Kramers degeneracy theorem in nonrelativistic QED. (English) Zbl 1183.47078
Consider the Pauli-Fierz Hamiltonian describing a system of an electron coupled to the quantized radiation field. The existence of a ground state for the Pauli-Fierz Hamiltonian is now folklore. Speaking of the uniqueness, while the ground state is unique in the absence of spin, it is no longer unique with spin included. In fact, F.Hiroshima and H.Spohn [Adv.Theor.Math.Phys.5, No.6, 1091–1104 (2001; Zbl 1014.81067)] proved exact double degeneracy of the ground state in the system with spin.
This paper uses the Kramers degeneracy theorem to give a simple proof of the at-least-double degeneracy that each eigenvalue is at least doubly degenerated. The authors first establish an abstract version of the Kramers degeneracy theorem and then apply it to the Pauli-Fierz Hamiltonian with spin 1/2, to the Pauli-Fierz Hamiltonian at fixed total momentum, and further to the N-electron system coupled to the radiation field.
This paper uses the Kramers degeneracy theorem to give a simple proof of the at-least-double degeneracy that each eigenvalue is at least doubly degenerated. The authors first establish an abstract version of the Kramers degeneracy theorem and then apply it to the Pauli-Fierz Hamiltonian with spin 1/2, to the Pauli-Fierz Hamiltonian at fixed total momentum, and further to the N-electron system coupled to the radiation field.
Reviewer: Miyeon Kwon (Platteville, WI)
MSC:
| 47N50 | Applications of operator theory in the physical sciences |
| 47B25 | Linear symmetric and selfadjoint operators (unbounded) |
| 81T10 | Model quantum field theories |
Keywords:
doubly degenerate eigenstates; atoms coupled to a quantised radiation field; Kramers’ degeneracy theoremCitations:
Zbl 1014.81067References:
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