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Gsponer, Andre; Hurni, Jean-Pierre

doi:10.1023/a:1012033412964

Cited by 37 publications

(28 citation statements)

References 13 publications

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“…[12,13,14] Further background and references can be found in a couple of recent papers. [15,16] In both the Cℓ 3 formulation and in Hestenes' analysis, the spinor plays the role of a relativistic transformation amplitude from the reference frame of the fermion to the lab frame. The orientation of the reference frame is not significant since global gauge transformations Ψ H → Ψ H R, where R is a fixed spatial rotor, can rotate it arbitrarily.…”

Section: Symmetry Of the Hestenes Equationmentioning

confidence: 99%

Comment on `Dirac theory in spacetime algebra'

Baylis¹

2002

J. Phys. A: Math. Gen.

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In contrast to formulations of the Dirac theory by Hestenes and by the current author, the formulation recently presented by W. P. Joyce The recent formulation by Joyce [1] of what he calls the "bivector Dirac equation" in the complex Dirac algebra (Clifford's geometric algebra of Minkowski spacetime taken over the complex field) can be decomposed into the Dirac equation in the Hestenes form [2,3,4,5] for mass +m plus another equation for mass −m. The purpose of this comment is to prove this claim and to discuss a few other aspects of the paper. The approach exploits the power of projectors in geometric algebras. To start, we first review the Dirac equation for a free electron and its formulation in algebraic form.

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Section: Symmetry Of the Hestenes Equationmentioning

confidence: 99%

Comment on `Dirac theory in spacetime algebra'

Baylis¹

2002

J. Phys. A: Math. Gen.

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“…Note added: Further details can be found in [9]. In 1933, Lemaitre [10], showed, though not the complete analytic extension of the Schwarzschild solution, (similarly as Eddington [4] did in 1924), that the surface r = 2m is a fictituous singularity.…”

Section: Discussionmentioning

confidence: 99%

Schwarzschild and Synge once again

Schmidt

2005

Gen Relativ Gravit

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“…Real quaternions form a noncommutative division algebra, while complex quaternions have divisors of zero; therefore, nothing is simple any more 5 . Biquaternions have been widely applied as the Pauli matrices 6 : [21][22][23][24][25]; some authors investigated the relationship between rotations, biquaternions and the Pauli matrices, projective representations of the Lorentz group, etc [26][27][28][29]. In the following work, we will focus onmaximal entanglement within the algebra of biquaternions-Ä  .…”

Section: Introductionmentioning

confidence: 99%

Patterns of maximally entangled states within the algebra of biquaternions

Obojska¹

2020

J. Phys. Commun.

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This paper proposes a description of maximally entangled bipartite states within the algebra of biquaternions-Ä  . We assume that a bipartite entanglement is created in a process of splitting one particle into a pair of two indiscernible, yet not identical particles. As a result, we describe an entangled correlation by the use of a division relation and obtain twelve forms of biquaternions, representing pure maximally entangled states. Additionally, we obtain other patterns, describing mixed entangled states. Finally, we show that there are no other maximally entangled states in Ä   than those presented in this work.1 2 1 2 3 4 because these two sets have different elements, and a set is uniquely determined by its elements.Mereology, as a collective set theory, takes into consideration relations between elements. In comparison, ZFC set theory neglects such connections, i.e., we have abstract wholes in which elements are treated as independent entities. Having in mind entanglement, we incorporated a kind of an entangled correlation and made it a founding relation in NAM. We analyzed properties of the obtained model and incorporated ZFC set theory within NAM [19]. Moreover, we represented NAM in terms of non-classic algebras [20]. Finally, we were able to express a bipartite entanglement by the use of quaternions [17]. The novelty of the proposed model stands in the fact that in an investigated universe we can have classical atoms and indecomposable, but composite atoms represented by entanglement, which are not elements of classical ZFC set theory.Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.1 NAM=Non-Antisymmetric Mereology. It is a model of mereology in which we assume that the inclusion relation-⊆ is only reflexive and transitive. We deny the antisymmetry of ⊆. 2 The ZFC set theory is a classical model of set theory. The abbreviation-ZFC follows from the names of mathematicians, which contributed to developing this model: E. Zermelo and A.Fraenkel. 'C' stands for the Axiom of Choice taken into consideration in ZFC. This model forms a basis of exact sciences.

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Untitled

Cited by 37 publications

References 13 publications

Comment on `Dirac theory in spacetime algebra'

Comment on `Dirac theory in spacetime algebra'

Schwarzschild and Synge once again

Patterns of maximally entangled states within the algebra of biquaternions

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