350 KB0 KB2025Movrin, Vitaštevilka:1letnik:1217 str.COBISSID_HOST:232935683ISSN:2385-8567URN:URN:NBN:SI:doc-74GFBV6LslZaložba Fakultete za matematiko in fiziko Univerze v LjubljaniMatrikaLorentz groupsLorentzove grupematrične Liejeve grupematrix Lie groupsspinor representationsspinorske upodobitvetransformacije Diracovih spinorjevtransformations of Dirac spinorsSpinorska upodobitev Lorentzove grupe|This paper discusses the spinor representation of the Lorentz group of rotations and boosts. It begins with a review of the basics of matrix Lie groups and representation theory. Then the Lorentz group and its associated Lie algebra are examined in detail, offering historical context for the Dirac equation, which serves as the primary motivation for introducing the spinor representation. The transformations of Dirac spinors are analyzed in detail, and their unusual transformation properties are explained through the existence of the so-called spin homomorphism ?${\rm SL}(2, {\mathbb C}) \to {\rm SO}^+(1, 3)$?. The article concludes with a description of all irreducible representations of the spin group of the Lorentz groupV članku je obravnavana spinorska upodobitev Lorentzove grupe rotacij in potiskov. Sprva so navadene osnove matričnih Liejevih grup in teorije upodobitev, nato pa se podrobneje obravnava Lorentzova grupa in pripadajoča Liejeva algebra. Podano je zgodovinsko ozadje Diracove enačbe, ki pravzaprav motivira vpeljavo spinorske upodobitve. Natančneje so opisane transformacije Diracovih spinorjev, njihove nenavadne transformacijske lastnosti pa so pojasnjene z obstojem t.i. spin homomorfizma ?${\rm SL}(2, {\mathbb C}) \to {\rm SO}^+(1, 3)$?. Na koncu so navedene še vse nerazcepne upodobitve spin grupe Lorentzove grupeTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of Slovenia