"Klein-Gordon equation"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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==introduction== | ==introduction== | ||
* in condensed matter physics it describes long wavelength optical phonons | * in condensed matter physics it describes long wavelength optical phonons | ||
| − | * there are real KG equation and complex KG equation | + | * there are real KG equation and complex KG equation |
** real case describes electrically neutral particles | ** real case describes electrically neutral particles | ||
| − | ** | + | ** complex case describes charged particles |
* <math>(\Box + m^2) \psi = 0</math> i.e. <math>(\Box + m^2) \psi =\psi_{tt}-\psi_{xx}-\psi_{yy}-\psi_{zz}+m^2\psi=0</math> | * <math>(\Box + m^2) \psi = 0</math> i.e. <math>(\Box + m^2) \psi =\psi_{tt}-\psi_{xx}-\psi_{yy}-\psi_{zz}+m^2\psi=0</math> | ||
| − | * correct interpretations | + | * correct interpretations of <math>\phi</math> requires the idea of quantum field rather than the particle wavefunction |
** negative probability density -> charge density | ** negative probability density -> charge density | ||
| − | * Dirac suggested Dirac sea by invoking the exclusion principle and then KG equation | + | * Dirac suggested Dirac sea by invoking the exclusion principle and then KG equation only applicable to spinless particles |
| − | ** for example, | + | ** for example, <math>\pi</math>-meson |
| − | * Thus | + | * Thus the Dirac equation comes in to deal with spin-<math>1/2</math> particles. |
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==Lorentz invariant commutation relation== | ==Lorentz invariant commutation relation== | ||
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==related items== | ==related items== | ||
| 36번째 줄: | 36번째 줄: | ||
[[분류:physics]] | [[분류:physics]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
| + | [[분류:QFT]] | ||
| + | [[분류:migrate]] | ||
2020년 12월 28일 (월) 04:16 기준 최신판
introduction
- in condensed matter physics it describes long wavelength optical phonons
- there are real KG equation and complex KG equation
- real case describes electrically neutral particles
- complex case describes charged particles
- \((\Box + m^2) \psi = 0\) i.e. \((\Box + m^2) \psi =\psi_{tt}-\psi_{xx}-\psi_{yy}-\psi_{zz}+m^2\psi=0\)
- correct interpretations of \(\phi\) requires the idea of quantum field rather than the particle wavefunction
- negative probability density -> charge density
- Dirac suggested Dirac sea by invoking the exclusion principle and then KG equation only applicable to spinless particles
- for example, \(\pi\)-meson
- Thus the Dirac equation comes in to deal with spin-\(1/2\) particles.