Linked Questions

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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." ...
13
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1answer
2k views

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 ...
12
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1answer
2k views

Identification of the state of particle types with representations of Poincare group

In the second chapter of the first volume of his books on QFT, Weinberg writes in the last paragraph of page 63: In general, it may be possible by using suitable linear combinations of the $\Psi_{p,...
4
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1answer
556 views

Why are one-particle states called irreducible representations of Poincaré group?

The one-particle states in the Hilbert space of a quantized relativistic field theory are said to form irreducible representations of the Poincaré group. Why is that? I mean, popular texts in QFT do ...
7
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4answers
644 views

How do (and don’t) particles emerge from fields?

I am aware of the following field- and particle-like notions: QFT particle, a unit of excitation in (the Fock space of) a QFT; SR field, an extremal $A = A(\mathbf x)$ of a Lorentz-invariant action; ...
3
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1answer
467 views

Group Theoretic definition of a particle

We intuitively have a sense of what a particle means in the conventional sense. But is it possible to have a group theoretical definition of a particle, I mean in terms of irreducible representations ...
6
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2answers
972 views

Why do single particle states furnish a rep. of the inhomogeneous Lorentz group?

Following up on this question: Weinberg says In general, it may be possible by using suitable linear combinations of the $\psi_{p,\sigma}$ to choose the $\sigma$ labels in such a way that $C_{\...
4
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1answer
333 views

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 ...
3
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177 views

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 ...
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89 views

Which fields/particles correspond to higher dimensional representations of the Lorentz group?

To establish the Dirac equation we use Clifford algebra to find the spinor representation of the Lorentz group. A four dimensional representation tells us that the Dirac spinor describes a quantum ...
1
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1answer
74 views

Poincare group and free theories

How exactly is the Poincare group related to the free relativistic theories in quantum field theory? I know Poincare group is the Lorentz group along with translations but don't see any connected why ...