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Connection between the spectrum condition and the Lorentz invariance ofP(φ)2

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Abstract

We prove that, for theP(φ)2 quantum field theory, the Wightman functions are Lorentz invariant if the energy-momentum spectrum lies in the forward light-cone. The ingredients of the proof are the following facts, established by Glimm and Jaffe: the field satisfies local commutativity, and also the estimates

$$\begin{gathered} \phi _V (f,t)\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } const||f||_1 (H_V + I) \hfill \\ \pi _V (g,t)\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \leqslant } ||g||_2 (H_V + I) \hfill \\ \end{gathered} $$

whereV is a space cut-off, uniformly inV.

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  1. Bedford College, London, England

    R. F. Streater

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  1. R. F. Streater
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Streater, R.F. Connection between the spectrum condition and the Lorentz invariance ofP(φ)2 . Commun.Math. Phys. 26, 109–120 (1972). https://doi.org/10.1007/BF01645698

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  • DOI: https://doi.org/10.1007/BF01645698

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