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/

Zendy Plus

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

Zendy Tools

Zendy Open

A search for fundamental (Galilean invariant) dynamical equations for two andfour-component spinor wave functions is conducted in Galilean space-time. Adynamical equation is considered as fundamental if it is invariant under thesymmetry operators of the group of the Galilei metric and if its statefunctions transform like the irreducible representations of the group of themetric. It is shown that there are no Galilean invariant equations fortwo-component spinor wave functions. A method to derive the L\'evy-Leblondequation for a four-component spinor wave function is presented. It is formallyproved that the L\'evy-Leblond and Schr\"odinger equations are the onlyGalilean invariant four-component spinor equations that can be obtained withthe Schr\"odinger phase factor. Physical implications of the obtained resultsand their relationships to the Pauli-Schr\"odinger equation are discussed.

Fundamental dynamical equations for spinor wave functions. I. Levy-Leblond and Schrodinger equations