Hamilton's equations and supersymplectic flows on (2,2)-dimensional superspace (Q1196138)

The authors write down Hamilton's equations on the supersymplectic superspace \(\mathbb{R}^{2\mid2}\) in full detail. These consist of six different sets of equations: one of them is Hamilton's equation on the underlying two-dimensional phase space, three are algebraic and two are dynamical. The algebraic equations play a crucial role in proving that the integral flow acts as a supersymplectic transformation of \(\mathbb{R}^{2\mid2}\) if and only if it is Hamiltonian. A remarkable fact is the appearance of a connection-type set of equations for parallel transport with structure group O\((1,1)\). Conditions under which the integral flow defines a supergroup action of \(\mathbb{R}^{1\mid1}\) are also presented.