# Spin Hall effect of photons in a static gravitational field

## Abstract

Starting from a Hamiltonian description of the photon within the set of Bargmann-Wigner equations we derive new semiclassical equations of motion for the photon propagating in a static gravitational field. These equations which are obtained in the representation diagonalizing the Hamiltonian at the order ({Dirac_h}/2{pi}), present the first order corrections to the geometrical optics. The photon Hamiltonian shows a new kind of helicity-torsion coupling. However, even for a torsionless space-time, photons do not follow the usual null geodesic as a consequence of an anomalous velocity term. This term is responsible for the gravitational birefringence phenomenon: photons with distinct helicity follow different geodesics in a static gravitational field.

- Authors:

- Universite Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF, UFR de Mathematiques, BP74, 38402 Saint Martin d'Heres, Cedex (France)
- Universite Paul Verlaine, Institut de Physique, ICPMB1-FR CNRS 2843, Laboratoire de Physique Moleculaire et des Collisions, 1, boulevard Arago, 57078 Metz (France)

- Publication Date:

- OSTI Identifier:
- 21020404

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.084035; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BIREFRINGENCE; CORRECTIONS; COSMOLOGY; COUPLING; EQUATIONS OF MOTION; GEODESICS; GRAVITATIONAL FIELDS; HALL EFFECT; HAMILTONIANS; HELICITY; OPTICS; PHOTONS; QUANTUM FIELD THEORY; SEMICLASSICAL APPROXIMATION; SPACE-TIME; SPIN; TORSION; VELOCITY

### Citation Formats

```
Gosselin, Pierre, Berard, Alain, and Mohrbach, Herve.
```*Spin Hall effect of photons in a static gravitational field*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.084035.

```
Gosselin, Pierre, Berard, Alain, & Mohrbach, Herve.
```*Spin Hall effect of photons in a static gravitational field*. United States. doi:10.1103/PHYSREVD.75.084035.

```
Gosselin, Pierre, Berard, Alain, and Mohrbach, Herve. Sun .
"Spin Hall effect of photons in a static gravitational field". United States.
doi:10.1103/PHYSREVD.75.084035.
```

```
@article{osti_21020404,
```

title = {Spin Hall effect of photons in a static gravitational field},

author = {Gosselin, Pierre and Berard, Alain and Mohrbach, Herve},

abstractNote = {Starting from a Hamiltonian description of the photon within the set of Bargmann-Wigner equations we derive new semiclassical equations of motion for the photon propagating in a static gravitational field. These equations which are obtained in the representation diagonalizing the Hamiltonian at the order ({Dirac_h}/2{pi}), present the first order corrections to the geometrical optics. The photon Hamiltonian shows a new kind of helicity-torsion coupling. However, even for a torsionless space-time, photons do not follow the usual null geodesic as a consequence of an anomalous velocity term. This term is responsible for the gravitational birefringence phenomenon: photons with distinct helicity follow different geodesics in a static gravitational field.},

doi = {10.1103/PHYSREVD.75.084035},

journal = {Physical Review. D, Particles Fields},

number = 8,

volume = 75,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}