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An analysis of the selfenergy problem for the electron in quantum electrodynamics Daykin, Philip Norman
Abstract
The selfenergy of the free electron at rest Is evaluated without the restriction that the selfinteraction be a purely retarded interaction. Both the oneelectron theory and the hole theory of the positron are treated. It is shown that in the oneelectron theory the normally quadratically divergent transverse part of the selfenergy vanishes if the selfinteraction is assumed to be one half retarded plus one half advanced, the remaining Coulomb part of the selfenergy being only linearly divergent. A similar theorem does not hold for the hole theory. A particular type of selfinteraction leads to a vanishing selfenergy in oneelectron theory. However this does not solve the selfenergy problem, as in this case radiation corrections to scattering will vanish as well. The selfenergy of a bound electron is evaluated in a similar manner. The decay probability of an excited state is calculated as the imaginary part of the selfenergy; the correct value is obtained only for a purely retarded selfinteraction in hole theory. In the special case in which the external field is a uniform magnetic field, again only this interaction in hole theory gives the correct value for the anomalous magnetic moment. It is therefore concluded that any solution of the selfenergy problem by introducing advanced selfinteractions is to be ruled out.
Item Metadata
Title 
An analysis of the selfenergy problem for the electron in quantum electrodynamics

Creator  
Publisher 
University of British Columbia

Date Issued 
1952

Description 
The selfenergy of the free electron at rest Is evaluated without the restriction that the selfinteraction be a purely retarded interaction. Both the oneelectron theory and the hole theory of the positron are treated. It is shown that in the oneelectron theory the normally quadratically divergent transverse part of the selfenergy vanishes if the selfinteraction is assumed to be one half retarded plus one half advanced, the remaining Coulomb part of the selfenergy being only linearly divergent. A similar theorem does not hold for the hole theory. A particular type of selfinteraction leads to a vanishing selfenergy in oneelectron theory. However this does not solve the selfenergy problem, as in this case radiation corrections to scattering will vanish as well.
The selfenergy of a bound electron is evaluated in a similar manner. The decay probability of an excited state is calculated as the imaginary part of the selfenergy; the correct value is obtained only for a purely retarded selfinteraction in hole theory. In the special case in which the external field is a uniform magnetic field, again only this interaction in hole theory gives the correct value for the anomalous magnetic moment.
It is therefore concluded that any solution of the selfenergy problem by introducing advanced selfinteractions is to be ruled out.

Subject  
Genre  
Type  
Language 
eng

Date Available 
20120229

Provider 
Vancouver : University of British Columbia Library

Rights 
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

DOI 
10.14288/1.0085108

URI  
Degree  
Program  
Affiliation  
Degree Grantor 
University of British Columbia

Campus  
Scholarly Level 
Graduate

Aggregated Source Repository 
DSpace

Item Media
Item Citations and Data
Rights
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.