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

Clifford geometric algebras of multivectors are treated in detail. Thesealgebras are build over a graded space and exhibit a grading or multivectorstructure. The careful study of the endomorphisms of this space makes it clear,that opposite Clifford algebras have to be used also. Based on thismathematics, we give a fully Clifford algebraic account on generatingfunctionals, which is thereby geometric. The field operators are shown to beClifford and opposite Clifford maps. This picture relying on geometry does notneed positivity in principle. Furthermore, we propose a transition fromoperator dynamics to corresponding generating functionals, which is based onthe algebraic techniques. As a calculational benefit, this transition isconsiderable short compared to standard ones. The transition is not injective(unique) and depends additionally on the choice of an ordering. We obtain adirect and constructive connection between orderings and the explicit form ofthe functional Hamiltonian. These orderings depend on the propagator of thetheory and thus on the ground state. This is invisible in path integralformulations. The method is demonstrated within two examples, a non-linearspinor field theory and spinor QED. Antisymmetrized and normal-orderedfunctional equations are derived in both cases.Comment: 23p., 76kB, plain LaTeX, Bertfried.Fauser@uni-tuebingen.d

On an easy transition from operator dynamics to generating functionals by Clifford algebras