Reparametrization invariance in scalar QFT: What does it mean, exactly? In the Cecotti's book "Supersymmetric Field Theories" he wrote " Physical quantities are independent of the fields we use to parametrize the configuration, that is, observables are invariant under field reparametrizations of the form  $\phi^i \rightarrow \varphi^i(\phi)$ " 
Can anyone explain to me what this means ? or, in other words, what is the principle to it he had referred ?
Edit: My question is: is this reparametrization invariance for all fields (e.g vector and spinor fields) or just for the scalar fields ?, is QFT a repametrization invariant theory? and can we consider the gauge invariance as a repametrization invariance? [I don't know also why one does not take this reparametrization invariance as a constraint, like the gauge invariance, which must reduce the number of degrees of freedom of the fields!!] 
 A: Have you read the whole page, not just this sentence? I really don't know how to explain that differently.
It's analog to the general relativity. You can perform coordinate diffeomorphisms,
$$x^\mu\mapsto \tilde{x}^\alpha(x^\mu)$$
and they all get compensated by change of the spacetime metrics $g_{\mu\nu}$,
$$g_{\mu\nu}\mapsto \tilde{g}_{\alpha\beta}=\frac{\partial\tilde{x}^\mu}{\partial x^\alpha}g_{\mu\nu}\frac{\partial\tilde{x}^\nu}{\partial x^\beta}$$
Likewise here you can compensate arbitrary field diffeomorphism you wrote by change of the target space metrics $g_{ij}$ i.e. metrics of the manifold for which the fields $\phi^i$ serve as coordinates. Note that it's different from the spacetime metrics! So you have two metrics - one for spacetime and the different one for the target space.
So this principle is similar to the general covariance of the general relativity. As a matter of fact it is the general covariance in the string theory. There the physical spacetime arises as a target space for fields $X^A(\tau,\sigma)$ on the two-dimensional worldsheet.
