Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2 |
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| Authors: | F Guerra L Rosen B Simon |
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| Institution: | (1) Joseph Henry Laboratories, Princeton, New Jersey, USA;(2) Princeton University, Jadwin Hall, 08540 Princeton, N.J., USA |
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| Abstract: | LetH
l
be the Hamiltonian in aP( )2 theory with sharp space cutoff in the interval (–l/2,l/2). LetE
l
=inf (H
l
),  (l)=–E
l
/l, and let  l be the vacuum forH
l
. discuss properties of (l) and
l
. In particular, asl  , there are finite constants  <0 and such that (l) , ((l)–)l , and hence (l)=+/l+o(l
–1). Moreover exp(–c
1
l) 
l
1exp(–c
2
l) forc
1,c
2 positive constants, where
l
1 is theL
1(Q, d 0) norm of 1 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.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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| Keywords: | |
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