Hypersymmetry: Physics of the Isotopic Field-Charge Spin Conservation (De Gruyter Textbook)

231 Pages·2020·4.669 MB·English

by  György Darvas

GyörgyDarvas
Hypersymmetry
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György Darvas
Hypersymmetry
Physics of the Isotopic Field-Charge Spin Conservation
Author
Dr.GyörgyDarvas
EötvösSt.29
Budapest1067
Hungary
[email protected]
ISBN978-3-11-071317-6
e-ISBN(PDF)978-3-11-071318-3
e-ISBN(EPUB)978-3-11-071348-0
LibraryofCongressControlNumber:2020943675
BibliographicinformationpublishedbytheDeutscheNationalbibliothek
TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie;
detailedbibliographicdataareavailableontheInternetathttp://dnb.dnb.de.
©2021WalterdeGruyterGmbH,Berlin/Boston
Coverimage:“Twobosonexchange”byKristófSarkady(8y)2010
Typesetting:IntegraSoftwareServicesPvt.Ltd.
Printingandbinding:CPIBooksGmbH,Leck
www.degruyter.com
Contents
ANOTHERVERSION OF FACTS
1 INTRODUCTION 3
ChapterI: FIELD-CHARGES
2 MASS 13
2.1 Equivalenceversusidentity 15
2.2 Examplesofthedistinctionbetweenidentityand
equivalence 17
2.2.1 Physicalapproach 17
2.2.2 Mathematicalapproach 19
2.3 Equivalencedoesnotmeanidentity 20
2.4 Theequivalenceprinciple 21
2.4.1 Equivalenceofthemassesofgravityandinertia 21
2.5 Transformationpropertiesofgravitationalandinertial
masses 22
2.6 Theroleofmassesinthestress–energytensorofGTR 25
2.7 Conservationofmass 26
2.8 Somepreliminaryconsequencesofthedistinctionbetween
massesofgravityandinertia 28
2.8.1 Wherecanonemeetseparatedinertialandgravitational
masses? 30
3 ELECTRICCHARGE 31
3.1 Distinctionbetweenelectriccharges 31
3.2 Sourcesoftheelectromagneticfield 34
3.3 Equivalenceprincipleforelectriccharges 36
3.4 Transformationofthetwotypesofelectromagneticcharges 36
3.5 Somepreliminaryconsequencesofthedistinctionbetween
field-chargesoftheelectromagneticfield 37
ChapterII: ISOTOPICFIELD-CHARGES
4 ISOTOPICFIELD-CHARGES(IFC) 43
4.1 Fieldsourcesinthestandardmodel(SM) 43
4.2 Isotopicfield-charges 44
4.2.1 Masses 44
VI Contents
4.2.2 Electriccharges 45
4.3 Theidentity-equivalencediversityontheexampleoftheisotopic
spin 46
4.4 3+1quantitiesinphysics 49
5 HYPERSYMMETRY(HySy) 51
5.1 Matrixalgebrafor3+1parametrictransformations 51
5.1.1 Vectoralgebraandquaternionalgebra 51
5.1.2 Vectorandquaternionalgebrasappliedtophysics 54
5.2 Thealgebraofhypersymmetry(HySy) 54
5.2.1 Introductiontotheτ-algebra 54
5.2.2 Theτ-algebra 55
5.2.3 Grouppropertiesoftheτ-matrices 56
5.2.4 Representationofthegroupcomposedbytheτ-matrices 59
5.2.5 ThegroupofHySy 60
5.3 Comparingtheτ-algebraandtheDiracalgebra 64
5.3.1 TheτandtheDirac(γ)matrices 64
5.3.2 Comparisonofthealgebrasoftheδ-andtheτ-matrices 65
5.3.3 Theτalgebrabeyondphysics(matrixgenetics) 66
5.4 Summaryoftheτalgebra 71
6 VELOCITYDEPENDENCEINPHYSICS 73
6.1 Velocity-dependentphenomena 73
6.2 Velocity-dependentfields 74
6.3 Velocitydependenceinthelightofconservationlawsand
symmetries 75
ChapterIII: ISOTOPICFIELD-CHARGE SPIN
7 CONSERVATIONLAWSANDHYPERSYMMETRY 81
7.1 Preliminaryassumptions 81
7.2 IntroductiontothemathematicsofthetwosimultaneousNoether
currentsinHySy 82
7.3 Noether’scurrentsforgaugeinvariancelocalisedinavelocity
field 84
7.4 Discussionofthemathematicalresults 90
7.5 Physicalconsiderations 92
Contents VII
8 CONSERVATIONOFTHEISOTOPICFIELD-CHARGESPIN(IFCS) 93
8.1 Firstconservedquantity:conservationofthefield‐charge(ך) 93
8.2 Secondconservedquantity:conservationoftheisotopic
field-chargespin(Δ) 94
8.3 Couplingofthetwoconservedquantities(ךandΔ) 95
8.4 Interpretationoftheisotopicfield-chargespin(Δ) 96
9 ISOTOPICFIELD-CHARGESINFUNDAMENTALINTERACTIONS 99
9.1 Isotopicfield-chargesinstrongandelectroweakinteractions 99
9.2 Summary:field-chargesinallthefourfundamental
interactions 101
9.3 QuantaoftheDfield 103
ChapterIV: INTERACTION BETWEEN ISOTOPICFIELD-CHARGES
10 ISOTOPICFIELD-CHARGES(ך˅andךτ)ININTERACTION 109
10.1 MechanismoftheinteractionbetweenIFC 109
10.1.1 Singleparticle’sIFCstates 109
10.1.1.1 Theprobabilisticmodel 110
10.1.1.2 Theharmonicoscillatormodel 111
10.1.1.3 Theflip-flopmodel 111
10.1.1.4 Theintermediateparticlemodel 111
10.1.2 Theintermediatemodelofinteractionbetweentwoparticles 112
10.1.2.1 Symmetricorasymmetricinteractingagents? 114
10.2 InterpretationoftheIFCSconservation 115
10.2.1 Ontherolesofthemassesonceagain 116
10.3 MassofdionsthatmediateHySytransformations 119
10.3.1 Massoftheδboson 120
10.3.2 TransformationinacoupledSMfieldandtheDfield–Theorigin
ofthemassofδ 121
10.3.3 SpontaneousbreakingpointofHySy 129
10.3.4 Themassofthemediatingbosonδinlightofthetransformation
oftheDfield 133
10.3.5 ConclusionsonthedionmassandthetransformationoftheD
field 134
11 IFCINTERACTIONSINSMFIELDS 135
11.1 MechanismofcommutingΔ 135
11.2 Hypersymmetryappliedtogravitationalinteraction 138
11.2.1 Applicationoftheτalgebraforthegravitationalstress–energy
tensor 139
VIII Contents
11.2.2 Hypersymmetryofthegravitationalequations 143
11.2.3 Theaffineconnectionfield 145
11.2.4 ThemechanismoftheΔexchangeingravitationalinteraction 146
11.3 Hypersymmetryappliedtoelectromagneticinteraction 147
11.3.1 IsotopicelectricchargesinclassicalEM 148
11.3.2 IsotopicelectricchargesinQED 149
11.3.3 Isotopicelectricchargesinthepresenceofakineticgauge
field 155
11.3.4 HypersymmetryoftheextendedDiracequation 157
11.3.5 ApplicationoftheHySyalgebrafortheextendedDiracequation 159
11.3.6 InvarianceoftheextendedDiracequation 161
11.3.7 MechanismoftheΔexchangeinelectromagneticinteraction 162
11.3.8 ModifiedDiracequationinthepresenceofisotopicelectric
chargesandakineticgaugefield 163
11.3.8.1 CoincidencewiththeclassicalDiracequationinboundarycase,
whennokineticfieldispresent 163
11.3.8.2 Themagneticandtheelectricmoments 163
11.3.8.3 Themagneto-kineticandelectro-kineticmoments 163
11.3.8.3.1 Themagneto-kineticmoment 165
11.3.8.3.2 Theelectro-kineticmoment 165
11.3.9 TheHamiltonianandtheLagrangianoftheelectromagnetic
interactioninthepresenceofisotopicgravitationalandelectric
chargesaswellasakineticgaugefield 168
11.3.9.1 Thefullmagneticandelectricmoments 168
11.3.9.2 Themomentuminakineticfieldandtheappearanceofavirtual
“coupling”spin 170
11.3.10 ThefieldtensorsoftheEMandthekineticfields 171
11.3.10.1 ThefieldtensoroftheEMfield 171
11.3.10.2 Thefieldtensorofthekineticfield 171
11.3.10.3 Thecurvatureoftheconnectionfield 172
11.3.11 TheLorentzforceinthepresenceofakineticfield 173
11.3.12 Theconservedcurrentsandtheconservedisotopicelectric
chargespin 174
11.3.13 Quantisation 175
11.3.14 Observationofadion(aδboson) 177
11.3.15 ConcludingremarkstoSection11.3 179
11.4 MechanismoftheΔexchangeinweakinteractions 181
11.5 MechanismoftheΔexchangeinstronginteractions 183
12 SUMMARY 185
12.1 ThebirthandchildhoodofIFChypersymmetry 185
12.2 SummaryofthefindingsintheHySymodel 188
Contents IX
12.2.1 SUSYandHySy 188
12.2.2 Whatarethoseisotopicfield-charges? 188
12.2.3 Whywehavenotfeaturedtheminourphysicalequations? 189
12.2.4 Thequestionoflocalisation 190
12.2.5 Interactionbetweenthedifferentcomponentsofa
Hamiltonian? 190
12.2.6 WhyonlyoppositeIFCSstateparticlescaninteractwitheach
other? 191
12.2.7 3+1typequantitiesinphysics 192
12.2.8 ThetransformationgroupofHySy 192
12.2.9 Velocity-dependentfield?Velocity-dependentquantitiesin
physics 192
12.2.10 Conservedcurrent–conservedquantity–mediatingboson
(dion) 193
12.2.11 Propertiesoftheisotopicfield-chargesandtheδbosons 194
12.2.12 Howmuchisthemassofadion? 194
12.2.13 MassivebosonsintheDfield? 194
12.2.14 Howmanykindsofdionaresought? 195
12.2.15 WhyisHySysimplerthantheSUSYmodel? 195
12.2.16 Inwhatfeaturesis(ifatall)HySymorecomplicatedthanthe
SUSYmodel? 195
12.2.17 Fermion–fermionandboson–bosonpairsinsteadoffermion–
bosonpairs 196
12.2.18 DothetwoconservedNoethercurrentsacttogetheror
separately? 196
12.2.19 TheSMandtheHySy 196
12.2.20 GUTandHySy 197
12.2.21 Darkparticles? 197
12.2.22 Wave-corpuscledualism 197
12.2.23 Whydoesnottheelectronrunaway? 198
12.2.24 Tableofafewpropertiesofisotopicfield-charges 198
12.3 Hypersymmetryandourpictureofthephysicalworld 199
12.4 Closingremarks 200
REFERENCES 203
INDEX 215