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Suppose, I have a relation of the form

[tex]

f(p_{\mu},q_{\mu})=0

[/tex]

Then can I multiply the both sides by [tex]p^{\mu}[/tex] and then contract?

[tex]

p^{\mu}f(p_{\mu},q_{\mu})=0

[/tex]

After this I want to use the identity [tex]p^{\mu}p_{\mu}=m^2[/tex] as known in special relativity. So I am first multiplying both sides by a contravariant tensor and then using the summation convention. The question is am I doing it right? I feel this is a valid operation and I have tested one simple example where this is valid but I am not able to prove it in general. Can anybody help? You may refer to some books or website also where I can look up.