29 questions linked to/from Idea of Covering Group
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### Do the spinor transformation matrices form a matrix representation of the corresponding Lorentz group?

Suppose $\Psi$ is a Dirac spinor, then let the transformation matrix $S$ be defined as usual: $\Psi'=S(\Lambda)\Psi$, where $\Lambda$ is the Lorentz transformation matrix. Then the questions is: for ...
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### $SU(2)$ vs $SO(3)$ in Quantum Mechancs [duplicate]

When we're talking about spatial rotations is quantum mechanics, why do we need to resort to $SU(2)$? Why isn't $SO(3)$ enough? I've read that $SO(3)$ isn't simply connected, and I've read about ...
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### Understanding Group Theory in QFT

Recently it was asked what the reason for Pauli's Exclusion Principle, and the most well-recieved response looks like hieroglyphics to me: I think that while these "explanations" are all dancing ...
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### The role of SO(3) and SU(2) in quantum mechanics [duplicate]

When studying the irreducible representations of SO(3) one usually looks at the irreps of the infinitesimal rotations instead, i.e. the ones of so(3), the Lie Algebra of SO(3). The Irreps of so(3) can ...
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### Which matrices represent unitary projective representations of ${\rm SO(3)}$?

I was reading this post which triggered the following question. The group ${\rm SO(3)}$ is real orthogonal. However, it is possible to consider representations of ${\rm SO(3)}$ on a complex vector ...
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### $\mathrm{SU}(2)$ as a representation of the rotation group

I have read in a book that the group $\mathrm{SU}(2)$ is one of the irreducible representations of the rotation group. The book begin saying that the rotation group has 3 generators $J_{1}, J_{2}$ and ...
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### Can a spinor be defined as any quantity which transforms linearly under Lorentz transformations?

Recently I’ve come across a few papers from China (e.g. Xiang-Yao Wu et al., arXiv:1212.4028v1 14 Dec 2012) that make the following statement: ...any quantity which transforms linearly under ...
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### Relation between projective representations, connectivity of a group manifold and number of equivalence classes of paths

The projective unitary representations of a multiply-connected group $G$ is defined as $$U(g_1)U(g_2)=c(g_1,g_2)U(g_1g_2)$$ where $c(g_1,g_2)$ is phase. Reading various articles, and this old post of ...
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### Helicity quantization of massless particles

In Appendix B of QFT in a nutshell by Zee, a review of group theory is given. In the last paragraph of the appendix on page 533, he briefly discusses the helicity quantization of massless particles. ...