# Gauge-invariant dynamical quantities of QED with decomposed gauge potentials

## Abstract

We discover an inner structure of the QED system; i.e., by decomposing the gauge potential into two orthogonal components, we obtain a new expansion of the Lagrangian for the electron-photon system, from which, we realize the orthogonal decomposition of the canonical momentum conjugate to the gauge potential with the canonical momentum's two components conjugate to the gauge potential's two components, respectively. Using the new expansion of Lagrangian and by the general method of field theory, we naturally derive the gauge invariant separation of the angular momentum of the electron-photon system from Noether theorem, which is the rational one and has the simplest form in mathematics, compared with the other four versions of the angular momentum separation available in literature. We show that it is only the longitudinal component of the gauge potential that is contained in the orbital angular momentum of the electron, as Chen et al. have said. A similar gauge invariant separation of the momentum is given. The decomposed canonical Hamiltonian is derived, from which we construct the gauge invariant energy operator of the electron moving in the external field generated by a proton [Phys. Rev. A 82, 012107 (2010)], where we show that the form of themore »

- Authors:

- Institute of Theoretical Physics, Beijing University of Technology, Beijing 100124 (China)
- (China)
- (World Lab.), P.O. Box 8730, Beijing 100080 (China)

- Publication Date:

- OSTI Identifier:
- 22068690

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 3; Other Information: (c) 2011 American Institute of Physics; Country of input: Syrian Arab Republic; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ELECTRONS; GAUGE INVARIANCE; HAMILTONIANS; KINETIC ENERGY; LAGRANGIAN FUNCTION; ORBITAL ANGULAR MOMENTUM; PHOTONS; POTENTIALS; PROTONS; QUANTUM ELECTRODYNAMICS; SPIN

### Citation Formats

```
Zhou Baohua, Huang Yongchang, Kavli Institute for Theoretical Physics China, CAS, Beijing 100080, and CCAST.
```*Gauge-invariant dynamical quantities of QED with decomposed gauge potentials*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.032505.

```
Zhou Baohua, Huang Yongchang, Kavli Institute for Theoretical Physics China, CAS, Beijing 100080, & CCAST.
```*Gauge-invariant dynamical quantities of QED with decomposed gauge potentials*. United States. doi:10.1103/PHYSREVA.84.032505.

```
Zhou Baohua, Huang Yongchang, Kavli Institute for Theoretical Physics China, CAS, Beijing 100080, and CCAST. Thu .
"Gauge-invariant dynamical quantities of QED with decomposed gauge potentials". United States. doi:10.1103/PHYSREVA.84.032505.
```

```
@article{osti_22068690,
```

title = {Gauge-invariant dynamical quantities of QED with decomposed gauge potentials},

author = {Zhou Baohua and Huang Yongchang and Kavli Institute for Theoretical Physics China, CAS, Beijing 100080 and CCAST},

abstractNote = {We discover an inner structure of the QED system; i.e., by decomposing the gauge potential into two orthogonal components, we obtain a new expansion of the Lagrangian for the electron-photon system, from which, we realize the orthogonal decomposition of the canonical momentum conjugate to the gauge potential with the canonical momentum's two components conjugate to the gauge potential's two components, respectively. Using the new expansion of Lagrangian and by the general method of field theory, we naturally derive the gauge invariant separation of the angular momentum of the electron-photon system from Noether theorem, which is the rational one and has the simplest form in mathematics, compared with the other four versions of the angular momentum separation available in literature. We show that it is only the longitudinal component of the gauge potential that is contained in the orbital angular momentum of the electron, as Chen et al. have said. A similar gauge invariant separation of the momentum is given. The decomposed canonical Hamiltonian is derived, from which we construct the gauge invariant energy operator of the electron moving in the external field generated by a proton [Phys. Rev. A 82, 012107 (2010)], where we show that the form of the kinetic energy containing the longitudinal part of the gauge potential is due to the intrinsic requirement of the gauge invariance. Our method provides a new perspective to look on the nucleon spin crisis and indicates that this problem can be solved strictly and systematically.},

doi = {10.1103/PHYSREVA.84.032505},

journal = {Physical Review. A},

issn = {1050-2947},

number = 3,

volume = 84,

place = {United States},

year = {2011},

month = {9}

}