The Complex Algebra of Physical Space: A Framework for Relativity

Baylis, W. E.; Keselica, J. D.

doi:10.1007/s00006-012-0347-3

Cited by 11 publications

(16 citation statements)

References 37 publications

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“…into the Pauli algebra also by complexification, which has been demonstrated by Baylis and Keselica in order to analyze the structure of the Dirac equation [51]. Furthermore, Mironov and Mironov applied the tensor product of a Pauli paravector model to reformulate differential equations in relativistic quantum physics [52,53].…”

Section: The Hyperbolic Pauli Algebra In Minkowski Spacementioning

confidence: 99%

Conformal relativity with hypercomplex variables

Ulrych¹

2014

Proc. R. Soc. A.

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Wehrenbachhalde 35, 8053 Zürich, SwitzerlandMajorana's arbitrary spin theory is considered in a hyperbolic complex representation. The underlying differential equation is embedded into the gauge field theories of Sachs and Carmeli. In particular, the approach of Sachs can serve as a unified theory of general relativity and electroweak interactions. The method is extended to conformal space with the intention to introduce the strong interaction. It is then possible to use the wave equation, operating on representation functions of the conformal group, to describe the dynamics of matter fields. The resulting gauge groups resemble closely the gauge symmetries of Glashow-Salam-Weinberg and the standard model.

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Section: The Hyperbolic Pauli Algebra In Minkowski Spacementioning

confidence: 99%

Conformal relativity with hypercomplex variables

Ulrych¹

2014

Proc. R. Soc. A.

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“…Hilbert spaces over the field of complex numbers are indispensable for mathematical structure of quantum mechanics [14] which in turn play a great role in molecular, atomic and subatomic phenomena. The work towards the generalization of quantum mechanics to bicomplex number system have been recently a topic in different quantum mechanical models [2,3,4,19,20]. More specifically, in [7,8] the authors made an in depth study of bicomplex Hilbert spaces and operators acting on them.…”

Section: Introductionmentioning

confidence: 99%

“…4) and T (z|φ ) = zT (|φ )(3.5) ∀|φ , |ψ ∈ M and ∀z ∈ C(i 1 ). Now, let w ∈ M(2) be an arbitrary bicomplex number.…”

mentioning

confidence: 99%

Infinite Dimensional Bicomplex Spectral Decomposition Theorem

Charak

Kumar

Rochon

2013

Adv. Appl. Clifford Algebras

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“…We can confirm from Eq. (7) that the two transformations (8) and (9) together leave the acceleration (and by integration, the proper velocity and the world line) of the massive particle unchanged.…”

Section: Gauge Transformationsmentioning

confidence: 99%

“…A simple classical equation of motion [7,8] follows from the Lorentz transformation p = ΛmΛ † and the unimodularity of Λ :…”

Section: Dirac Equationmentioning

confidence: 99%

Quantum/Classical Interface: A Geometric Approach from the Classical Side

Baylis

NATO Science Series II: Mathematics, Physics and Chemistry

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Classical relativistic physics in Clifford's geometric algebra has a spinorial formulation that is closely related to the standard quantum formalism. The algebraic use of spinors and projectors, together with the bilinear relations of spinors to observed currents, gives quantum-mechanical form to many classical results, and the clear geometric content of the algebra makes it an illuminating probe of the quantum/classical interface. The aim of this lecture is to close the conceptual gap between quantum and classical phenomena while highlighting their essential differences. The paravector representation of spacetime in APS is used in particular to provide insight into what many pioneering quantum physicists have considered classically indescribable: spin-1/2 systems and their measurement.

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The Complex Algebra of Physical Space: A Framework for Relativity

Cited by 11 publications

References 37 publications

Conformal relativity with hypercomplex variables

Conformal relativity with hypercomplex variables

Infinite Dimensional Bicomplex Spectral Decomposition Theorem

Quantum/Classical Interface: A Geometric Approach from the Classical Side

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