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equations:klein-gordon_equation

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equations:klein-gordon_equation [2019/07/30 08:32]
60.52.77.62 [Klein-Gordon Equation]
equations:klein-gordon_equation [2019/07/30 08:46]
60.52.77.62 [Klein-Gordon Equation]
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   * $\partial _{\mu} $ denotes the partial derivative and $\partial _{\mu} \partial ^{\mu}$ stands for a sum using the Einstein sum convention, i.e. $\partial _{\mu} \partial ^{\mu} =  \partial _0 \partial^0 - \partial _1 \partial^1 -\partial _2 \partial^2 -\partial _3 \partial^3$,​   * $\partial _{\mu} $ denotes the partial derivative and $\partial _{\mu} \partial ^{\mu}$ stands for a sum using the Einstein sum convention, i.e. $\partial _{\mu} \partial ^{\mu} =  \partial _0 \partial^0 - \partial _1 \partial^1 -\partial _2 \partial^2 -\partial _3 \partial^3$,​
   * $m$ denotes the mass of the particle,   * $m$ denotes the mass of the particle,
-  * $\Phi$ ​is either the wave function of the spin $0$ particle ​if we use the Klein-Gordon equation ​in a particle ​theory, or describes the spin $0$ field if we work in a field theory. ​+  * $\Phi$ ​describes ​the spin $0$ field if we work in a field theory.  
 +  * Note: $\Phicannot be interpreted as a wavefunction because it is a real valued ​field; it is its own anti-particle like the Majorana fermion. Only in the case that it is the U(1)-charged (requires 2 independent real Klein Gordon fields that are symmetry transform into each other) is naive wavefunction interpretation possible. Basically, you get a relativistic scalar superfluid ​field. Nevertheless,​ there are single particle wavefunctions lurking in the single real Klein-Gordon ​theory. But you need to use the coherent state representation to see the 1st quantized operators from the complex annihilation and creation operators. Essentially undoing the second quantization
  
  
equations/klein-gordon_equation.txt · Last modified: 2023/04/02 03:24 by edi