Matches in SemOpenAlex for { <https://semopenalex.org/work/W1570530077> ?p ?o ?g. }
Showing items 1 to 80 of
80
with 100 items per page.
- W1570530077 abstract "We represent vector rotation operators in terms of bras or kets of half-angle exponentials in Clifford (geometric) algebra Cl_{3,0}. We show that SO_3 is a rotation group and we define the dihedral group D_4 as its finite subgroup. We use the Euler-Rodrigues formulas to compute the multiplication table of D_4 and derive its group algebra identities. We take the linear combination of rotation operators in D_4 to represent the four Fermion matrices in Sakurai, which in turn we use to decompose any 2x2 matrix. We show that bra and ket operators generate left- and right-acting matrices, respectively. We also show that the Pauli spin matrices are not vectors but vector rotation operators, except for sigma_2 which requires a subsequent multiplication by the imaginary number i geometrically interpreted as the unit oriented volume." @default.
- W1570530077 created "2016-06-24" @default.
- W1570530077 creator A5022549505 @default.
- W1570530077 creator A5059744955 @default.
- W1570530077 creator A5066258484 @default.
- W1570530077 date "2008-11-24" @default.
- W1570530077 modified "2023-09-27" @default.
- W1570530077 title "A geometric algebra reformulation of 2x2 matrices: the dihedral group D_4 in bra-ket notation" @default.
- W1570530077 cites W1646566974 @default.
- W1570530077 cites W1965540060 @default.
- W1570530077 cites W1965574294 @default.
- W1570530077 cites W2028434692 @default.
- W1570530077 cites W2042876241 @default.
- W1570530077 cites W2061855547 @default.
- W1570530077 cites W2104980312 @default.
- W1570530077 cites W2244241401 @default.
- W1570530077 cites W615881649 @default.
- W1570530077 hasPublicationYear "2008" @default.
- W1570530077 type Work @default.
- W1570530077 sameAs 1570530077 @default.
- W1570530077 citedByCount "1" @default.
- W1570530077 crossrefType "posted-content" @default.
- W1570530077 hasAuthorship W1570530077A5022549505 @default.
- W1570530077 hasAuthorship W1570530077A5059744955 @default.
- W1570530077 hasAuthorship W1570530077A5066258484 @default.
- W1570530077 hasConcept C100856211 @default.
- W1570530077 hasConcept C114614502 @default.
- W1570530077 hasConcept C121332964 @default.
- W1570530077 hasConcept C136119220 @default.
- W1570530077 hasConcept C202444582 @default.
- W1570530077 hasConcept C207570611 @default.
- W1570530077 hasConcept C2524010 @default.
- W1570530077 hasConcept C2780595030 @default.
- W1570530077 hasConcept C2781311116 @default.
- W1570530077 hasConcept C33923547 @default.
- W1570530077 hasConcept C62520636 @default.
- W1570530077 hasConcept C72409365 @default.
- W1570530077 hasConcept C74050887 @default.
- W1570530077 hasConcept C83633838 @default.
- W1570530077 hasConceptScore W1570530077C100856211 @default.
- W1570530077 hasConceptScore W1570530077C114614502 @default.
- W1570530077 hasConceptScore W1570530077C121332964 @default.
- W1570530077 hasConceptScore W1570530077C136119220 @default.
- W1570530077 hasConceptScore W1570530077C202444582 @default.
- W1570530077 hasConceptScore W1570530077C207570611 @default.
- W1570530077 hasConceptScore W1570530077C2524010 @default.
- W1570530077 hasConceptScore W1570530077C2780595030 @default.
- W1570530077 hasConceptScore W1570530077C2781311116 @default.
- W1570530077 hasConceptScore W1570530077C33923547 @default.
- W1570530077 hasConceptScore W1570530077C62520636 @default.
- W1570530077 hasConceptScore W1570530077C72409365 @default.
- W1570530077 hasConceptScore W1570530077C74050887 @default.
- W1570530077 hasConceptScore W1570530077C83633838 @default.
- W1570530077 hasLocation W15705300771 @default.
- W1570530077 hasOpenAccess W1570530077 @default.
- W1570530077 hasPrimaryLocation W15705300771 @default.
- W1570530077 hasRelatedWork W1592316920 @default.
- W1570530077 hasRelatedWork W1598794789 @default.
- W1570530077 hasRelatedWork W1990054654 @default.
- W1570530077 hasRelatedWork W1999048077 @default.
- W1570530077 hasRelatedWork W2022401809 @default.
- W1570530077 hasRelatedWork W2074143910 @default.
- W1570530077 hasRelatedWork W2082861624 @default.
- W1570530077 hasRelatedWork W2154742673 @default.
- W1570530077 hasRelatedWork W2168205712 @default.
- W1570530077 hasRelatedWork W229895329 @default.
- W1570530077 hasRelatedWork W2550865757 @default.
- W1570530077 hasRelatedWork W2597701017 @default.
- W1570530077 hasRelatedWork W2949133980 @default.
- W1570530077 hasRelatedWork W3011640037 @default.
- W1570530077 hasRelatedWork W3029740315 @default.
- W1570530077 hasRelatedWork W3107494207 @default.
- W1570530077 hasRelatedWork W3118565411 @default.
- W1570530077 hasRelatedWork W3177882801 @default.
- W1570530077 hasRelatedWork W43268865 @default.
- W1570530077 hasRelatedWork W766450594 @default.
- W1570530077 isParatext "false" @default.
- W1570530077 isRetracted "false" @default.
- W1570530077 magId "1570530077" @default.
- W1570530077 workType "article" @default.