Here, is the Killing form on g, and thus the first term is the standard kinetic term of quantum field theory.
The second piece is the gauge field superpotential that produces the kinetic terms for the gauge bosons and gauginos.
However, finding suitable kinetic terms for the resulting massive spin connection, free of ghosts and tachyons, remains an open problem.
The motion of a free particle on a curved surface still has exactly the same form as above, i.e. consisting entirely of a kinetic term.
This Hamiltonian consists entirely of the kinetic term.
The "interacting" part can very well also contain quadratic kinetic terms.
This kinetic term can be considered a string field theory in its own right: the string field theory of free strings.
In fact, it has been proven that the activation energy for the chloride ion is very low, hence favorable in kinetic terms.
The equation of motion derived from such a Lagrangian contains differential operators which are generated by the kinetic term.
A free particle can be represented by a mass term, and a kinetic term which relates to the "motion" of the fields.