1971
DOI: 10.1007/bf03157082
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On the trace of the product of Pauli and Dirac matrices

Abstract: Several m e t h o d s for the d e t e r m i n a t i o n of the trace of the p r o d u c t of an a r b i t r a r y n u mber of Pauli matrices are established. F o r m u l a e are derived lar the evaluation of various types of products of two traces when terms ~~f theŸ a i l a i 2 . . . ~in occur in b o t h o f them. Expressions are found for the p r o d u c t of two different traces and the square of the trace of an a r b i t r a r y n u m b e r of Pauli matrices. Similar formulae are obtained when Dirac matric… Show more

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Cited by 9 publications
(8 citation statements)
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“…From considerations of QCD fragmentation, 16,17,18,19 copious photons are then expected to be produced. 20,21,22 In the Z-burst scenario 23,24,25 (ZB), photons are generated via the resonant production of Z bosons by UHE neutrinos annihilating on the relic neutrino background. In more "conventional" cosmic-ray models, nuclear primaries are accelerated at suitable astrophysical sites to ultra-high energy.…”
Section: Uhe Photons As Cosmic Raysmentioning
confidence: 99%
“…From considerations of QCD fragmentation, 16,17,18,19 copious photons are then expected to be produced. 20,21,22 In the Z-burst scenario 23,24,25 (ZB), photons are generated via the resonant production of Z bosons by UHE neutrinos annihilating on the relic neutrino background. In more "conventional" cosmic-ray models, nuclear primaries are accelerated at suitable astrophysical sites to ultra-high energy.…”
Section: Uhe Photons As Cosmic Raysmentioning
confidence: 99%
“…A significant fraction of the UHE cosmic rays are predicted by these models to be photons (see e.g. [4,5]). For instance, UHE photons may be produced uniformly in the universe by the decay/annihilation of relic topological defects (TD) [11].…”
Section: Photons As Cosmic-ray Primariesmentioning
confidence: 99%
“…It should be noted that the photon flux arriving at Earth for a specific source model is subject to uncertainties arising from photon propagation: assumptions concerning the very low frequency (few MHz) radio background and inter-galactic magnetic fields must be made [4,5]. The typical range of energy loss lengths usually adopted for photons are 7-15 Mpc at 10 EeV and Average depth of shower maximum <X max > versus energy simulated for primary photons, protons and iron nuclei.…”
Section: Photons As Cosmic-ray Primariesmentioning
confidence: 99%
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“…Also in the Z-burst model [5], large photon fractions are predicted. Stringent upper limits to photons would disfavour many realizations of these topdown models, although some uncertainty exists in calculating the propagation of UHE photons [6].…”
Section: Cosmic-ray Photonsmentioning
confidence: 99%