Abstract
LetH l be the Hamiltonian in aP(φ)2 theory with sharp space cutoff in the interval (−l/2,l/2). LetE l =infσ(H l ), α(l)=−E l /l, and let Ωl be the vacuum forH l . discuss properties of α(l) and Ω l . In particular, asl→∞, there are finite constants β∞<0 and α∞ such that α(l)↑α∞, (α(l)−α∞)l↓β∞, and hence α(l)=α∞+β∞/l+o(l −1). Moreover exp(−c 1 l)≦∥Ω l ∥1≦exp(−c 2 l) forc 1,c 2 positive constants, where ∥Ω l ∥1 is theL 1(Q, dμ0) norm of Ω1 with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH l in the infinite volume limit.
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Research sponsored by AFOSR under Contract No. F44620-71-C-0108.
On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.
A. Sloan Foundation Fellow.
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Guerra, F., Rosen, L. & Simon, B. Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2 . Commun.Math. Phys. 27, 10–22 (1972). https://doi.org/10.1007/BF01649655
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DOI: https://doi.org/10.1007/BF01649655