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On P(φ)_2 interactions at positive temperature

Robl, Florian 2012. On P(φ)_2 interactions at positive temperature. PhD Thesis, Cardiff University.
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The Schwinger functions of the thermal P (φ)2 model on the real line and the vacuum P (φ)2 model on the circle are equal up to interpretation of their time and space coordinates. This is called Nelson symmetry. In the present work this correspondence is exploited to construct and prove results for the thermal P (φ)2 model. The results are existence of the thermal Wightman functions, the relativistic KMS condition, verification of the Wightman axioms and spatial exponential decay. A H ̈lder inequality for general KMS states is proven, employing non-commutative o Lp -spaces. This inequality is key in the proof of the existence of the thermal Wightman functions. For the vacuum P (φ)2 model on the circle a version of the Glimm-Jaffe φ-bound is proven. Furthermore the K ̈ll ́n-Lehmann representation for general vacuum two-point a e functions are proven and general facts about the damping factor are established. The consequences for the damping factor in the thermal case are briefly discussed.

Item Type: Thesis (PhD)
Date Type: Completion
Status: Unpublished
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Date of First Compliant Deposit: 30 March 2016
Last Modified: 19 Aug 2021 13:06

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