Abstract
For theP(ϕ)2 field theory, we prove that the falloff of the (vacuum subtracted) two point Schwinger function dominates the higher order (vacuum subtracted) Schwinger functions. As applications, we prove that for even polynomials, the first excited state is odd, and that when there is a one particle state in the infinite volume limit, it is coupled to the vacuum by a single power of the field. The main inputs are the theory of Markov fields and the F.K.G. inequalities.
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Simon, B. Correlation inequalities and the mass gap inP(φ)2 . Commun.Math. Phys. 31, 127–136 (1973). https://doi.org/10.1007/BF01645740
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DOI: https://doi.org/10.1007/BF01645740