# Spectral Analysis of the Dirac Polaron

### Itaru Sasaki

Shinshu University, Matsumoto, Japan

## Abstract

A system of a Dirac particle interacting with the radiation field is considered. The Hamiltonian of the system is defined by $H=α⋅(p^ −qA(x^))+mβ+H_{f}$, where $q∈R$ is a coupling constant, $A(x^)$ the quantized vector potential and $H_{f}$ the free photon Hamiltonian. Since the total momentum is conserved, $H$ is decomposed with respect to the total momentum with fiber Hamiltonian $H(p),(p∈R_{3})$. Since the self-adjoint operator $H(p)$ is bounded from below, one can define the lowest energy $E(p,m):=fσ(H(p))$. We prove that $E(p,m)$ is an eigenvalue of $H(p)$ under the following conditions: (i) infrared regularization and (ii) $E(p,m)<E(p,0)$. We also discuss the polarization vectors and the angular momentums.

## Cite this article

Itaru Sasaki, Spectral Analysis of the Dirac Polaron. Publ. Res. Inst. Math. Sci. 50 (2014), no. 2, pp. 307–339

DOI 10.4171/PRIMS/135