Can Adding a Constant to the D'Alembertian Maintain Relativistic Invariance?

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SUMMARY

The discussion centers on the concept of adding a constant multiplied by the scalar field \(\phi\) to the D'Alembertian operator while maintaining relativistic invariance, as highlighted in Feynman's Lectures on Physics, Volume 2, Section 28-6. The key conclusion is that the sum of two invariant quantities remains invariant, and since the derivative of a constant with respect to any variable is zero, this addition does not disrupt the invariance. A mathematical proof is sought to further elucidate this concept.

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In Feynman lectures in physics v2 28-6, Feynman points out that we can add a constant times [itex]\phi[/itex] to D'Alembertian without distrupting the relativistic invariance. How and why?? Can someone work out a mathematical proof?

Thanks in advance.
 
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The sum of two invariant quantities is an invariant quantity.
 
The derivative of a constant wrt any variable is zero.
 

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