2016
DOI: 10.1142/s0219887817500141
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Dirac equation in four time and four space dimensions

Abstract: The Dirac equation in four time and four space dimensions (or (4+4)dimensions) is considered.Step by step we show that such an equation admits Majorana and Weyl solutions. In order to obtain the Majorana or Weyl spinors we used a method based on the construction of Clifford algebra in terms of 2x2-matrices. We argue that our approach can be useful in supergravity, superstrings and qubit theory.

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Cited by 9 publications
(8 citation statements)
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“…Moreover, in Ref. [20] it was shown that the Dirac equation in (4 + 4)-dimensions leads to the surprising result that a complex spinor associated with 1 2 -spinor in (1 + 3)-dimensions can be understood as a Majorana-Weyl spinor in (4 + 4)-dimensions. So, one would expect that the Majorana-Weyl vector-spinor Ψ D of the Rarita-Schwinger field equation in (4 + 4)dimensions (66) can be associated with a complex spinor vector-spinor in (1+3)-dimensions.…”
Section: Final Remarksmentioning
confidence: 99%
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“…Moreover, in Ref. [20] it was shown that the Dirac equation in (4 + 4)-dimensions leads to the surprising result that a complex spinor associated with 1 2 -spinor in (1 + 3)-dimensions can be understood as a Majorana-Weyl spinor in (4 + 4)-dimensions. So, one would expect that the Majorana-Weyl vector-spinor Ψ D of the Rarita-Schwinger field equation in (4 + 4)dimensions (66) can be associated with a complex spinor vector-spinor in (1+3)-dimensions.…”
Section: Final Remarksmentioning
confidence: 99%
“…In Ref. [20] it was shown that massless Second, it is interesting that in (4 + 4)-dimensions one may consider the chain of maximal embeddings and branches, so(4, 4) ⊃ s(2, R) ⊕ so(2, 3) ⊃ so(1, 1) ⊕ sl(2, R) ⊕ sl (2,2).…”
Section: Introductionmentioning
confidence: 99%
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“…Fortunately, there are already a number of works with interesting results in the (4 + 4)-world that can be considered as additional motivation for increasing interest in such a scenario. First, the Dirac equation in (4 + 4)-dimensions is consistent with Majorana-Weyl spinors which give exactly the same number of components as the complex spinor of 1/2spin particles such as the electron or quarks [6,7]. Second, the most general Kruskal-Szekeres transformation of a blackhole coordinates in (1+3)-dimensions leads to 8-regions (instead of the usual 4-regions), which can be better described in (4 + 4)-dimensions [8].…”
Section: Introductionmentioning
confidence: 88%
“…In the process, we discover that in 4-dimensions the cosmological constant 0 Λ > associated with the de Sitter space ( 0 Λ < , anti de Sitter space) is dual to the cosmological constant There are at least two frameworks where a (4 + 4)-world has emerged as interesting physical scenario. First, it has been proved [6] that the Dirac equation in (4 + 4)-dimensions admit a Majorana-Weyl physical spinor state with only 8 real components which can be identified with the 4-complex components of the usual electron components. Second, in Ref.…”
Section: Introductionmentioning
confidence: 99%