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Quantum Field Theory: Motivating the Axiom of MicrocausalityWright, Jessey January 2012 (has links)
Axiomatic quantum field theory is one approach to the project of merging the special theory of relativity with that of ordinary quantum mechanics. The project begins with the postulation of a set of axioms. Axioms should be motivated by reasonable physical principles in a way that illustrates how a given axiom is true. Motivations are often grounded in the principles of the parent theories: ordinary quantum mechanics or the theory of special relativity. Amongst the set of axioms first proposed by Haag and Kastler in 1963 is the axiom of microcausality. Microcausality requires the observables of regions at space-like separation to commute. This thesis seeks to answer the question ‘What principles from the special theory of relativity or ordinary quantum mechanics motivate, or justify, accepting microcausality as an axiom?’ The first chapter will provide the necessary background to investigate this question and the second chapter will undertake that investigation. In conclusion, microcausality cannot be well-motivated by individual principles rooted in the special theory of relativity or ordinary quantum mechanics.
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Quantum Field Theory: Motivating the Axiom of MicrocausalityWright, Jessey January 2012 (has links)
Axiomatic quantum field theory is one approach to the project of merging the special theory of relativity with that of ordinary quantum mechanics. The project begins with the postulation of a set of axioms. Axioms should be motivated by reasonable physical principles in a way that illustrates how a given axiom is true. Motivations are often grounded in the principles of the parent theories: ordinary quantum mechanics or the theory of special relativity. Amongst the set of axioms first proposed by Haag and Kastler in 1963 is the axiom of microcausality. Microcausality requires the observables of regions at space-like separation to commute. This thesis seeks to answer the question ‘What principles from the special theory of relativity or ordinary quantum mechanics motivate, or justify, accepting microcausality as an axiom?’ The first chapter will provide the necessary background to investigate this question and the second chapter will undertake that investigation. In conclusion, microcausality cannot be well-motivated by individual principles rooted in the special theory of relativity or ordinary quantum mechanics.
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Haag's theorem in renormalisable quantum field theoriesKlaczynski, Lutz 04 March 2016 (has links)
Wir betrachten eine Reihe von Trivialitäts- resultaten und No-Go-Theoremen aus der Axiomatischen Quantenfeldtheorie. Von besonderem Interesse ist Haags Theorem. Im Wesentlichen sagt es aus, dass der unitäre Intertwiner des Wechselwirkungsbildes nicht existiert oder trivial ist. Als wichtigste Voraussetzung von Haags Theorem arbeiten wir die unitäre Äquivalenz heraus und unterziehen die kanonische Störungstheorie skalarer Felder einer Kritik um zu argumentieren, dass die kanonisch renormierte Quantenfeldtheorie Haags Theorem umgeht, da sie genau diese Bedingung nicht erfüllt. Der Hopfalgebraische Zugang zur perturbativen Quantenfeldtheorie bietet die Möglichkeit, Dyson-Schwinger-und Renormierungsgruppengleichungen mathematisch sauber herzuleiten, wenn auch mit rein kombinatorischem Ausgangspunkt. Wir präsentieren eine Beschreibung dieser Methode und diskutieren eine gewöhnliche Differentialgleichung für die anomale Dimension des Photons. Eine Spielzeugmodellversion dieser Gleichung lässt sich exakt lösen; ihre Lösung weist eine interessante nichtstörunsgtheoretische Eigenschaft auf, deren Auswirkungen auf die laufende Kopplung und die Selbstenergie des Photons wir untersuchen. Solche nichtperturbativen Beiträge mögen die Existenz eines Landau-Pols ausschliessen, ein Sachverhalt, den wir ebenfalls diskutieren. Unter der Arbeitshypothese, dass die anomale Dimension eines Quantenfeldes in die Klasse der resurgenten Funktionen fällt, studieren wir, welche Bedingungen die Dyson-Schwinger-und Renormierungsgruppengleichungen an ihre Transreihe stellen. Wir stellen fest, dass diese unter bestimmten Bedingungen kodieren, wie der perturbative Sektor den nichtperturbativen vollständig determiniert. / We review a package of triviality results and no-go theorems in axiomatic quantum field theory. Of particular interest is Haag''s theorem. It essentially says that the unitary intertwiner of the interaction picture does not exist unless it is trivial. We single out unitary equivalence as the most salient provision of Haag''s theorem and critique canonical perturbation theory for scalar fields to argue that canonically renormalised quantum field theory bypasses Haag''s theorem by violating this very assumption. The Hopf-algebraic approach to perturbative quantum field theory allows us to derive Dyson-Schwinger equations and the Callan-Symanzik equation in a mathematically sound way, albeit starting with a purely combinatorial setting. We present a pedagogical account of this method and discuss an ordinary differential equation for the anomalous dimension of the photon. A toy model version of this equation can be solved exactly; its solution exhibits an interesting nonperturbative feature whose effect on the running coupling and the self-energy of the photon we investigate. Such nonperturbative contributions may exclude the existence of a Landau pole, an issue that we also discuss. On the working hypothesis that the anomalous dimension of a quantum field falls into the class of resurgent functions, we study what conditions Dyson-Schwinger and renormalisation group equations impose on its resurgent transseries. We find that under certain conditions, they encode how the perturbative sector determines the nonperturbative one completely.
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On the Construction of Quantum Field Theories with Factorizing S-Matrices / Über die Konstruktion von quantenfeldtheoretischen Modellen mit faktorisierenden S-MatrizenLechner, Gandalf 24 May 2006 (has links)
No description available.
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Spectral theory of automorphism groups and particle structures in quantum field theory / Die Spektraltheorie von Automorphismengruppen und Teilchenstrukturen in der QuantenfeldtheorieDybalski, Wojciech Jan 15 December 2008 (has links)
No description available.
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