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

Fulvio Melia, M. Fatuzzo

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)253-261
Number of pages9
JournalIl Nuovo Cimento B
Volume106
Issue number3
DOIs
StatePublished - Mar 1991
Externally publishedYes

Fingerprint

wave functions
electric fields
matrices
magnetic fields
spectral emission
Dirac equation
simplification
gravitational fields
neutron stars
tensors
conductivity
electrical resistivity
evaluation
interactions

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

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

In: Il Nuovo Cimento B, Vol. 106, No. 3, 03.1991, p. 253-261.

Research output: Contribution to journalArticle

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