GEOMETRIC ALGEBRA IN PHYSICS
CON TEN TS IN TRO DUCTION SOME HISTORY AND RECEN T DEV ELOPMEN TS AXIOMS AND DE NITIONS THE GEOMETRIC PRO DUCT THE GEOMETRIC ALGEBRA OF THE PLANE THE GEOMETRIC ALGEBRA OF SPACE REECTIONS AND ROTATIONS THE GEOMETRIC ALGEBRA OF SPACETIME LINEAR ALGEBRA LINEAR F UNCTIONS AND THE OUTERMORPHISM NONORTHONORMAL F RAMES GRASSMANN ALGEBRA AND BEREZIN CALCULUS GRASSMANN ALGEBRA V ERSUS CLIORD ALGEBRA THE GEOMETRISATION OF BEREZIN CALCULUS EXAMPLE ITHE GRAUSS IN TEGRAL EXAMPLE I ITHE GRASSMANN F OURIER T RANSFORM SOME F URTHER DEV ELOPMEN TS LIE GROUPS AND SPIN GROUPS SPIN GROUPS AND THEIR GENERATORS THE UNITARY GROUP AS A SPIN GROUP THE GENERAL LINEAR GROUP AS A SPIN GROUP ENDOMORPHISMS OF N THE REMAINING CLASSICAL GROUPS COMPLEXI CATION SON C QUATERNIONIC STRUCTURES SPN AND SO N THE COMPLEX AND QUATERNIONIC GENERAL LINEAR GROUPS THE SYMPLECTIC GROUPS SPN R AND SPN C SUMMARY SPINOR ALGEBRA P AULI SPINORS P AULI OP ERATORS MULTIPARTICLE P AULI STATES THE NONRELATIVISTIC SINGLET STATE NONRELATIVISTIC MULTIPARTICLE OBSERV ABLES DIRAC SPINORS CHANGES OF REPRESEN TATION W EYL SPINORS THE MULTIPARTICLE SPACETIME ALGEBRA THE LOREN TZ SINGLET STATE SPINOR CALCULUS SPINOR OBSERV ABLES THE SPINOR INNER PRO DUCT THE NULL T ETRAD THE R A A OP ERATOR APPLICATIONS P OIN TPARTICLE LAGRANGIANS THE MULTIV ECTOR DERIV ATIV E SCALAR AND MULTIV ECTOR LAGRANGIANS NO ETHERS THEOREM SCALAR P ARAMETERISED T RANSFORMATIONS MULTIV ECTOR P ARAMETERISED T RANSFORMATIONS APPLICATIONS MO DELS FOR SPINNING P OIN T P ARTICLES FIELD THEORY THE FIELD EQUATIONS AND NO ETHERS THEOREM SPACETIME T RANSFORMATIONS AND THEIR CONJUGATE T ENSORS APPLICATIONS MULTIV ECTOR T EC HNIQUES FOR F UNCTIONAL DIEREN TIATION GRA VIT Y AS A GAUGE THEORY GAUGE THEORIES AND GRA VIT Y LO CAL P OINCAR E IN V ARIANCE GRA VITATIONAL ACTION AND THE FIELD EQUATIONS THE MATTERFIELD EQUATIONS COMPARISON WITH OTHER APPROAC HES P OIN T SOURCE SOLUTIONS RADIALLYSYMME TRIC STATIC SOLUTIONS KERRT YP E SOLUTIONS EXTENDED MATTER DISTRIBUTIONS CONCLUSIONS