...S.Ansoldi¹

E-mail address: ansoldi@trieste.infn.it

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...A.Aurilia²

E-mail address: aaurilia@csupomona.edu

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...E.Spallucci³

E-mail address: spallucci@vstst0.ts.infn.it

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... constant⁴

The normalization constant will be fixed after all the functional integrations are carried out, by imposing the boundary condition

$$lim _{A \rightarrow 0} K[ x (s) , x _{0} (s) ; A ] = \delta [ x (s) , x _{0} (s)] \ .$$ (16)

Such a procedure effectively amounts to a renormalization of the field-dependent determinants produced by gaussian integration.

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...$\delta / \delta \sigma ^{\mu\nu} (s)$⁵

Functional and area derivatives are related by [13]

$$\frac{\delta}{\delta x ^{\mu} (s)} = x ^{\, \prime \, \nu} ... ...quad x ^{\, \prime \, \nu} \equiv \frac{dx ^{\nu}}{ds} \ .$$

Therefore, the functional wave equation can be written in terms of either type of derivative. Contrary to the statement in ref.[7], area derivatives are regular even when ordinary functional derivatives are not [13].

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