Thesis or Dissertation Spectral Analysis of a Charged Scalar Field Model with Cutoffs

和田, 和幸

A quantum system of a massless charged scalar field with a self-interaction is in-vestigated. By introducing a spacial cut-off function, a Hamiltonian of the quantumsystem is realized as a linear operator on a Boson Fock space. Under certain conditions,it is proven that the Hamiltonian is bounded below, self-adjoint and has a ground statefor an arbitrary coupling constant. Moreover the Hamiltonian strongly commutes withthe total charge operator. This fact implies that the state space of the charged scalarfield is decomposed into the infinite direct sum of fixed total charge spaces. A totalcharge of an eigenstate is discussed
Hokkaido University(北海道大学). 博士(理学)

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