Dirac and Majorana spinors on non-orientable Riemann surfaces
type: Item
instance of: scholarly article
title: Dirac and Majorana spinors on non-orientable Riemann surfaces
zbMATH Open document ID: 0628.53016
DOI: 10.1007/BF01219078
author: Ryan Rohm
author: Benjamín Grinstein
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: It is known that Weyl spinors cannot be consistently defined on non- orientable manifolds. In the present note the authors prove that Dirac spinors may be defined on non-orientable Riemann surfaces, and that Majorana spinors cannot be defined on closed non-orientable Riemann surfaces having an odd Euler number. The latter result shows that a procedure in superstring theory proposed by \textit{A. M. Polyakov} [Phys. Lett. 103 B, 207-210 (1981); ibid., 211-213 (1981)] is inconsistent.
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 53C80
zbMATH DE Number: 4022059
zbMATH Keywords: Dirac spinors
zbMATH Keywords: non-orientable Riemann surfaces
zbMATH Keywords: Euler number
zbMATH Keywords: superstring theory
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
cites work: Clifford modules
cites work: Q3660524
cites work: Topological quantization and cohomology
cites work: Characteristic Classes. (AM-76)
cites work: Q5522742
description: scientific article; zbMATH DE number 4022059