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equations:dirac_equation [2018/03/26 17:16] jakobadmin |
equations:dirac_equation [2018/04/16 09:11] jakobadmin [Intuitive] |
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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 ====== | ||
<tabbox Intuitive> | <tabbox Intuitive> | ||
+ | The Dirac equation describes how the state of a relativistic (= fast moving) quantum system with half-integer spin changes in time. | ||
+ | |||
+ | The analogous equation for systems without spin is the [[equations:klein-gordon_equation|Klein-Gordon equation]]. | ||
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+ | If the system only moves slowly, the Dirac equation becomes the [[equations:pauli_equation|Pauli equation]]. | ||
- | <note tip> | ||
- | Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. | ||
- | </note> | ||
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<tabbox Concrete> | <tabbox Concrete> | ||
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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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