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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Dirac Hamiltonian $H^{\left(D\right)}$ for relativistic charged fermionsminimally coupled to (possibly time-dependent) electromagnetic fields istransformed with a purpose-built flow equation method, so that the result ofthat transformation is unitary equivalent to $H^{\left(D\right)}$ and grantedto strive towards a limiting value $H^{\left(NW\right)}$ commuting with theDirac $\beta$-matrix. Upon expansion of $H^{\left(NW\right)}$ to order$\frac{v^2}{c^2}$ the nonrelativistic Hamiltonian $H^{\left(SP\right)}$ ofSchr\"odinger-Pauli quantum mechanics emerges as the leading order term addingto the rest energy $mc^2$. All the relativistic corrections to$H^{\left(SP\right)}$ are explicitly taken into account in the guise of aMagnus type series expansion, the series coefficients generated to order$\left(\frac{v^{2}}{c^{2}}\right)^{n}$ for $n\geq2$ comprising partial sums ofiterated commutators only. In the special case of static fields the equivalenceof the flow equation method with the well known energy-separating unitarytransformation of Eriksen is established on the basis of an exact solution of areverse flow equation transforming the $\beta$-matrix into the energy-signoperator associated with $H^{\left(D\right)}$. That way the identity$H^{\left(NW\right)}=\beta\sqrt{H^{\left(NW\right)}H^{\left(NW\right)}}$ isestablished implying $H^{\left(NW\right)}$ being determined unambiguously.

A Flow Equation Approach Striving Towards an Energy-Separating  Hamiltonian Unitary Equivalent to the Dirac Hamiltonian with Coupling to  Electromagnetic Fields