equations:dirac_equation
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equations:dirac_equation [2018/03/26 17:16] jakobadmin |
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| - | ====== Dirac Equation: $ \quad (i\gamma_\mu \partial^\mu - m ) \Psi =0 $ ====== | + | <WRAP lag>$ (i\gamma_\mu \partial^\mu - m ) \Psi =0 $</WRAP> |
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| + | ====== Dirac Equation ====== | ||
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| * $\partial _{\mu} $ denotes the partial derivative and $ \gamma_{\mu} \partial^{\mu}$ stands for a sum using the Einstein sum convention, i.e. $\gamma_{\mu} \partial ^{\mu} = \gamma_0 \partial^0 - \gamma_1 \partial^1 -\gamma_2 \partial^2 -\gamma_3 \partial^3$, | * $\partial _{\mu} $ denotes the partial derivative and $ \gamma_{\mu} \partial^{\mu}$ stands for a sum using the Einstein sum convention, i.e. $\gamma_{\mu} \partial ^{\mu} = \gamma_0 \partial^0 - \gamma_1 \partial^1 -\gamma_2 \partial^2 -\gamma_3 \partial^3$, | ||
| * $m$ denotes the mass of the particle, | * $m$ denotes the mass of the particle, | ||
| - | * $\Psi$ is either the wave function of the spin $1/2$ particle if we use the Dirac equation in a particle theory, or describes the spin $1/2$ field if we work in a field theory, | + | * $\Psi$ is either the wave function of the spin $1/2$ particle if we use the Dirac equation in a particle theory, or describes the spin $1/2$ field if we work in a field theory. In any case, $\Psi$ is not a vector but a [[advanced_tools:spinors|spinor]]. |
| * $\gamma_\mu$ are the Dirac gamma matrices. | * $\gamma_\mu$ are the Dirac gamma matrices. | ||
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equations/dirac_equation.txt · Last modified: 2023/04/02 03:11 by edi
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