  Effect of the temperature and magnetic field induced martensitic
transformation (MT) on the electronic structure and some physical properties of
bulk Fe$_{45.2}$Mn$_{25.9}$Ga$_{28.9}$ Heusler alloy has been investigated.
{According to the experimental results of DSC, magnetic and transport
measurements direct and reverse martensitic transformation without external
magnetic field takes place within 194 $\leq T \leq$ 328 K temperature range
with a hysteresis up to $\Delta T \approx$ 100 K defined as $\Delta T$ =
$A_{f,s}$ - $M_{s,f}$, where $A_{f,s}$ and $M_{s,f}$ are the critical
temperatures of direct and reverse martensitic transformation. External
magnetic field of $\mu_{0}H$ = 5 T causes a high-temperature shift of MT
temperatures.} MT from parent austenite L2$_{1}$ phase to martensitic
tetragonally distorted L2$_{1}$ one (i. e. to L1$_{0}$) causes significant
changes in the electronic structure of alloy, a drastic increase in alloy
magnetization, a decrease in the alloy resistivity, and a reversal of the sign
of the temperature coefficient of resistivity from negative to positive. At the
same time experimentally determined optical properties of
Fe$_{45.6}$Mn$_{25.9}$Ga$_{28.9}$ Heusler alloy in austenitic and martensitic
states look visually rather similar being noticeable different in microscopic
nature as can be concluded from first-principle calculations. Experimentally
observed changes in the physical properties of the alloy are discussed in terms
of the electronic structures of an austenite and martensite phases.
