Spinors in the hyperbolic algebra. (English) Zbl 1247.81195
Summary: The three-dimensional universal complex Clifford algebra \(\overline{C}_{3,0}\) is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.
MSC:
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 15A66 | Clifford algebras, spinors |
| 30G35 | Functions of hypercomplex variables and generalized variables |
| 15B33 | Matrices over special rings (quaternions, finite fields, etc.) |
Keywords:
hyperbolic complex Clifford algebra; algebraic spinor; hyperbolic numbers; paracomplex numbers; split-complex numbersReferences:
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