- #1
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Hi,
I have a question about counting (how difficult should that be ;) )
I have the set of tensors in D dimensions
<br /> \{h_{\mu\nu}, H^{\mu\nu}, t_{\mu}, T^{\mu}\}<br />
with the relations
<br /> H^{\mu\nu} h_{\nu\rho} = \delta^{\mu}_{\rho} - T^{\mu}t_{\rho}<br />
<br /> T^{\mu}t_{\mu} = 1<br />
<br /> H^{\mu\nu}t_{\nu} = h_{\mu\nu}T^{\nu} = 0 <br />
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?
I have a question about counting (how difficult should that be ;) )
I have the set of tensors in D dimensions
<br /> \{h_{\mu\nu}, H^{\mu\nu}, t_{\mu}, T^{\mu}\}<br />
with the relations
<br /> H^{\mu\nu} h_{\nu\rho} = \delta^{\mu}_{\rho} - T^{\mu}t_{\rho}<br />
<br /> T^{\mu}t_{\mu} = 1<br />
<br /> H^{\mu\nu}t_{\nu} = h_{\mu\nu}T^{\nu} = 0 <br />
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?