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

We propose a symmetry law for a doublet of different form fields, which resembles gauge transformations for matter fields. This may be done for general Lie groups, resulting in an extension of Lie algebras and group manifolds. It is also shown that nonassociative algebras naturally appear in this formalism, which are briefly discussed. Afterwards, a general connection which includes a two-form field is settled-down, solving the problem of setting a gauge theory for the Kalb–Ramond field for generical groups. Topological Chern–Simons theories can also be defined in four dimensions, and this approach clarifies their relation to the so-called B ∧ F theories. We also revise some standard aspects of Kalb–Ramond theories in view of these new perspectives. Since this gauge connection is built upon a pair of fields consisting of a one-form and a two-form, one may define Yang–Mills theories as usually and, remarkably, also minimal coupling with bosonic matter, where the Kalb–Ramond field appears naturally as mediator; so, a new associated conserved charge can be defined. For the Abelian case, we explicitly construct the minimal interaction between B-field and matter following a "gauge principle" and find a novel conserved tensor current. This is our most significative result from the physical viewpoint. This framework is also generalized in such a way that any p-rank tensor may be formulated as a gauge field.

DOUBLET GROUPS, EXTENDED LIE ALGEBRAS, AND WELL DEFINED GAUGE THEORIES FOR THE TWO-FORM FIELD