# Tagged Questions

Group theory is a branch of abstract algebra. A group is a set of objects, together with a binary operation, that satisfies four axioms. The set must be closed under the operation and contain an identity object. Every object in the set must have an inverse, and the operation must be associative. ...

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### How can the Gallilean transformations form a group?

In class my professor said the Galilean transformations form a group of order 10. $$x'=x-vt\\ y'=y\\ z'=z\\ t'=t\\$$ But how do these form a group? I don't see 10 things to interpret as elements. I ...
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### Different ways of derivation of Gell-Mann-Okubo mass formula

Recently my teacher told me that there are many ways of deriving the Gell-Mann-Okubo mass formula by using group representation theory (by using dynamical group etc). Where can I read about these ways?...
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### Vector spaces for the irreducible representations of the Lorentz Group

EDIT: The vector space for the $(\frac{1}{2},0)$ Representation is $\mathbb{C}^2$ as mentioned by Qmechanic in the comments to his answer below! The vector spaces for the other representations remain ...
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### What is “a vector of $SO(n)$”?

I'm watching (or trying to watch) this lecture from NPTEL on classical field theory. I've understood everything in the series up till this point, including the first half of the lecture on elementary ...
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### Why is only the third component of weak isospin used as a conserved quantity?

Using Noether's theorem $$\partial_0 \int d^3x \left(\frac{\partial L}{\partial(\partial_0\Psi)} \delta \Psi \right) = 0$$ we get three conserved quantites $Q_i$ from ...
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### Is the Standard Model an invariant subgroup of $SU(5)$?

It is well known that the Standard Model (SM) gauge group is a subgroup of $SU(5)$: $$SU(3) \times SU(2)\times U(1) ~\subset~SU(5)$$ This can be easily checked using the ...
### Difference between the 1/2 representation of $SU(2)$ and the (1/2,1) representation of $SU(2)\times SU(2)$? [closed]
What's the difference between the $j = 1/2$ representation of $SU(2)$ and the $(j,j') = ( 1/2 , 1 )$ representation of $SU(2)\times SU(2)$?