Spin-One Klein Gordon Equation

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SUMMARY

The spin-one Klein-Gordon equation, also known as the Proca equation, is represented by the formula $$(\square - m^2)A^\mu = \partial^\mu \partial^\nu A_\nu$$. This equation describes fields with definite mass and is derived from the Klein-Gordon equation $$(\square - m^2)\phi=0$$ by applying the additional condition $$\partial_\nu A^\nu=0$$. Understanding this equation is crucial for analyzing quantum fields associated with spin-one particles.

PREREQUISITES
  • Familiarity with the Klein-Gordon equation
  • Understanding of quantum field theory
  • Knowledge of four-vectors in physics
  • Basic concepts of mass and spin in particle physics
NEXT STEPS
  • Study the derivation of the Proca equation in detail
  • Explore applications of the Proca equation in quantum field theory
  • Learn about the implications of gauge invariance in spin-one fields
  • Investigate the relationship between the Klein-Gordon equation and other field equations
USEFUL FOR

Physicists, particularly those specializing in quantum field theory, particle physicists, and students studying advanced theoretical physics concepts related to spin and mass.

Jogging-Joe
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TL;DR
The spin zero Klein Gordon equation is commonly discussed. How about the spin one Klein Gordon Equation?
What is the spin one Klein Gordon Equation? What is the formula for the conserved current, i.e. the electric current density four-vector?
 
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I don't know what do you understand by the spin-one KG equation...
But the KG equation is just ##(\square - m^2)\phi=0##.
So I would say that the KG equation for spin-one is just $$(\square - m^2)A^\mu=0$$
 
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Gaussian97 said:
I don't know what do you understand by the spin-one KG equation...
But the KG equation is just ##(\square - m^2)\phi=0##.
So I would say that the KG equation for spin-one is just $$(\square - m^2)A^\mu=0$$
Yes, and it's called Proca equation.
 
Well, technically the Proca equation is ##(\square - m^2)A^\mu = \partial^\mu \partial^\nu A_\nu##.
Klein-Gordon equation should (as far as I know), be fulfilled by any field with definite mass, since it's the quantum version of ##p^2 + m^2 = 0##.
To obtain the Proca equation you need the extra condition ##\partial_\nu A^\nu=0##.
 
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