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RaritaSchwinger equationIn theoretical physics, the RaritaSchwinger equation is the relativistic field equation of spin3/2 fermions. It is similar to the Dirac equation for spin1/2 fermions. This equation was first introduced by William Rarita and Julian Schwinger in 1941. In modern notation it can be written as: Additional recommended knowledgewhere ε^{μνρσ} is the LeviCivita symbol, γ^{5} and γ_{ν} are Dirac matrices, m is the mass and ψ_{μ} is a vectorvalued spinor with additional components compared to the four component spinor in the Dirac equation. It corresponds to the representation of the Lorentz group, or rather, its part. This field equation can be derived from the following Lagrangian: where the bar above ψ_{μ} denotes the Dirac adjoint. As in the case of the Dirac equation, electromagnetic interaction can be added simply by promoting the partial derivative to gauge covariant derivative: The massless RaritaSchwinger equation has a gauge symmetry, under the gauge transformation of , where is an arbitrary spinor field. "Weyl" and "Majorana" versions of the RaritaSchwinger equation also exist. This equation is useful for the wave function of composite objects like Delta (Δ) baryons or for proposed elementary fields like the gravitino. So far, no fundamental particle with spin 3/2 has been found experimentally. Drawbacks of the formalism
The current description of massive, higher spin fields through either RaritaSchwinger or Fierz–Pauli formalisms is afflicted with several maladies. Upon gauging, high spin fields suffer from acausal, superluminal propagation; besides, the quantization of these systems in interaction with electromagnetism is essentially flawed. Also, algebraic inconsistencies appear upon gauging which can only be avoided by requiring that all equations involving derivatives be obtainable from a Lagrangian, a procedure that becomes involved because of the need of introducing auxiliary fields in order to obtain all constraints from the Lagrangian. In 1969, Velo and Zwanziger showed that the Rarita–Schwinger lagrangian coupled to electromagnetism leads to equation with solutions representing wavefronts, some of which propagate faster than light. There are some Lorentz frames that allow the consistent formulation of quantum mechanics and quantum field theory; there are some others that don’t. References


This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "RaritaSchwinger_equation". A list of authors is available in Wikipedia. 