Hovhannes Khudaverdyan (UMIST and Joint Institute of Nuclear Research)
khudian@umist.ac.uk
For a given configuration space M and a Lie algebra g acting on M we study the space V of Lagrangians for which the left-hand sides of the equations of motion are g-invariant. The problem is reformulated in terms of the double complex of the Lie algebra cochains taking values in the complex of Lagrangians. Calculating the cohomology of this complex by spectral sequences we arrive at the hierarchy in the space V which is a filtration of V by the kernels of certain homomorphisms taking values in the cohomology of the algebra g and the configuration space M. On the other hand, each such subspace is characterized by its physical properties which are revealed at the quantum-mechanical level.
Reference: http://www.emis.de/proceedings/SCCP97/8.html