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### Particle definition [duplicate]

I came across this statement in the book "Quantum Field theory and the Standard Model". "A particle can be defined as a set of states that mix only among themselves under Poincare transformations." ...
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### Why particles are thought as irreducible representation in plain English?

I'm a PhD student in mathematics and I have no problem in understanding what irriducible representation are. I mean that the mathematical side is not a particular problem. Nevertheless I have some ...
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### What is the mathematical definition of a classical elementary particle?

In the (non-statistical) setting of quantum mechanics, the rôle of the state space is played by a projective Hilbert space $\mathbf{P}(\mathscr{H})$. Elementary particles are then more or less defined ...
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### Significance of Irreducible Representations

I am reading texts on QFT and they place a lot of emphasis on finding irreducible representations of the Lorentz/Poincare Group. I also recall some level of discussion from non-relativistic quantum ...