文档介绍：GeometricAlgebraanditsApplicationtoMathematicalPhysicsChrisJ
L
DoranSidneySussexCollegeAdissertationsubmittedforthedegreeofDoctorofPhilosophyintheUniversityofCambridge
February
PrefaceThisdissertationistheresultofworkcarriedoutintheDepartmentofAppliedMathe
maticsandTheoreticalPhysicsbetweenOctober
andOctober
Sectionsofthedissertationhaveappearedinaseriesofcollaborativepapers
Exceptwhereexplicitreferenceismadetotheworkofothers
theworkcontainedinthisdissertationismyown
AcknowledgementsManypeoplehavegivenhelpandsupportoverthelastthreeyearsandIamgratefultothemall
Ioweagreatdebttomysupervisor
NickManton
forallowingmethefreedomtopursuemyowninterests
andtomytwoprinciplecollaborators
AnthonyLasenbyandStephenGull
whoseideasandinspirationwereessentialinshapingmyresearch
panyonanarduousjourneytoPoland
Aboveall
pletionofthiswork
Finally
IthankStuartRankinandMargaretJamesformanyhappyhoursintheMill
MikeandRachael
TimandImogen
Paul
AlanandmyothercolleaguesinDAMTPandMRAO
Igratefullyacknowledge
nancialsupportfromtheSERC
DAMTPandSidneySussexCollege
TomyparentsContents
Introduction
SomeHistoryandRecentDevelopments
AxiomsandDe
nitions
TheGeometricProduct
TheGeometricAlgebraofthePlane
TheGeometricAlgebraofSpace
Re
ectionsandRotations
TheGeometricAlgebraofSpacetime
LinearAlgebra
LinearFunctionsandtheOutermorphism
Non
OrthonormalFrames
GrassmannAlgebraandBerezinCalculus
GrassmannAlgebraversusCli
ordAlgebra
TheGeometrisationofBerezinCalculus
ExampleI
The
Grauss
Integral
ExampleII
TheGrassmannFourierTransform
SomeFurtherDevelopments
LieGroupsandSpinGroups
SpinGroupsandtheirGenerators