric forms and the emergence of Jordan blocks in analytically extended quantum theory

Abstract

The justification and rationale for analytically continuing quantum mechanics into the complex plane are recognized and briefly discussed. This extension is described by a complex symmetric representation, which is derived and demonstrated to include general Jordan block forms of Segrè characteristics larger than one. Various applications in physics and chemistry, in which this extension appears necessary, are pointed out.

Keywords:

• analytic continuation
• complex symmetry
• resonances
• Jordan block
• Segrè characteristic
• coherent-dissipative structure
• relativity

2000 AMS Subject Classification :

• 83A05

Acknowledgements

The author is indebted to Prof. Bruce Wade and Prof. Jésus Vigo-Aguiar for generous support and hospitality. Supported in part by the Swedish Foundation for Strategic Research.