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arXiv · 1211.4965

Essential spectrum of a fermionic quantum field model

Toshimitsu Takaesu
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Abstract

An interaction system of a fermionic quantum field is considered. The state space is defined by a tensor product space of a fermion Fock space and a Hilbert space. It is assumed that the total Hamiltonian is a self-adjoint operator on the state space and bounded from below. Then it is proven that a subset of real numbers is the essential spectrum of the total Hamiltonian. It is applied to the system of a Dirac field coupled to a Klein-Gordon field. Then the HVZ theorem for the system is obtained.

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Toshimitsu Takaesu. 2014-01-15. Essential spectrum of a fermionic quantum field model. https://arxiv.org/abs/1211.4965

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