2002/02/28 by Stephen C. Anco, Juha Pohjanpelto
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conserved current #Conserved quantity #Cosmology and Gravitation Theories #Electromagnetic field #Graviton #Massless particle #Parity (physics) #Pulsars and Gravitational Waves Research #Spin (aerodynamics) #Spinor #Tensor (intrinsic definition) #math-ph #math.MP #msc:35Q75 #msc:70S10 #msc:81R25
paper · pdf · doi:10.1098/rspa.2002.1070
published as Proc.Roy.Soc.Lond. A459 (2003) 1215-1240 · 26 pages; final version with minor changes, accepted in Proc. Roy. Soc. A (London)
arxiv created 2002/10/12 · openalex publication_date 2003/05/08 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A complete and explicit classification of all locally constructed conserved currents and underlying conserved tensors is obtained for massless linear symmetric spinor fields of any spin s ≤1/2 in four–dimensional flat spacetime. These results generalize the recent classification in the spin s = 1 case of all conserved currents locally constructed from the electromagnetic spinor field. The present classification yields spin s ≤1/2 analogues of the well–known electromagnetic stress–energy tensor and Lipkin's zilch tensor, as well as a spin s ≤1/2 analogue of a novel chiral tensor found in the spin s = 1 case. The chiral tensor possesses odd parity under a duality symmetry (i.e. a phase rotation) on the spin–s field, in contrast to the even parity of the stress–energy and zilch tensors. As a main result, it is shown that every locally constructed conserved current for each s ≤1/2 is equivalent to a sum of elementary linear conserved currents, quadratic conserved currents associated with the stress–energy, zilch and chiral tensors, and higher–derivative extensions of these currents in which the spin–s field is replaced by its repeated conformally weighted Lie derivatives with respect to conformal Killing vectors of flat spacetime. Moreover, all of the currents have a direct unified characterization in terms of Killing spinors. The cases s = 2, s = 1/2 and s = 3/2 provide a complete set of conserved quantities for propagation of gravitons (i.e. linearized gravity waves), neutrinos and gravitinos, respectively, on flat spacetime. The physical meaning of the zilch and chiral quantities is discussed.