Twistörler ve Killing Spinörleri Arasındaki Bir Ilişki Üzerine

Yıl 2018, Cilt: 39 Sayı: 4, 954 - 969, 24.12.2018

Özgür Açık

https://doi.org/10.17776/csj.434630

Öz

Killing-Yano formları ve kapalı konformal
Killing-Yano formlarından, konformal Killing-Yano formları oluşturabilme sonucundan
esinlenmek suretiyle, bu çalışma Killing spinörlerinden twistörler inşa etmek
için bir yöntem içermektedir ki bu benzeşik olarak arka-zemin kütle-çekimsel
alanlarda kuantum elektrodinamiksel çift yokoluşu olarak yorumlanabilmektedir.
Eğer bu makalede yapıldığı gibi (homojen olmaması muhtemel) Killing-Yano
formları için yardımcı vektör alanlarından muhaf yeni tanımlayıcı bir
diferensiyel denklem tanıtılırsa ilk sonuç kolyaca doğrulanabilir. Bu bakış
açısıyla kütleli ve kütlesiz Dirac denkleminin simetri işlemcileri arasında
muntazam bir ilişki tanıtılabilmektedir. Bazı diğer fiziksel yorumlar da
içerilmektedir.

Anahtar Kelimeler

Clifford cebirleri ve spinörler, Twistörler, Killing-Yano formları, Killing spinörleri

On a Relation Between Twistors and Killing Spinors

Öz

Inspiring from the consequence of constructing
conformal Killing-Yano forms out of Killing-Yano forms and closed conformal
Killing-Yano forms, this work includes a method for building up twistors from
Killing spinors which can be analogously interpreted as the quantum
electrodynamical pair annihilation process in background gravitational fields.
The former consequence is easily verified if one introduces a new defining
differential equation for (possibly inhomogeneous) Killing-Yano forms which is
free from auxiliary vector fields, as is done in this text. From this point of
view a neat relation between the symmetry operators of massive and massless
Dirac equation is also introduced. Some other physical interpretations are also
included.

Anahtar Kelimeler

Clifford Algebras and Spinors, Twistors, Killing-Yano forms, Killing spinors

Kaynakça

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• [37]. Of course in almost all geometric theories of gravity metric is the fundamental field, especially in General Relativity.
• [38]. Although we have used the term pseudo-Riemannain in the abstract and in the introduction, we go against this usage with the same lines of thought as R. Toretti [13], and instead we prefer to use Riemannian spacetime generally and especially Lorentzian spacetime for manifolds endowed with one time-like direction in a local g-frame.
• [39]. We use the term Yano form to indicate a KY form or a CCKY form, then the term dual Yano form indicates a CCKY form or a KY form respectively.
• [40]. Confusion with the Riemann curvature R tensor should be avoided.
• [41]. The properties associated to these projectors are given at the Appendix A of [1].