Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-11-06
Int.J.Mod.Phys.A24:1333-1358,2009
Physics
High Energy Physics
High Energy Physics - Theory
LateX, 24 pages. This version includes the analysis of the case of massive field
Scientific paper
10.1142/S0217751X09042943
The problem of finding a formulation of Noether's theorem in noncommutative geometry is very important in order to obtain conserved currents and charges for particles in noncommutative spacetimes. In this paper, we formulate Noether's theorem for translations of kappa-Minkowski noncommutative spacetime on the basis of the 5-dimensional kappa-Poincare' covariant differential calculus. We focus our analysis on the simple case of free scalar theory. We obtain five conserved Noether currents, which give rise to five energy-momentum charges. By applying our result to plane waves it follows that the energy-momentum charges satisfy a special-relativity dispersion relation with a generalized mass given by the fifth charge. In this paper we provide also a rigorous derivation of the equation of motion from Hamilton's principle in noncommutative spacetime, which is necessary for the Noether analysis.
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