Received 26 September 2016; revised 6 October 2016; accepted 21
December 2016
Majorana spinors are constructed in terms
of the multivectors of relativistic Cl1,3
algebra. Such spinors are found to be multiplied by primitive
idempotents which drastically change spinor properties.
Running electronic waves are used to solve the real
Dirac–Majorana equation transformed to Cl1,3
algebra. From the analysis of the solution it is concluded
that free Majorana particles do not exist, because
relativistic Cl1,3 algebra requires the
massive Majorana particle to move with light velocity.
Keywords: Majorana
spinors, Dirac–Majorana equation, geometric algebra, Clifford
algebra
PACS: 03.65.-w,
04.20.Gz, 04.50.-h
Pritaikius geometrinės algebros
multivektorius buvo sudaryti ir išnagrinėti Majoranos spinoriai,
turintys realų, o ne labiau įprastą kompleksinį pavidalą.
Parodyta, kad tokie spinoriai savyje turi primityvų idempotentą,
kuris iš esmės keičia spinoriaus savybes. Gauti spinoriai
pritaikyti reliatyvistinės Dirako-Majoranos lygties spektrui –
dalelės energijos priklausomybei nuo jos impulso – apskaičiuoti
taikant geometrinę Cl1,3 algebrą. Išspręstas
bėgančios elektroninės bangos uždavinys. Iš sprendinio analizės
prieita prie išvados, kad Majoranos tipo laisvosios dalelės
neegzistuoja, nes gauto spektro savybės nesiderina su
šiuolaikinės fizikos įvaizdžiu, kadangi masę turinčios dalelės
greitis negali viršyti arba būti lygus šviesos greičiui.
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Similar formula for the Majorana spinor was published in this
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https://doi.org/10.1007/BF01883678
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