Fundamental particles and representations of the Poincare' group

Jamie

Hi everybody,
I've recently encountered the statement that irreducible unitary
representations of the Poincare group are parameterised by mass and
spin; or, in other words, every fundamental particle defines an irrep
of the Poincare group. This seems pretty important, but I can't find a
QFT textbook that goes into this in any depth whatsoever. Can anybody
give me a clear explanation, or point me towards one?
Thanks,
Jamie.

Arnold Neumaier

Jamie wrote:

> I've recently encountered the statement that irreducible unitary
> representations of the Poincare group are parameterised by mass and
> spin; or, in other words, every fundamental particle defines an irrep
> of the Poincare group. This seems pretty important, but I can't find a
> QFT textbook that goes into this in any depth whatsoever. Can anybody
> give me a clear explanation, or point me towards one?

Weinberg's quantum field theory contains an excellent discussion of it.
See also the relevant sections of my theoretical physics FAQ at
http://www.mat.univie.ac.at/~neum/physics-faq.txt
(in particular those currently labelled S2c-e).

Arnold Neumaier