Spinors in euclidean field theory, complex structures and discrete symmetries

Understand

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.