Mathematical physics and field equations

In the field of mathematical physics, new equations for massless fields which are invariant under the Galilei transformation have been derived in papers [1-4] by contraction of relativistic wave equations. The resulting equations can be used for description of many physically consistent systems, e.g. electromagnetic fields in many different media or within the framework of Galilean Chern-Simons models. Classification of all linear and non linear Galilean invariant equations for massless fields has been accomplished as well. A new superfield approach to supersymmetric mechanics using the biharmonic superspace has been suggested in paper [5]. It is an extension of superspace by means of two sets of harmonic variables corresponding to two SU(2) factors of the R-symmetric SO(4) group of the Poincare superalgebra. The main advantage of the biharmonic superspace method is the fact that it makes it possible to deal with the supermultiplets with finite number of off-shell components in the same manner as with their mirror counterparts.

Significant publications

[1] J. Niederle and A. G. Nikitin: Galilean equations for massless fields. J. Phys. A: Math. Theor. 42 (2009) 105207 (19p)

[2] J. Niederle and A. G. Nikitin, Galilei-invariant equations for massive fields. J. Phys. A: Math. Theor. 42 (2009) 245209 (25p)

[3] J. Niederle and A. G. Nikitin: Galilean massless fields. In: Proceedings of 4th workshop Group Analysis of Differential Equations and Integrable Systems", Protaras, Cyprus, ISBN 978-9963-869-12-5, Cyprus University, 2009, pp. 164-172

[4] J. Niederle, A.G. Nikitin and O. Kuriksha, Maxwell-Chern-Simons models: their symmetries, exact solutions and non-relativistic limits. Proc of Niederle Fest. 2009, 10p

[5] E. Ivanov, J. Niederle: Biharmonic superspace for N=4 mechanics. Phys. Rev. D 80, 065027 (2009) [23 pages]

Researcher:

Jiří Niederle