Clifford approach to metric manifolds

Chisholm, J. S. R. ; Farwell, R. S.

Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1991), p. [123]-133 / Harvested from

Résumé

[For the entire collection see Zbl 0742.00067.]For the purpose of providing a comprehensive model for the physical world, the authors set up the notion of a Clifford manifold which, as mentioned below, admits the usual tensor structure and at the same time a spin structure. One considers the spin space generated by a Clifford algebra, namely, the vector space spanned by an orthonormal basis $\lbrace e_j: j=1,\dots ,n\rbrace $ satisfying the condition $\lbrace e_i,e_j\rbrace \equiv e_ie_j=e_je_i=2I\eta _{ij}$, where $I$ denotes the unit scalar of the algebra and ($\eta _{ij}$) the nonsingular Minkowski metric of signature ($p,q$), ($p+q=n$). Then, for a raw manifold structure with local chart ($x^i$), one assigns the vector basis $\lbrace e_\mu (x): \mu =1,\dots ,n\rbrace $, by the rule $e_\mu (x)=h_\mu ^i(x)e_i$, $(\text{det}(h_\mu ^i)\ne 0)$, so that $g_{\lambda \mu }(x)=h^i_{\lambda }(x)h^j_\mu (x)e_{ij}$ becomes a metric. A differentiable ma!

Détail

MR MR1151897 | Zbl 0752.53014

EUDML-ID : urn:eudml:doc:219957
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