Weyl version of the Rarita-schwinger equation

[yola]

Hello,
Can someone please give me the form of the "Weyl" version of the Rarita-Schwinger equation.
Thanks

 

[dextercioby]

I don't know what you mean. What's the Weyl version of other equation ?

 

[yola]

i want the expression in terms of two component spinors and not Dirac spinors.

 

[dextercioby]

There are no Dirac spinors in that equation, but Rarita-Schwinger spinors.

 

[yola]

yes you're right.
what if i want to express it in terms of sigmas instead of gamma matrices. by what i can replace the levi-civita?

 

[dextercioby]

http://en.wikipedia.org/wiki/Rarita-Schwinger_equation

The Weyl form is apparently the so-called <chiral representation> of the Dirac algebras, as opposed to the Majorana and Dirac representations.

 

[Bill_K]

∂_abφ^aa1a2...al_b1b2...bk = iκ χ^a1a2...al_b1b2...bk
∂^abχ^a1a2...al_bb1b2...bk = iκ φ^aa1a2...al_bb1b2...bk

Here both spinors φ and χ are symmetric. κ is the mass. φ has l+1 undotted (raised) and k dotted (lowered) indices; χ has l undotted and k+1 dotted indices. The underlying representation of the field equations is therefore ((l+1)/2 , k/2) ⊕ (l/2 , (k+1)/2).