... 1
E-mail address: ansoldi@trieste.infn.it 
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... Castro2
E-mail address: castro@ctsps.cau.edu 
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...E.Spallucci3
E-mail address: spallucci@vstst0.ts.infn.it 
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... dimensions4
If we keep $m_{p+1}\ne 0$ the brane coordinates have canonical dimension of length, while the world and the induced metric are dimensionless (in units $\hbar=1$, $c=1$), i.e. $[ Y^\mu ]=M^{-1}$, $[ \gamma_{mn} ]=[ g_{mn} ]=1$. 
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... trajectory5
The same kind of ``collapse'' around the classical trajectory has been introduced in string theory [11] to pick up the Eguchi ``Area dynamics'' [12]. For a pedagogical introduction to this new path-integral manipulation see [13], where it has been applied to a simpler case, the non-relativistic point particle propagator. 
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