Rarita–Schwinger equation

In theoretical physics, the Rarita -Schwinger equation is a relativistic field equation for Spin-3/2-Fermionen. It is similar to the Dirac equation Spin-1/2-Fermionen and can be derived from this. It was first formulated and published in 1941 by William Rarita and Julian Schwinger. In modern notation it is written as follows:

Here is the Levi- Civita symbol, and are the Dirac matrices, is the rest mass of the fermion, and is a vector- spinor with additional components compared to the four components of the spinor in the Dirac equation. The representation corresponds to the, or representation of the Lorentz group.

The field equation can be derived from the following Lagrangian:

It refers to the adjoint spinor. As in the Dirac equation, the interaction with an electromagnetic field by the minimal gauge invariant coupling:

Be considered. The Rarita -Schwinger equation has a gauge symmetry for particles with rest mass 0 with respect to the gauge transformation. It is an arbitrary, complex gauge field.

From the Rarita -Schwinger equation and Weyl and Majorana representations, which do not differ with respect to the physical results of the original equation exist. It is usually used to composite particles, such as to describe the delta ( Δ ) baryon and investigate. Sometimes this equation is also used for hypothetical Teilchenfelder as the gravitino. It remains to be that so far no stable elementary particle with spin 3/2 could be detected experimentally.

Article

  • W. Rarita and J. Schwinger, On a Theory of Particles with Half- Integral Spin Phys. Rev. 60, 61 ( 1941).
  • Collins PDB, Martin AD, Squires EJ Particle physics and cosmology (1989 ) Wiley, Section 1.6.
  • G. Velo, D. Zwanziger, Propagation and quantization of Rarita -Schwinger Waves in an External Electromagnetic Potential, Phys. Rev. 186, 1337 (1969).
  • G. Velo, D. Zwanziger, Noncausality and Other Defects of Interaction Lagrangians for Particles with Spin One and Higher, Phys. Rev. 188, 2218 (1969).
  • M. Kobayashi, A. Shamaly, Minimal Electro Magnetic coupling for massive spin -two fields, Phys. Rev. D 17.8, 2179 (1978).
  • Walter Greiner: Theoretical Physics. Volume 6: Relativistic quantum mechanics. Wave equations. 2nd revised and enlarged edition. German, Thun et al, 1987, ISBN 3-8171-1022-7.

Credentials

  • Quantum mechanics
  • Partial Differential Equations
Minimal coupling
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