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Clifford Algebras and their Applications in Mathematical Physics [electronic resource] : Volume 1: Algebra and Physics /
The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.
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| Language: | eng |
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Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser,
2000
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| Subjects: | Mathematics., Differential geometry., Physics., Differential Geometry., Mathematical Methods in Physics., Theoretical, Mathematical and Computational Physics., |
| Online Access: | http://dx.doi.org/10.1007/978-1-4612-1368-0 |
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Mathematics. Differential geometry. Physics. Mathematics. Differential Geometry. Mathematical Methods in Physics. Theoretical, Mathematical and Computational Physics. Mathematics. Differential geometry. Physics. Mathematics. Differential Geometry. Mathematical Methods in Physics. Theoretical, Mathematical and Computational Physics. |
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Mathematics. Differential geometry. Physics. Mathematics. Differential Geometry. Mathematical Methods in Physics. Theoretical, Mathematical and Computational Physics. Mathematics. Differential geometry. Physics. Mathematics. Differential Geometry. Mathematical Methods in Physics. Theoretical, Mathematical and Computational Physics. Abłamowicz, Rafał. editor. Fauser, Bertfried. editor. SpringerLink (Online service) Clifford Algebras and their Applications in Mathematical Physics [electronic resource] : Volume 1: Algebra and Physics / |
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The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1. |
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Mathematics. Differential geometry. Physics. Mathematics. Differential Geometry. Mathematical Methods in Physics. Theoretical, Mathematical and Computational Physics. |
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Abłamowicz, Rafał. editor. Fauser, Bertfried. editor. SpringerLink (Online service) |
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Abłamowicz, Rafał. editor. Fauser, Bertfried. editor. SpringerLink (Online service) |
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Abłamowicz, Rafał. editor. |
| title |
Clifford Algebras and their Applications in Mathematical Physics [electronic resource] : Volume 1: Algebra and Physics / |
| title_short |
Clifford Algebras and their Applications in Mathematical Physics [electronic resource] : Volume 1: Algebra and Physics / |
| title_full |
Clifford Algebras and their Applications in Mathematical Physics [electronic resource] : Volume 1: Algebra and Physics / |
| title_fullStr |
Clifford Algebras and their Applications in Mathematical Physics [electronic resource] : Volume 1: Algebra and Physics / |
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Clifford Algebras and their Applications in Mathematical Physics [electronic resource] : Volume 1: Algebra and Physics / |
| title_sort |
clifford algebras and their applications in mathematical physics [electronic resource] : volume 1: algebra and physics / |
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Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, |
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2000 |
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http://dx.doi.org/10.1007/978-1-4612-1368-0 |
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AT abłamowiczrafałeditor cliffordalgebrasandtheirapplicationsinmathematicalphysicselectronicresourcevolume1algebraandphysics AT fauserbertfriededitor cliffordalgebrasandtheirapplicationsinmathematicalphysicselectronicresourcevolume1algebraandphysics AT springerlinkonlineservice cliffordalgebrasandtheirapplicationsinmathematicalphysicselectronicresourcevolume1algebraandphysics |
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KOHA-OAI-TEST:1821282018-07-30T23:02:58ZClifford Algebras and their Applications in Mathematical Physics [electronic resource] : Volume 1: Algebra and Physics / Abłamowicz, Rafał. editor. Fauser, Bertfried. editor. SpringerLink (Online service) textBoston, MA : Birkhäuser Boston : Imprint: Birkhäuser,2000.engThe plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.1 Physics — Applications and Models -- Multiparavector Subspaces of C?n: Theorems and Applications -- Quaternionic Spin -- Pauli Terms Must Be Absent in the Dirac Equation -- Electron Scattering in the Spacetime Algebra -- 2 Physics — Structures -- Twistor Approach to Relativistic Dynamics and to the Dirac Equation — A Review -- Fiber with Intrinsic Action on a 1 + 1 Dimensional Spacetime -- Dimensionally Democratic Calculus and Principles of Polydimensional Physics -- A Pythagorean Metric in Relativity -- Clifford-Valued Clifforms: A Geometric Language for Dirac Equations -- 3 Geometry and Logic -- The Principle of Duality in Clifford Algebra and Projective Geometry -- Doing Geometric Research with Clifford Algebra -- Clifford Algebra of Quantum Logic -- 4 Mathematics — Deformations -- Hecke Algebra Representations in Ideals Generated by q-Young Clifford Idempotents -- On q-Deformations of Clifford Algebras -- Dirac Operator, Hopf Algebra of Renormalization and Structure of Space-time -- Non-commutative Spaces for Graded Quantum Groups and Graded Clifford Algebras -- 5 Mathematics — Structures -- Clifford Algebras and the Construction of the Basic Spinor and Semi-Spinor Modules -- On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form -- Covariant Derivatives on Minkowski Manifolds -- An Introduction to Pseudotwistors: Spinor Solutions vs. Harmonic Forms and Cohomology Groups -- Ordinary Differential Equation: Symmetries and Last Multiplier -- Universal Similarity Factorization Equalities Over Complex.The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.Mathematics.Differential geometry.Physics.Mathematics.Differential Geometry.Mathematical Methods in Physics.Theoretical, Mathematical and Computational Physics.Springer eBookshttp://dx.doi.org/10.1007/978-1-4612-1368-0URN:ISBN:9781461213680 |