On conformally covariant spinor field equations

Budini, P.

doi:10.1007/bf01603799

Cited by 14 publications

(16 citation statements)

References 9 publications

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“…[41][42][43][44][45][46][47][48]. To keep the invariance of x 2 1 + x 2 2 + x 2 3 = 0, one defines the matrix…”

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%

“…In this section we separately present the spatial/operator representation and unitary/spinor representation of the 4-dimensional Conformal group [2,40], including their generators and commutations among them. The spatial representation is mainly referencing to that of Ref.…”

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%

“…The spatial representation is mainly referencing to that of Ref. [40,41] and the unitary representation is derived by applying Cartan method [3] to SO(6) − SU (4) transform. The unitary representation is the focus of this section.…”

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%

“…A special expression of the differential forms in 4-dimension spatial representation can be derived directly from the above equation. In derivation we need to apply the following variables [40] x µ = η µ K , where K = η 5 + i η 6 , where µ = 1, 2, 3, 4…”

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%

“…The route of inquiring the concrete matrices following Cartan method as above could be a shortcut that rarely mentioned in literature. It is can be checked that the commutations among U i , V µ , W µ , Y µ are just those for conformal group [40,41], accordingly the mapping from these matrices to differential forms turns out to be…”

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%

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Structure Group and Fermion-Mass-Term in General Nonlocality

Han

Wang

2015

Int J Theor Phys

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In our previous work [J. Math. Phys. 49, 033513 (2008)] two problems remain to be resolved. One is that we lack a minimal group to replace GL(4,C), the other is that the Equation of Motion (EoM) for fermion has no mass term. After careful investigation we find these two problems are linked by conformal group, a subgroup of GL(4,C) group. The Weyl group, a subgroup of conformal group, can bring about the running of mass, charge etc. while making it responsible for the transformation of interaction vertex. However, once concerning the generation of the mass term in EoM, we have to resort to the whole conformal group, in which the generators $K_\mu $ play a crucial role in making vacuum vary from space-like (or light-cone-like)to time-like. Physically the starting points are our previous conclusion, $\vec E^2-\vec B^2\neq 0$ for massive bosons, and the two-photon process yielding $e^+ e^-$ pair. Finally we get to the conclusion that the mass term of strong interaction is linearly relevant to (chromo-)magnetic flux as well as angular momentum.Comment: 14 pages, no figure. Int.J.Theor.Phys.54 (2015

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“…[41][42][43][44][45][46][47][48]. To keep the invariance of x 2 1 + x 2 2 + x 2 3 = 0, one defines the matrix…”

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%

Section: The Spatial and Spinor Representations For Conformal Groupmentioning

confidence: 99%