# Quantum electrodynamics based on self-fields, without second quantization: A nonrelativistic calculation of g-2

## Abstract

Using a formulation of quantum electrodynamics that is not second quantized, but rather based on self-fields, we compute the anomalous magnetic moment of the electron to first order in the fine-structure constant ..cap alpha... In the nonrelativistic (NR) case and in the dipole approximation, our result is a/sub e/equivalent(g-2)/2 = (4..lambda../3m)(..cap alpha../2..pi..), where ..lambda.. is a positive photon energy cutoff and m the electron mass. A reasonable choice of cutoff, ..lambda../m = (3/4, yields the correct sign and magnitude for g-2 namely, a/sub e/ = +..cap alpha../2..pi... In our formulation the sign of a/sub 3/ is correctly positive, independent of cutoff, and the demand that a/sub e/ = +..cap alpha../2..pi.. implies a unique value for ..lambda... This is in contradistinction to previous NR calculations of a/sub e/ that employ electromagnetic vacuum fluctuations instead of self-fields; in the vacuum fluctuation case the sign of a/sub e/ is cutoff dependent and the equation a/sub e/ = ..cap alpha../2..pi.. does not have a unique solution in ..lambda...

- Authors:

- Publication Date:

- Research Org.:
- Department of Physics, Campus Box 390, University of Colorado, Boulder, Colorado 80309

- OSTI Identifier:
- 6736458

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev. A; (United States)

- Additional Journal Information:
- Journal Volume: 38:9

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ELECTRONS; MAGNETIC MOMENTS; QUANTUM ELECTRODYNAMICS; SELF-ENERGY; ENERGY DENSITY; RADIATIVE CORRECTIONS; SOMMERFELD CONSTANT; CORRECTIONS; ELECTRODYNAMICS; ELEMENTARY PARTICLES; ENERGY; FERMIONS; FIELD THEORIES; LEPTONS; QUANTUM FIELD THEORY; 645400* - High Energy Physics- Field Theory

### Citation Formats

```
Barut, A O, Dowling, J P, and van Huele, J F.
```*Quantum electrodynamics based on self-fields, without second quantization: A nonrelativistic calculation of g-2*. United States: N. p., 1988.
Web. doi:10.1103/PhysRevA.38.4405.

```
Barut, A O, Dowling, J P, & van Huele, J F.
```*Quantum electrodynamics based on self-fields, without second quantization: A nonrelativistic calculation of g-2*. United States. doi:10.1103/PhysRevA.38.4405.

```
Barut, A O, Dowling, J P, and van Huele, J F. Tue .
"Quantum electrodynamics based on self-fields, without second quantization: A nonrelativistic calculation of g-2". United States. doi:10.1103/PhysRevA.38.4405.
```

```
@article{osti_6736458,
```

title = {Quantum electrodynamics based on self-fields, without second quantization: A nonrelativistic calculation of g-2},

author = {Barut, A O and Dowling, J P and van Huele, J F},

abstractNote = {Using a formulation of quantum electrodynamics that is not second quantized, but rather based on self-fields, we compute the anomalous magnetic moment of the electron to first order in the fine-structure constant ..cap alpha... In the nonrelativistic (NR) case and in the dipole approximation, our result is a/sub e/equivalent(g-2)/2 = (4..lambda../3m)(..cap alpha../2..pi..), where ..lambda.. is a positive photon energy cutoff and m the electron mass. A reasonable choice of cutoff, ..lambda../m = (3/4, yields the correct sign and magnitude for g-2 namely, a/sub e/ = +..cap alpha../2..pi... In our formulation the sign of a/sub 3/ is correctly positive, independent of cutoff, and the demand that a/sub e/ = +..cap alpha../2..pi.. implies a unique value for ..lambda... This is in contradistinction to previous NR calculations of a/sub e/ that employ electromagnetic vacuum fluctuations instead of self-fields; in the vacuum fluctuation case the sign of a/sub e/ is cutoff dependent and the equation a/sub e/ = ..cap alpha../2..pi.. does not have a unique solution in ..lambda...},

doi = {10.1103/PhysRevA.38.4405},

journal = {Phys. Rev. A; (United States)},

number = ,

volume = 38:9,

place = {United States},

year = {1988},

month = {11}

}