Local Scale Invariance (LSI) is a theory for anisotropic critical phenomena
designed in the spirit of conformal invariance. For a given representation of
its generators it makes non-trivial predictions about the form of universal
scaling functions. In the past decade several representations have been
identified and the corresponding predictions were confirmed for various
anisotropic critical systems. Such tests are usually based on a comparison of
two-point quantities such as autocorrelation and response functions. The
present work highlights a potential problem of the theory in the sense that it
may predict any type of two-point function. More specifically, it is argued
that for a given two-point correlator it is possible to construct a
representation of the generators which exactly reproduces this particular
correlator. This observation calls for a critical examination of the predictive
content of the theory.Comment: 17 pages, 2 eps figure
