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Math Help - Index notation meaning

  1. #1
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    Index notation meaning

    I'm studying Group Theory by myself and I face the basic concept regarding superscript and subscript indices on the Kronecker delta tensor:

    <br />
\delta^{\alpha\beta}<br />

    <br />
\delta^{\alpha}_{\beta}<br />

    What is the meaning (or difference) of these symbols?
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  2. #2
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    Quote Originally Posted by intervoxel View Post
    I'm studying Group Theory by myself and I face the basic concept regarding superscript and subscript indices on the Kronecker delta tensor:

    <br />
\delta^{\alpha\beta}<br />

    <br />
\delta^{\alpha}_{\beta}<br />

    What is the meaning (or difference) of these symbols?
    I thought I knew what the "Kroneker delta" was but it certainly isn't a tensor! [itex]\delta_{\alpha\beta}[/itex] is the array that is 1 if [itex]\alpha= \beta[/itex] and 0 otherwise. That doesn't depend on any coordinate system and so does not transform as a tensor would under a change of coordinate systems.
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  3. #3
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    Actually what I'm trying to understand are the following expressions which appeared when studying the SU(2) group:

    <br />
X^{\alpha}_{~\alpha'}X^{\beta}_{~\beta'}\delta^{\a  lpha'}_{ \beta'} = \delta^{\alpha}_{ \beta}<br />

    <br />
X^{\alpha}_{~\alpha'}X^{\beta}_{~\beta'}\delta^{\a  lpha'\beta'} \neq \delta^{\alpha\beta}<br />
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