I'm a beginning QFT student, trying to slog my way through Slansky's http://www.sciencedirect.com/scienc...id=4422&md5=c09eed961c9201786651592d71de94f3"...(adsbygoogle = window.adsbygoogle || []).push({});

I have some basic questions, the answers to which everyone around me seems to take for granted. Any help would be appreciated! It would also be great if we could strike up a conversation on group theory as it relates to particle physics, too...

I'll start with page 7, where Slansky discusses "construction of the fermion kinetic energy and fermion mass in a Yang-Mills Lagrangian." He says that the goal is to show that "the kinetic energy couplesf_{R}andf_{L}."

First, what aref_{R}andf_{L}? In the paragraph above, he uses them in a sentence like this: "the left-handed fermions transforming asf_{L}" so I take it that he means some sort of representation... but what does this actually mean mathematically? Matrix? Vector?

Second, it seems that people talk about matrices and states interchangeably when they talk about group representations... I completely understand matrix representations. But how can states (like Dirac spinors) represent anything?

As an example, SO(3) refers to a set of matrices used to multiply vectors. The vectors themselves don't tell me anything about SO(3). Or do they?

Third, what exactly does the notationf_{R}[tex]\times[/tex]f_{L}mean? Cartesian product? Direct product? Tensor product?

Fourth, what is the conjugate of something likef_{R}? Is this the same as the adjoint representation?

I have so many questions, but I'll leave it here for now.

-j

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# R. Slansky, Group theory for unified model building

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