query: Why does $(\frac{1}{2}, \frac{1}{2})$ representation of $SO(1,3)$ Lorentz group act on $2\times2$ Hermitian matrices?
positive_passages.docid: 153205
positive_passages.text: Why is the $(\frac{1}{2},\frac{1}{2})$ representation of the Lorentz group realized as the vector space of Hermitian $2\times 2$ matrices?
negative_passages.docid: 72548
negative_passages.text: Lie group embeddings $SO(10) \supset SU(3) \times SU(2) \times U(1)?$
negative_passages.docid: 100142
negative_passages.text: Is the Pauli group for $n$-qubits a basis for $\mathbb{C}^{2^n\times 2^n}$?
negative_passages.docid: 71245
negative_passages.text: $2 \times 2 $ Orthogonal Group
negative_passages.docid: 58445
negative_passages.text: What does the Canonical Commutation Relation (CCR) tell me about the overlap between Position and Momentum bases?
negative_passages.docid: 38723
negative_passages.text: Can Poincare representations be embedded in non-standard Lorentz representations?
negative_passages.docid: 50572
negative_passages.text: Is there a general theorem stating why the restricted Lorentz group's exponential map is surjective?
negative_passages.docid: 22024
negative_passages.text: How to prove that orthochronous Lorentz transformations $O^+(1,3)$ form a group?
negative_passages.docid: 68014
negative_passages.text: Prove that $\mathfrak{su}(2)$ is not isomorphic to $\mathfrak{sl}(2,\mathbb R)$
negative_passages.docid: 83747
negative_passages.text: $2$ out of $3$ property of the unitary group
negative_passages.docid: 7530
negative_passages.text: Why this $\sigma \pi \sigma^{-1}$ keeps appearing in my group theory book? (cycle decomposition)
negative_passages.docid: 90778
negative_passages.text: Faithful representation of the Heisenberg group
negative_passages.docid: 156543
negative_passages.text: What is the significance of Lie groups $SO(3)$ and $SU(2)$ to particle physics?
negative_passages.docid: 143315
negative_passages.text: How does the Lorentz group act on a 4-vector in the spinor-helicity formalism $p_{\alpha\dot{\alpha}}$?
negative_passages.docid: 68267
negative_passages.text: $SU(3)$ irreducible representations with tensor method
negative_passages.docid: 54119
negative_passages.text: Product of $SU(2)$ representations
negative_passages.docid: 43004
negative_passages.text: Why are there $|G/G'|$ 1-dimensional representations of $G$?