The Wightman axioms and particle structure in the $\mathscr{P}(\phi)_2$ quantum field model


The $\mathscr{P}(\phi)_2$ quantum field model with small coupling constant satisfies the Weightman axioms. The spectrum of the mass operator $M=(H^2-P^2)^{1/2}$ contains two isolated eigenvalues: $0$ and $m>0$. Hence the model describes the scattering of particles of mass $m>0$. The proof contains an $n$-particle cluster expansion and an analysis of the subspace of states with energy less than $(n+1)m(1-\varepsilon)$.


James Glimm

Arthur Jaffe

Thomas Spencer