Poincare Invariance of Hamiltonian Semiclassical Field Theory

摘要

Semiclassical Hamiltonian field theory is investigated from the axiomaticpoint of view. A notion of a semiclassical state is introduced. An "elementary"semiclassical state is specified by a set of classical field configuration andquantum state in this external field. "Composed" semiclassical states viewed asformal superpositions of "elementary" states are nontrivial only if the Maslovisotropic condition is satisfied; the inner product of "composed" semiclassicalstates is degenerate. The mathematical proof of Poincare invariance ofsemiclassical field theory is obtained for "elementary" and "composed"semiclassical states. The notion of semiclassical field is introduced; itsPoincare invariance is also mathematically proved.