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The fact that the Pauli matrices, along with the identity matrix I, form an orthogonal basis for the Hilbert space of all 2 × 2 complex matrices , over , means that we can express any 2 × 2 complex matrix M as = + where c is a complex number, and a is a 3-component, complex vector.
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= ¯ (′) where B μ is the U(1) gauge field; Y W is the weak hypercharge (the generator of the U(1) group); W μ is the three-component SU(2) gauge field; and the components of τ are the Pauli matrices (infinitesimal generators of the SU(2) group) whose eigenvalues give the weak isospin.
Pauli matrices, also called the "Pauli spin matrices". Generalizations of Pauli matrices; Gamma matrices, which can be represented in terms of the Pauli matrices.
The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli. The Pauli group on n {\displaystyle n} qubits, G n {\displaystyle G_{n}} , is the group generated by the operators described above applied to each of n {\displaystyle n} qubits in the tensor product Hilbert space ( C 2 ) ⊗ n {\displaystyle ...
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We first define the generators of 𝔰𝔲(N), based on a generalisation of the Pauli matrices and of the Gell-Mann matrices (using the bra-ket notation where | | is the matrix unit). There are N ( N − 1 ) / 2 {\displaystyle N(N-1)/2} symmetric matrices,