Particles and Group Representations

I wonder if someone can suggest the perfect book for me to read.

My goal is to have a clear conceptual understanding of what it means
to say that a particle "is" an irreducible group representation.

Here is what I already do and do not know:

1) I have a rudimentary understanding of quantum mechanics, at the
level, say, of the first few chapters of the Cohen-Tannoudji/Diu/Laloe
textbook. That is, I understand the formalism of bras and kets, the
basic postulates, and the Schrodinger equation.

2) I at one time understood Noether's theorem on symmetry and
conservation laws and I assume I could learn it again, though I've
misplaced much of my past understanding.

3) I understand the basics of group theory, representation theory
and character theory. I have a pretty thorough understanding of the
theory for finite groups. My knowledge of Lie Groups is pretty
limited---I am not sure what the Borel-Weil theorem says, etc.---but
I feel confident I can learn this.

4) I know about manifolds, metrics, connections, vector bundles and
principal bundles. Here I speak the language of mathematics but I
can presumably learn to translate from the language of physics.

5) I have a (fairly recently acquired) reasonably good understanding
of Maxwell's equations, in case this is relevant.

6) I understand how various Lie groups act on the state spaces
of quantum mechanical systems, and that I can think of these actions
as representations of the Lie groups (either on vector spaces or
quotient of vector spaces). I understand that I can write these
representations as direct sums of irreducible representations. I have
the vague sense that this is somehow related to what I really want
to understand, which is:

A) How does an irreducible representation yield a particle? And
B) how do the properties of that representation predict properties
of the particle, e.g. its mass?


I am more interested in understanding all this at a conceptual level
than in being able to solve problems and do calculations. I will
probably be more comfortable with a text written for mathematicians
than a text written for physicists, but I can deal with either.
.

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