Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-02-18
Physics
High Energy Physics
High Energy Physics - Theory
extended version, detailed discussion of four-dimensional euclidean Majorana spinors, extended descripton of complex structure
Scientific paper
We discuss fermions for arbitrary dimensions and signature of the metric, with special emphasis on euclidean space. Generalized Majorana spinors are defined for $d=2,3,4,8,9$ mod 8, independently of the signature. These objects permit a consistent analytic continuation of Majorana spinors in Min-kowski space to euclidean signature. Compatibility of charge conjugation with complex conjugation requires for euclidean signature a new complex structure which involves a reflection in euclidean time. The possible complex structures for Minkowski and euclidean signature can be understood in terms of a modulo two periodicity in the signature. The concepts of a real action and hermitean observables depend on the choice of the complex structure. For a real action the expectation values of all hermitean multi-fermion observables are real. This holds for arbitrary signature, including euclidean space. In particular, a chemical potential is compatible with a real action for the euclidean theory. We also discuss the discrete symmetries of parity, time reversal and charge conjugation for arbitrary dimension and signature.
No associations
LandOfFree
Spinors in euclidean field theory, complex structures and discrete symmetries does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spinors in euclidean field theory, complex structures and discrete symmetries, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spinors in euclidean field theory, complex structures and discrete symmetries will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-406426