  Some problems with the recent stimulating proposal of a ``Gauge Theory of
Finance'' by Ilinski and collaborators are outlined. First, the derivation of
the log-normal distribution is shown equivalent both in information and
mathematical content to the simpler and well-known derivation, dating back from
Bachelier and Samuelson. Similarly, the re-derivation of Black-Scholes equation
is shown equivalent to the standard one because the limit of no uncertainty is
equivalent to the standard risk-free replication argument. Both re-derivations
of the log-normality and Black-Scholes result do not provide a test of the
theory because it is degenerate in the limits where these results apply. Third,
the choice of the exponential form a la Boltzmann, of the weight of a given
market configuration, is a key postulate that requires justification. In
addition, the ``Gauge Theory of Finance'' seems to lead to ``virtual''
arbitrage opportunities for pure Markov random walk market when there should be
none. These remarks are offered in the hope to improve the formulation of the
``Gauge Theory of Finance'' into a coherent and useful framework.
