A special irreducible matrix representation of the real Clifford algebra C(3,1)

4x4 Dirac (gamma) matrices (irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many calculations in quantum physics. Although the final physical results do not depend on the applied representation of the Dirac matrices (e.g. due to the invariance of traces of products of Dirac matrices), the appropriate choice of the representation used may facilitate the analysis. The present paper introduces a particularly symmetric real representation of 4x4 Dirac matrices (Majorana representation) which may prove useful in the future. As a byproduct, a compact formula for (transformed) Pauli matrices is found. The consideration is based on the role played by isoclinic 2-planes in the geometry of the real Clifford algebra C(3,0) which provide an invariant geometric frame for it. It can be generalized to larger Clifford algebras.Comment: 23 pages LaTeX, to appear in the J. Math. Phys. (v2: appendix B on Pauli matrices and references are added, minor other changes

Case report 511

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46792/1/256_2004_Article_BF00366771.pd

Case report 511

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46790/1/256_2004_Article_BF00364055.pd

Dermacentor reticulatus: a vector on the rise

Dermacentor reticulatus is a hard tick species with extraordinary biological features. It has a high reproduction rate, a rapid developmental cycle, and is also able to overcome years of unfavourable conditions. Dermacentor reticulatus can survive under water for several months and is cold-hardy even compared to other tick species. It has a wide host range: over 60 different wild and domesticated hosts are known for the three active developmental stages. Its high adaptiveness gives an edge to this tick species as shown by new data on the emergence and establishment of D. reticulatus populations throughout Europe. The tick has been the research focus of a growing number of scientists, physicians and veterinarians. Within the Web of Science database, more than a fifth of the over 700 items published on this species between 1897 and 2015 appeared in the last three years (2013–2015). Here we attempt to synthesize current knowledge on the systematics, ecology, geographical distribution and recent spread of the species and to highlight the great spectrum of possible veterinary and public health threats it poses. Canine babesiosis caused by Babesia canis is a severe leading canine vector-borne disease in many endemic areas. Although less frequently than Ixodes ricinus, D. reticulatus adults bite humans and transmit several Rickettsia spp., Omsk haemorrhagic fever virus or Tick-borne encephalitis virus. We have not solely collected and reviewed the latest and fundamental scientific papers available in primary databases but also widened our scope to books, theses, conference papers and specialists colleagues’ experience where needed. Besides the dominant literature available in English, we also tried to access scientific literature in German, Russian and eastern European languages as well. We hope to inspire future research projects that are necessary to understand the basic life-cycle and ecology of this vector in order to understand and prevent disease threats. We conclude that although great strides have been made in our knowledge of the eco-epidemiology of this species, several gaps still need to be filled with basic research, targeting possible reservoir and vector roles and the key factors resulting in the observed geographical spread of D. reticulatus. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13071-016-1599-x) contains supplementary material, which is available to authorized users