Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have a question about counting (how difficult should that be ;) )

I have the set of tensors in D dimensions

[tex]

\{h_{\mu\nu}, H^{\mu\nu}, t_{\mu}, T^{\mu}\}

[/tex]

with the relations

[tex]

H^{\mu\nu} h_{\nu\rho} = \delta^{\mu}_{\rho} - T^{\mu}t_{\rho}

[/tex]

[tex]

T^{\mu}t_{\mu} = 1

[/tex]

[tex]

H^{\mu\nu}t_{\nu} = h_{\mu\nu}T^{\nu} = 0

[/tex]

and h and H are symmetric tensors of rank (D-1).

The question now is: how many independent components does this set of fields constitute? Mathematica gives as answer 1\2D(D+1), the same amount as for a symmetric rank D tensor, but how can I derive this analytically?

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# Counting independent components

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