New answers tagged

1

They shouldn't be thought of as operators i.e. $q$-numbers; instead, they should be thought of as $c$-numbers. They're mutually anticommuting but otherwise they play exactly the same role as $\Delta x^\mu$ for translations or angles $\varphi$ for rotations. They're spinor variables which means that under a Lorentz transformation $\Lambda\in SO(3,1)$, they ...


2

All the alternatives to the Dirac Lagrangian are actually forbidden by the requirement of requiring the hamiltonian to be well behaved (bounded from below and unbounded from above) and hermiticity of the action. To see this most simply we write the Lagrangian in terms of the fundamental left and right handed fields, $ \psi \equiv \left( \begin{array}{c} ...


5

Pauli matrices are the particular 3 Hermitian matrices with the 3 times 4 matrix entries or, more generally, three matrices obeying $$\sigma_a \sigma_b = i\epsilon_{abc} \sigma_c + 2\delta_{ab} {\bf 1} $$ Like density matrices for a 2-state system, they are $2\times 2$ matrices. But they cannot be density matrices themselves because their trace is zero ...


4

By definition, density matrices are positive semi-definite matrices with trace one. Pauli matrices are neither positive semi-definite nor do they have trace one (they have zero trace). Therefore, they cannot in any way be density matrices for states of spin systems. Of course, there is a connection to density matrices in the following way: The Pauli ...



Top 50 recent answers are included