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## Main Question or Discussion Point

I've been trying to understand representations of the Lorentz group. So as far as I understand, when an object is in an (m,n) representation, then it has two indices (let's say the object is ##\phi^{ij}##), where one index ##i## transforms as ##\exp(i(\theta_k-i\beta_k)A_k)## and the other index as ##\exp(i(\theta_k+i\beta_k)B_k)##, where A and B are commuting su(2) generators of dimension (2m+1) and (2n+1) respectively and ##\theta## are the rotation angles and ##\beta## the rapidities.

It is often said (for example I am reading the Schwartz QFT book, where it is mentioned), that the (n/2,n/2) representation corresponds to a tensor with n indices.

How is this the case? How can I see it?

Is the meaning of the tensor representation that each index transforms using the usual 4x4 Lorentz transformation matrix? How is it the same as a two index object where each index transforms under a (n+1) dimensional su(2) representation?

It is often said (for example I am reading the Schwartz QFT book, where it is mentioned), that the (n/2,n/2) representation corresponds to a tensor with n indices.

How is this the case? How can I see it?

Is the meaning of the tensor representation that each index transforms using the usual 4x4 Lorentz transformation matrix? How is it the same as a two index object where each index transforms under a (n+1) dimensional su(2) representation?