Spinor fields describing particles of zero rest mass satisfy the so-called zero rest mass equations. Examples of zero rest mass particles include the neutrino (a fermion) and the gauge bosons (as long as gauge symmetry is not violated) such as the photon.
If 
is the spinor field describing a particle of spin
(where upper case Latin indices are spinor indices which can take the values 0 and
1), then it is symmetric and has 
indices. If the particle is also of zero rest mass, then
satisfies the zero rest mass equation
 |
Here, in a Lorentz transformation, primed spinors transform under the conjugate of the transformation
for unprimed ones, Einstein summation is used
throughout, and 
denotes the spinor, which is equivalent to the Levi-Civita
connection on Minkowski space.
has one index for the neutrino, two for the photon, and four for the graviton. For
the photon, the equation obtained states the vanishing of the divergence of the field
strength tensor. For the graviton, it gives the Bianchi
identity for a linearized Weyl tensor.
