Common Representations
- (0,0) the Lorentz scalar representation. This representation is carried by relativistic scalar field theories.
- (1/2,0) is the left-handed Weyl spinor and (0,1/2) is the right-handed Weyl spinor representation.
- (1/2,0) ⊕ (0,1/2) is the bispinor representation (see also Dirac spinor).
- (1/2,1/2) is the four-vector representation. The electromagnetic vector potential lives in this rep. It is a 1-form field.
- (1,0) is the self-dual 2-form field representation and (0,1) is the anti-self-dual 2-form field representation.
- (1,0) ⊕ (0,1) is the representation of a parity invariant 2-form field. The electromagnetic field tensor transforms under this representation.
- (1,1/2) ⊕ (1/2,1) is the Rarita-Schwinger field representation.
- (1,1) is the spin-2 representation of the traceless metric tensor.
Read more about this topic: Representation Theory Of The Lorentz Group
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