On the graded Lie algebra of quantisable forms

Josef Janyška and Marco Modugno

E-mail: janyska@math.muni.cz, modugno@dma.unifi.it

Abstract. A quantisable form is defined to be a form on the 1-jet space of spacetime whose Hamiltonian lift is a tangent valued form projectable on spacetime. The quantisable forms constitute a graded Lie algebra with respect to a natural bracket. A natural homomorphism from the algebra of quantisable forms to the Fr\"olicher--Nijenhuis algebra of tangent valued forms on the spacetime is exhibited.

AMSclassification. 53C05, 58A20, 70H40, 81S10, 83C10

Keywords. Galilei spacetime, phase space, jets, connections, Hamiltonian lift, quantisable form