Fock space, factorisation and beam splittings: characterisation and applications in the natural sciences [Elektronische Ressource] / vorgelegt von Markus Gäbler

Fock Space, Factorisation and Beam Splittings:Characterisation and Applicationsin the Natural SciencesVon der Fakult at fur Mathematik, Naturwissenschaften und Informatikder Brandenburgischen Technischen Universit at Cottbuszur Erlangung des akademischen GradesDoktor der Naturwissenschaften(Dr. rer. nat.)genehmigte Dissertationvorgelegt vonDiplom-WirtschaftsmathematikerMarkus Gablergeboren am 10. Oktober 1977 in Forst (Lausitz)Gutachter: Prof. Dr. rer. nat. Wolfgang FreudenbergGutachter: Prof. Dr. rer. nat. Karl-Heinz FichtnerGutachter: Prof. Ph.D. Dr.Sc. Masanori OhyaTag der mundlic hen Prufung: 3. November 2010To:The LightThe TruthThe LifeI would like to thank Wolfgang Freudenberg and Prof. K.-H. Fichtner for stating themathematical problem and patiently supervising and accompanying its solution. I amalso grateful to Prof. M. Ohya for the opportunity to present some of these results atthe QBIC 2010 conference and to Prof. L. Accardi for pointing me to useful references.Finally, I thank my family: my parents and in-laws, my wife Rebekka and my childrenJakob, Elias, Emma and Paulina for their encouragement, support, sometimes sacri ceand, above all, giving meaning and variety to my life.M. G ablerContentsList of Figures and Tables 4Introduction 51 The Bosonic Fock Space 91.1 From Classical to Quantum Systems . . . . . . . . . . . . . . . . . . . . 91.2 Point Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.