Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 31, No. 1, pp. 121-137 (2015)

Dual spaces, particle singularities and quartic geometry

Peter Rowlands

University of Liverpool

Abstract: Relativistic quantum mechanics and the properties of Dirac fermions can be generated in a particularly powerful way using two vector spaces which are commutative to each other and which contain identical information. The apparently broken symmetry between the two spaces observed through the quadratic geometry of ordinary space becomes a perfect and unbroken symmetry in the quartic geometry which defines the single physical quantity through which the two spaces can be combined.

Keywords: Dual vector spaces, nilpotent quantum mechanics, vacuum space, fermion singularity, H4 algebra.

Classification (MSC2000): 53B40; 53B50, 81Q05, 81R05, 81R25

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