  We report optical and infrared photometric and spectroscopic observations
that identify the counterpart to the 358.6-s X-ray transient pulsar SAX
J2103.5+4545 with a moderately reddened V=14.2 B0Ve star. This identification
makes SAX J2103.5+4545 the Be/X-ray binary with the shortest orbital period
known, Porb= 12.7 days. The amount of absorption to the system has been
estimated to be Av=4.2+-0.3, which for such an early-type star implies a
distance of about 6.5 kpc. The optical spectra reveal major and rapid changes
in the strength and shape of the Halpha line. The Halpha line was initially
observed as a double peak profile with the ratio of the intensities of the blue
over the red peak greater than one (V/R > 1). Two weeks later this ratio
reversed (V/R< 1). Subsequently, in less than a month, the emission ceased and
Halpha appeared in absorption. This fast spectral variability is interpreted
within the viscous decretion disc model and demonstrates the significant role
of the neutron star on the evolution of the circumstellar disc around the Be
star. The implications of the small orbit and moderate eccentricity on the spin
period of the neutron star are discussed.
