# Tagged Questions

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### What is the matrix representation of the momentum operator (generator of translations) that is used in the commutators of the Poincaré Group?

So the commutators of the Poincareé group are given by \begin{eqnarray} [J_{i},P_{j}]=i\epsilon_{ijk}P_{k}, \quad [J_{i},J_{j}]=i\epsilon_{ijk}J_{k}, \quad [J_{i},K_{j}]=i\epsilon_{ijk}K_{k}, \quad [...
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### Spinors in 2+1 dimensions

I am trying to understand representations of the Poincare/Lorentz group, and in particular spinors, in 2+1 dimensions. I know some of the math, but I'm not sure about the physical interpretation of it ...
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### How to evaluate possible values of spin of two photon system?

Photon hasn't well defined quantity such as spin. Instead of it, it is characterized by helicity $h$. Let's assume state of two photons in CM frame (with $\mathbf k$ being the momentum of one of ...
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### Why are one-particle states called representations of Poincaré group?

The one-particle states in the Hilbert space of a quantized relativistic field theory are said to form representations of the Poincaré group. Why is that? I mean, popular texts in QFT do not ...
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### Does every Hilbert Space carry a representation of Poincare group?

We know all infinite dimensional Hilbert Spaces are unitarily equivalent. It should follow therefore that if I have an unitary representation of say Lorentz or Poincare group on one infinite ...
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### Galileons and the brane origins of their Galilean invariance

I've been reading through a paper on Galileons by K. Hinterbichler et al. in which they discuss the brane origin of their Galilean invariance (starting on page 9) http://arxiv.org/abs/1008.1305 The ...
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### Why is the Poincaré group non-abelian?

Based on what I've learned, I gather the Poincaré group is the group of isometries of Minkowski spacetime and it is a non-abelian Lie group. Why is it non-abelian? Or perhaps rather, does the fact ...
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