Einstein summation notation, ambiguity?

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  • Thread starter Hiero
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  • #1
Hiero
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If I see ##f(x_ie_i)## I assume it means ##f(\Sigma x_ie_i)## (summing in the domain of f) but what if I instead wanted to write ##\Sigma f(x_ie_i)## (summing in the range)?

Is there a way to distinguish between these in Einstein’s summation notation?
 

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  • #2
PAllen
Science Advisor
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This is an odd case, but I think if you want the latter, in a context where Einstein summation is implied, you have to write it explicitly, overriding the convention. Only first case is handled by the summation convention.
 
  • #3
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Is there a way to distinguish between these in Einstein’s summation notation?
So ##f(\Sigma x^{\mu}e_{\mu})## is ##f(x^{\mu}e_{\mu})## and ##\Sigma f(x^{\mu}e_{\mu})## is ##f(x^{\mu}e_{\nu})\delta^{\nu}_{\mu}##
 
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Likes andresB, sophiecentaur, PeroK and 1 other person
  • #4
Hiero
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So ##f(\Sigma x^{\mu}e_{\mu})## is ##f(x^{\mu}e_{\mu})## and ##\Sigma f(x^{\mu}e_{\mu})## is ##f(x^{\mu}e_{\nu})\delta^{\nu}_{\mu}##
Oh wow, that’s clever! Thanks for the insight.
 

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