Titlebook: Clifford Algebras and their Applications in Mathematical Physics; Volume 1: Algebra an Rafa? Ab?amowicz,Bertfried Fauser Book 2000 Springer

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Dirac Operator, Hopf Algebra of Renormalization, and Structure of Spacetime geometry of spacetime itself may be dictated by the renormalization processes in quantum field theories. Two recently discovered and intimately related Hopf algebras — the Hopf algebra for the computation of the local index formula of transversally hypoelliptic operators and the algebra of renormal

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Rochelle Gladys Kemitare,Joshua Mugambwaspaces whose elements can be associated with the tangent and momentum vectors of trajectories in the manifold. The fiber also contains a subspace whose elements are associated with the local flow of action of each trajectory. The condition of minimum action translates into a constraint on the original vector . in the direct product structure.

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Multiparavector Subspaces of C?n: Theorems and Applicationse representations of such entities, for example by modeling spacetime vectors by paravectors (sums of scalars and vectors). This contribution explores the geometry of subspaces generated by paravectors of .?., the Clifford algebra of . -dimensional Euclidean space, and its applications to physical phenomena.

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Electron Scattering in the Spacetime Algebrandependent of spin, we can provide manifestly spin-independent results. Spin basis states are not needed, and we do no spin sums, instead dealing with the spin orientation directly. We perform some example calculations for single electron scattering and briefly discuss more complicated cases in QED.

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