### Abstract

Interactions taking place in superstrong gravitational and magnetic fields can account for a wide variety of spectral emissions from compact objects such as neutron stars. A quantum treatment of the particle transport in these environments, e.g., needed to calculate the anisotropic electrical conductivity, depends on the evaluation of matrix elements with solutions to the Dirac equation in oblique electric (E) and magnetic (H) fields. However, due to the complexity of the bispinors, these overlap integrals are often extremely difficult to compute. Indeed, no normalized wave function yet exists. Here we show that, in the special case when E/H≲10^{-4}, a simplification of the matrix elements permits an analytic integration that yields explicit expressions for the normalization constant and other overlap integrals. Physical quantities, such as the conductivity tensor, that depend directly on these matrix elements may then be computed in a straightforward way.

Original language | English (US) |
---|---|

Pages (from-to) | 253-261 |

Number of pages | 9 |

Journal | Il Nuovo Cimento B |

Volume | 106 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1991 |

Externally published | Yes |

### Fingerprint

### Keywords

- PACS 11.10.Qr Relativistic wave equations
- PACS 3.50.De Maxwell theory: general mathematical aspects
- PACS 52.40.Mj Particle beam interactions in plasma (including intese charged-particle beams)
- PACS 97.10.Ld Magnetic and electric fields
- polarization and starlight

### Cite this

*Il Nuovo Cimento B*,

*106*(3), 253-261. https://doi.org/10.1007/BF02759770

**Computing the normalized dirac wave function for oblique electric and magnetic fields.** / Melia, Fulvio; Fatuzzo, M.

Research output: Contribution to journal › Article

*Il Nuovo Cimento B*, vol. 106, no. 3, pp. 253-261. https://doi.org/10.1007/BF02759770

}

TY - JOUR

T1 - Computing the normalized dirac wave function for oblique electric and magnetic fields

AU - Melia, Fulvio

AU - Fatuzzo, M.

PY - 1991/3

Y1 - 1991/3

N2 - Interactions taking place in superstrong gravitational and magnetic fields can account for a wide variety of spectral emissions from compact objects such as neutron stars. A quantum treatment of the particle transport in these environments, e.g., needed to calculate the anisotropic electrical conductivity, depends on the evaluation of matrix elements with solutions to the Dirac equation in oblique electric (E) and magnetic (H) fields. However, due to the complexity of the bispinors, these overlap integrals are often extremely difficult to compute. Indeed, no normalized wave function yet exists. Here we show that, in the special case when E/H≲10-4, a simplification of the matrix elements permits an analytic integration that yields explicit expressions for the normalization constant and other overlap integrals. Physical quantities, such as the conductivity tensor, that depend directly on these matrix elements may then be computed in a straightforward way.

AB - Interactions taking place in superstrong gravitational and magnetic fields can account for a wide variety of spectral emissions from compact objects such as neutron stars. A quantum treatment of the particle transport in these environments, e.g., needed to calculate the anisotropic electrical conductivity, depends on the evaluation of matrix elements with solutions to the Dirac equation in oblique electric (E) and magnetic (H) fields. However, due to the complexity of the bispinors, these overlap integrals are often extremely difficult to compute. Indeed, no normalized wave function yet exists. Here we show that, in the special case when E/H≲10-4, a simplification of the matrix elements permits an analytic integration that yields explicit expressions for the normalization constant and other overlap integrals. Physical quantities, such as the conductivity tensor, that depend directly on these matrix elements may then be computed in a straightforward way.

KW - PACS 11.10.Qr Relativistic wave equations

KW - PACS 3.50.De Maxwell theory: general mathematical aspects

KW - PACS 52.40.Mj Particle beam interactions in plasma (including intese charged-particle beams)

KW - PACS 97.10.Ld Magnetic and electric fields

KW - polarization and starlight

UR - http://www.scopus.com/inward/record.url?scp=51649155669&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51649155669&partnerID=8YFLogxK

U2 - 10.1007/BF02759770

DO - 10.1007/BF02759770

M3 - Article

AN - SCOPUS:51649155669

VL - 106

SP - 253

EP - 261

JO - Il Nuovo Cimento B Series 10

JF - Il Nuovo Cimento B Series 10

SN - 0369-3554

IS - 3

ER -