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

This paper summarizes and generalizes a recently proposed mathematicalframework that unifies the standard formalisms of special relativity andquantum mechanics. The framework is based on Hilbert spaces H of functions offour space-time variables x,t, furnished with an additional indefinite innerproduct invariant under Poincar\'e transformations, and isomorphisms of thesespaces that preserve the indefinite metric. The indefinite metric isresponsible for breaking the symmetry between space and time variables and forselecting a family of Hilbert subspaces that are preserved under Galileotransformations. Within these subspaces the usual quantum mechanics withSchr\"odinger evolution and t as the evolution parameter is derived.Simultaneously, the Minkowski space-time is isometrically embedded into H,Poincar\'e transformations have unique extensions to isomorphisms of H and theembedding commutes with Poincar\'e transformations. The main new result is aproof that the framework accommodates arbitrary pseudo-Riemannian space-timesfurnished with the action of the diffeomorphism group.

A possible mathematics for the unification of quantum mechanics and general relativity