English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The second order symmetry operators that commute with the Dirac operator withexternal vector, scalar and pseudo-scalar potentials are computed on a generaltwo-dimensional spin-manifold. It is shown that the operator is defined interms of Killing vectors, valence two Killing tensors and scalar fields definedon the background manifold. The commuting operator that arises from anon-trivial Killing tensor is determined with respect to the associated systemof Liouville coordinates and compared to the the second order operator thatarises from that obtained from the unique separation scheme associated withsuch operators. It shown by the study of several examples that the operatorsarising from these two approaches coincide.

Symmetry operators and separation of variables for Dirac's equation on two-dimensional spin manifolds with external fields