On P(φ)_2 interactions at positive temperature

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

The relativistic KMS condition for the thermal n-point functions of the P(φ)_2 model

Thermal quantum field theories are expected to obey a relativistic KMS condition, which replaces both the relativistic spectrum condition of Wightman quantum field theory and the KMS condition, which characterises equilibrium states in quantum statistical mechanics. In a previous work it has been shown that the two-point function of the thermal $P(\phi)_2$ model satisfies the relativistic KMS condition. Here we extend this result to general $n$-point functions

The H\"older Inequality for KMS States

We prove a H\"older inequality for KMS States, which generalises a well-known trace-inequality. Our results are based on the theory of non-commutative $L_p$-spaces.Comment: 10 page