caa a22 4500 463197313 CHVBK 20180406164926.0 cr unu---uuuuu 170326e20070501xx s 000 0 eng 10.1007/s10773-006-9273-2 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9273-2 Dick Rainer Physics & Engineering Physics, University of Saskatchewan, 116 Science Place, S7N 5E2, Saskatoon, SK, Canada aut Half-Differentials versus Spinor Formalism for Fermions in Low-Dimensional Systems [Elektronische Daten] [Rainer Dick] The description of fermions on curved manifolds or in curvilinear coordinates usually requires a vielbein formalism to define Dirac γ-matrices or Pauli matrices on the manifold. Derivatives of the vielbein also enter equations of motion for fermions through the spin connection, which gauges local rotations or Lorentz transformations of tangent planes. The present paper serves a dual purpose. First we will see how the zweibein formalism on surfaces emerges from constraining fermions to submanifolds of Minkowski space. In the second part, I will explain how in two dimensions the zweibein can be absorbed into the spinors to form half-order differentials. The interesting point about half-order differentials is that their derivative terms along a two-dimensional submanifold of Minkoski space look exactly like ordinary spinor derivatives in Cartesian coordinates on a planar surface, although there is a prize to pay in the form of a local mass term. The advantage of half-order differentials is that they allow for the use of the conformal field concept of conformal field theory even in low-dimensional fermion systems without conformal symmetry. Springer Science+Business Media, LLC, 2007 spinors nationallicence fermions in low-dimensional systems nationallicence International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/5(2007-05-01), 1334-1359 0020-7748 46:5<1334 2007 46 10773 https://doi.org/10.1007/s10773-006-9273-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9273-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dick Rainer Physics & Engineering Physics, University of Saskatchewan, 116 Science Place, S7N 5E2, Saskatoon, SK, Canada aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/5(2007-05-01), 1334-1359 0020-7748 46:5<1334 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer