Finite-particle representations and states of the canonical commutation relations

Interacting quantum fields and the chronometric principle

“…It can be deduced (see ref. 7) that the number of particles at time t in a given (terminal) state, assuming a given initial state at time 0, is mathematically quite well defined, despite the absence of a convergent evolution law for the corresponding Schrbdinger wave functions.…”

Representations of the CCR in the (φ4)3 model: Independence of space cutoff

“…It is natural to ask under which conditions are the two algebras 91(B, g) and 9.I(B, g') unitarily equivalent, which in turn would signify that the representation does not depend on the space cutoff g. Similar problems have been treated in the literature. Chaiken [3] has developed necessary and sufficient criteria for representations of the CCR (in fact, Weyl systems) to be equivalent to the Fock representation. In addition, necessary and sufficient conditions for the equivalence of quasiflee representations of the CCR have been given by van Daele, Verbeure [20] and Araki [t].…”

“…In point (2) and point (3) important properties of the Hamiltonian H~(g) are derived. Point (2) is a proof of the semiboundedness of the Hamiltonian H~(g).…”

“…Point (2) is a proof of the semiboundedness of the Hamiltonian H~(g). This problem, and point (3) are under investigation by Glimm and Jaffe. Point (3) is the construction of a unique selfadjoint limit of the The convexity of B is inessential and we have restricted ourselves to this case for convenience.…”

“…Point (3) is the construction of a unique selfadjoint limit of the The convexity of B is inessential and we have restricted ourselves to this case for convenience. 3 The program, conjectures and allusions to techniques being used in proofs which are still under work have been kindly communicated to me by Prof. Glimm in private discussions. operators Ho,~(g ).…”