Electron self-energy in nonlocal field theory

✍ Scribed by G.V Efimov; M.A Ivanov; O.A Mogilevsky

• Book ID: 102987007
• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 682 KB
• Volume: 103
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(77)90267-6

✦ Synopsis

In the framework of quantum electrodynamics with the nonlocal interaction it is shown that the correspondence principle holds in the problem on the self-mass of an electron and a particle with arbitrary spin. It appears that the second order of perturbation theory in the limit fi -f 0 gives just the classical expression for the electron self-energy, and all higher order corrections are zero.

where Y,, is the cutoff radius and v is a dimensionless parameter depending of the electron charge distribution.

Comparing (1) with (2) it is clear that the quantum correction to mass, unlike the classical one, depends on the electron mass and diverges only logarithmically in the limit r, -+ 0. Taking the limit h --f 0 in (2), i.e., the transition to the classical limit, gives nonsense, therefore no correspondence principle exists there.

From the above it follows, though implicitly, that in theory there should be some parameter r. independent of constants A, nz, c, e and the theory should be organized in such a way that 169