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Charge conjugation and Maiorana spinors in dimension 8

Pertti Lounesto (1996)

Banach Center Publications

It is a common belief among theoretical physicists that the charge conjugation of the Dirac equation has an analogy in higher dimensional space-times so that in an 8-dimensional space-time there would also be Maiorana spinors as eigenspinors of a charge conjugation, which would swap the sign of the electric charge of the Dirac equation. This article shows that this mistaken belief is based on inadequate distinction between two kinds of charge conjugation: the electric conjugation swapping the sign...

Cocycle condition for multi-pullbacks of algebras

Piotr M. Hajac, Bartosz Zieliński (2012)

Banach Center Publications

Take finitely many topological spaces and for each pair of these spaces choose a pair of corresponding closed subspaces that are identified by a homeomorphism. We note that this gluing procedure does not guarantee that the building pieces, or the gluings of some pieces, are embedded in the space obtained by putting together all given ingredients. Dually, we show that a certain sufficient condition, called the cocycle condition, is also necessary to guarantee sheaf-like properties of surjective multi-pullbacks...

Contractions of Lie algebras and algebraic groups

Dietrich Burde (2007)

Archivum Mathematicum

Degenerations, contractions and deformations of various algebraic structures play an important role in mathematics and physics. There are many different definitions and special cases of these notions. We try to give a general definition which unifies these notions and shows the connections among them. Here we focus on contractions of Lie algebras and algebraic groups.

Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations

Angel Ballesteros, Mariano del Olmo (1997)

Banach Center Publications

Contractions of Poisson-Lie groups are introduced by using Lie bialgebra contractions. As an application, contractions of SL(2,R) Poisson-Lie groups leading to (1+1) Poincaré and Heisenberg structures are analysed. It is shown how the method here introduced allows a systematic construction of the Poisson structures associated to non-coboundary Lie bialgebras. Finally, it is sketched how contractions are also implemented after quantization by using the Lie bialgebra approach.

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