equations:dirac_equation
| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
|
equations:dirac_equation [2018/03/26 17:15] jakobadmin |
equations:dirac_equation [2018/03/28 10:24] jakobadmin |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | ====== Dirac Equation: $ \quad (i\gamma_\mu \partial^\mu - m ) \Psi =0 $ ====== | + | <WRAP lag>$ (i\gamma_\mu \partial^\mu - m ) \Psi =0 $</WRAP> |
| + | ====== Dirac Equation ====== | ||
| - | </note> | ||
| - | + | <tabbox Intuitive> | |
| - | <tabbox Why is it interesting?> | + | |
| - | + | ||
| - | The Dirac equation is the correct equation of motion that describes free [[basic_notions:spin|spin]] $1/2$ particles. | + | |
| - | + | ||
| - | + | ||
| - | + | ||
| - | <blockquote>In fact, Dirac's equation for the electron must be rated, alongside the [[equations:maxwell_equations|Maxwell]] and [[equations:einstein_equation|Einstein equations]], as one of the Great Field Equations of physics.<cite>page 289 in "The Emperors new Mind" by Penrose</cite></blockquote> | + | |
| - | <tabbox Layman> | + | |
| <note tip> | <note tip> | ||
| Line 18: | Line 10: | ||
| </note> | </note> | ||
| | | ||
| - | <tabbox Student> | + | <tabbox Concrete> |
| * A nice discussion can be found in [[http://www.quantumfieldtheory.info/website_Chap04.pdf |chapter 4 of Klauber's Student Friendly QFT book]] | * A nice discussion can be found in [[http://www.quantumfieldtheory.info/website_Chap04.pdf |chapter 4 of Klauber's Student Friendly QFT book]] | ||
| Line 32: | Line 24: | ||
| * For a nice description, see section 7.4.3 "Diracology" in the book The Conceptual Framework of Quantum Field Theory by Duncan | * For a nice description, see section 7.4.3 "Diracology" in the book The Conceptual Framework of Quantum Field Theory by Duncan | ||
| - | <tabbox Researcher> | + | <tabbox Abstract> |
| <note tip> | <note tip> | ||
| The motto in this section is: //the higher the level of abstraction, the better//. | The motto in this section is: //the higher the level of abstraction, the better//. | ||
| </note> | </note> | ||
| + | |||
| + | <tabbox Why is it interesting?> | ||
| + | |||
| + | The Dirac equation is the correct equation of motion that describes free [[basic_notions:spin|spin]] $1/2$ particles. | ||
| + | |||
| + | |||
| + | |||
| + | <blockquote>In fact, Dirac's equation for the electron must be rated, alongside the [[equations:maxwell_equations|Maxwell]] and [[equations:einstein_equation|Einstein equations]], as one of the Great Field Equations of physics.<cite>page 289 in "The Emperors new Mind" by Penrose</cite></blockquote> | ||
| <tabbox Definitions> | <tabbox Definitions> | ||
| Line 43: | Line 43: | ||
| * $\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. | ||
| | | ||
equations/dirac_equation.txt · Last modified: 2023/04/02 03:11 by edi
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
