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CCCC – p. 7
Energy conservation
[with M Kagan, G Hossain, C Tomlin: arXiv:1302.5695]
N √ deth∇ µ T µ 0 = −N ∂H matter
∂t
−N a∂Dmatter a
∂t
+L ⃗N C matter [N,N a ]+ ∂h ab
∂t
+∂ b
(
N 2 h ab D matter
a
δH matter
δh ab
)
+2N c h baδH matter
δh ac
Classical off-shell algebra: ∂H matter /∂t = {H matter ,H[N,N a ]}
cancels ∂ a (N 2 D matter
a ), only one term from ∂ b T b 0.
→ Deformed algebra cannot be taken care of by modified
coefficients in ∇ µ T µ ν = 0.
→ No energy conservation if off-shell algebra broken
(or unchecked in gauge-fixed/deparameterized models).