# Questions tagged [group-theory]

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. Groups are used in physics to describe symmetry operations of physical systems.

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### What is light cone? Explain to mathematicians who understand the Lorentz group but not light cone

Mathematically the Lorentz group is precisely the $O(1,3)$ is the 4-vector rotation preserving the inner product of 4-vector under this metric $$\eta_{\mu \nu}=(+1,-1,-1,-1).$$ There are four ...
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### Physically, what is a pseudoreal representation?

There are three kinds of representations: real, complex, and pseudoreal. A complex representation is not equivalent to its conjugate, and a real one is, which is pretty straightforward. A pseudoreal ...
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### Parameters in Lie group theory

This is from P.Woit's "Quantum Theory, Groups and Representations", p. 151. If the Hilbert space is the space of complex-valued square-integrable functions on the circle, we want to find the ...
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### How to determine which irrep the Hilbert space of states carry?

Is the following statement ([1]) correct? [1] If the universe has a symmetry under a group $G$, does this mean the Hilbert space carries a unitary representation formed by taking the direct product of ...
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### Why is group theory important in General Relativity?

I came across the Poincaré group, and most importantly the Lorentz group while studying GR. What is the significance of these groups as well as any other groups used in GR? I mean, why should I care ...
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### Missing complex conjugate in (1/2,1/2) representation of Lorentz group Ticciati QFT

I've been working through some computations involving representations of the Lorentz group (now using the fantastic Ticciati QFT textbook). After some work, Ticciati gives the following formula D^{...
### 10-dimensional and 15-dimensional matrix representations of $SU(5)$: explicit 24 Lie algebra generators
There are some previous discussions in this post Representation of the $\rm SU(5)$ model in GUT which confused me. So I want to follow up with a new question. It is easy to write down the 5-...