標(biāo)題: Titlebook: Clifford Algebras and their Applications in Mathematical Physics; Volume 1: Algebra an Rafa? Ab?amowicz,Bertfried Fauser Book 2000 Springer [打印本頁] 作者: 手鐲 時間: 2025-3-21 17:09
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作者: 奇怪 時間: 2025-3-21 23:36
978-1-4612-7116-1Springer Science+Business Media New York 2000作者: 揉雜 時間: 2025-3-22 04:01 作者: 爭吵 時間: 2025-3-22 05:05 作者: Perennial長期的 時間: 2025-3-22 10:10
Rochelle Gladys Kemitare,Joshua Mugambwaich the ‘Pauli terms’ are formed. We find that these violate a basic axiom of any *-algebra when Dirac’s ψ is canonical. Then the Dirac operator is spanned only by the 10 elements 1, iγ5, γ., γ.γ5 (which don’t form a basis of .. because the σ. are excluded).作者: CUMB 時間: 2025-3-22 14:01
Lucas Gumbi,Hossana Twinomurinzin developing and employing in our research on a Clifford algebra approach to hyperbolic geometry and automated geometry theorem proving. Our work shows that, following this approach, not only can we reformulate existing results with improvements and generalizations, but we also can make new discoveries作者: CUMB 時間: 2025-3-22 19:04
Lecture Notes in Computer Science geometry of spacetime itself may be dictated by the renormalization processes in quantum field theories. Two recently discovered and intimately related Hopf algebras — the Hopf algebra for the computation of the local index formula of transversally hypoelliptic operators and the algebra of renormalization — lie behind these ideas.作者: 助記 時間: 2025-3-22 23:09 作者: Adulterate 時間: 2025-3-23 04:39
Quaternionic Spinsless particles on an equal footing. The resulting description has the correct number of spin/helicity states to be a generation of leptons. Furthermore, precisely three such generations naturally combine into an octonionic description of the 10-dimensional massless Dirac equation, as previously discussed in [1].作者: Enteropathic 時間: 2025-3-23 07:11 作者: IRATE 時間: 2025-3-23 09:51 作者: Catheter 時間: 2025-3-23 15:48 作者: Eructation 時間: 2025-3-23 18:10
https://doi.org/10.1007/978-3-319-55206-4ditional applications use only homogeneous elements (elements of a single grade) to model physical entities such as spacetime vectors in relativity and their transformations. Lower-dimensional realizations of the structures inherent in physical systems are sometimes afforded by exploiting mixed-grad作者: 調(diào)情 時間: 2025-3-24 01:29 作者: Outwit 時間: 2025-3-24 03:43
Rochelle Gladys Kemitare,Joshua Mugambwaich the ‘Pauli terms’ are formed. We find that these violate a basic axiom of any *-algebra when Dirac’s ψ is canonical. Then the Dirac operator is spanned only by the 10 elements 1, iγ5, γ., γ.γ5 (which don’t form a basis of .. because the σ. are excluded).作者: 莎草 時間: 2025-3-24 08:10 作者: 遵循的規(guī)范 時間: 2025-3-24 11:03
Pradnya Vishwas Chitrao,Suruchi Pandeyess particle with a non-vanishing helicity [1]. A relativistic extended phase space of a massive spinning charged particle [2, 3] may be regarded as “embedded” in a two twistor phase space [4, 5, 6] . which is simply . with its diagonal deleted (in the sense of a symplectic reduction). We describe a作者: Ataxia 時間: 2025-3-24 18:30 作者: fixed-joint 時間: 2025-3-24 20:29 作者: palliate 時間: 2025-3-25 00:37
https://doi.org/10.1007/978-3-319-41731-8 and the Pythagorean norm of the corresponding element . ∈ ?. are equal, ii) the “space” parts of . and . are proportional, and iii) the transformation properties of . are induced by those of .. With the aid of such a mapping, a new interpretation of the rest energy of a particle of special relativi作者: 使出神 時間: 2025-3-25 07:03
Beyond Method and Towards Accountability,tities” and of “the distinction, if any exists, between exterior forms and exterior differential forms.” The three series of indices that enter the . of the Kahler calculus are then interpreted..When endowed with a vector-valued potential (the potential and wave-function of electrodynamics being sca作者: gain631 時間: 2025-3-25 09:36
Libu?e Svobodová,Dorota Bednarska-Olejniczakuct * and the dual inner product o, and sheds new light on the duality relation between the progressive and regressive outer products of the Clifford algebra. On the firm base of this dual approach, the projective principle of duality is formulated in this completeness for the first time in the lang作者: coalition 時間: 2025-3-25 11:54
Lucas Gumbi,Hossana Twinomurinzin developing and employing in our research on a Clifford algebra approach to hyperbolic geometry and automated geometry theorem proving. Our work shows that, following this approach, not only can we reformulate existing results with improvements and generalizations, but we also can make new discover作者: 織布機 時間: 2025-3-25 15:49 作者: jeopardize 時間: 2025-3-25 22:08 作者: conscribe 時間: 2025-3-26 01:31 作者: 亂砍 時間: 2025-3-26 06:57
Lecture Notes in Computer Science geometry of spacetime itself may be dictated by the renormalization processes in quantum field theories. Two recently discovered and intimately related Hopf algebras — the Hopf algebra for the computation of the local index formula of transversally hypoelliptic operators and the algebra of renormal作者: LAIR 時間: 2025-3-26 11:03
Multiparavector Subspaces of C?n: Theorems and Applicationsditional applications use only homogeneous elements (elements of a single grade) to model physical entities such as spacetime vectors in relativity and their transformations. Lower-dimensional realizations of the structures inherent in physical systems are sometimes afforded by exploiting mixed-grad作者: 加劇 時間: 2025-3-26 15:15
Quaternionic Spinsless particles on an equal footing. The resulting description has the correct number of spin/helicity states to be a generation of leptons. Furthermore, precisely three such generations naturally combine into an octonionic description of the 10-dimensional massless Dirac equation, as previously dis作者: echnic 時間: 2025-3-26 17:40 作者: 傷心 時間: 2025-3-26 23:00 作者: 小步舞 時間: 2025-3-27 03:16
Twistor Approach to Relativistic Dynamics and to the Dirac Equation — A Reviewess particle with a non-vanishing helicity [1]. A relativistic extended phase space of a massive spinning charged particle [2, 3] may be regarded as “embedded” in a two twistor phase space [4, 5, 6] . which is simply . with its diagonal deleted (in the sense of a symplectic reduction). We describe a作者: 啤酒 時間: 2025-3-27 05:21
Fiber with Intrinsic Action on a 1 + 1 Dimensional Spacetime . formed from the direct product of two copies of an element . in the .. = .. ? .. finite group algebra over the real numbers. The fiber contains subspaces whose elements can be associated with the tangent and momentum vectors of trajectories in the manifold. The fiber also contains a subspace whos作者: 大洪水 時間: 2025-3-27 12:51
Dimensionally Democratic Calculus and Principles of Polydimensional Physicsh each geometric element has its own coordinate. This leads us to propose that all the laws of physics should obey new polydimensional metaprinciples, for which Clifford algebra is the natural language of expression, just as tensors were for general relativity. Specifically, phenomena and physical l作者: Headstrong 時間: 2025-3-27 16:16 作者: palpitate 時間: 2025-3-27 21:45
Clifford-Valued Clifforms: A Geometric Language for Dirac Equationstities” and of “the distinction, if any exists, between exterior forms and exterior differential forms.” The three series of indices that enter the . of the Kahler calculus are then interpreted..When endowed with a vector-valued potential (the potential and wave-function of electrodynamics being sca作者: amorphous 時間: 2025-3-27 22:30 作者: Outspoken 時間: 2025-3-28 06:00
Doing Geometric Research with Clifford Algebran developing and employing in our research on a Clifford algebra approach to hyperbolic geometry and automated geometry theorem proving. Our work shows that, following this approach, not only can we reformulate existing results with improvements and generalizations, but we also can make new discover作者: incisive 時間: 2025-3-28 07:33
Clifford Algebra of Quantum Logicderstand why logic is connected with the standard model of physics and the quantum structure of spacetime, respectively. “It is not the substance which is in space,” as Alfred North Whitehead had pointed out, “but the attributes”. Accordingly, as we consider the Dirac algebra Mat(4, C), annihilation作者: enterprise 時間: 2025-3-28 10:52 作者: 皮薩 時間: 2025-3-28 17:38 作者: Type-1-Diabetes 時間: 2025-3-28 20:41
Dirac Operator, Hopf Algebra of Renormalization, and Structure of Spacetime geometry of spacetime itself may be dictated by the renormalization processes in quantum field theories. Two recently discovered and intimately related Hopf algebras — the Hopf algebra for the computation of the local index formula of transversally hypoelliptic operators and the algebra of renormal作者: 石墨 時間: 2025-3-29 02:22 作者: 大笑 時間: 2025-3-29 06:32 作者: foodstuff 時間: 2025-3-29 07:45
Rochelle Gladys Kemitare,Joshua Mugambwaspaces whose elements can be associated with the tangent and momentum vectors of trajectories in the manifold. The fiber also contains a subspace whose elements are associated with the local flow of action of each trajectory. The condition of minimum action translates into a constraint on the original vector . in the direct product structure.作者: lactic 時間: 2025-3-29 12:45 作者: 抗體 時間: 2025-3-29 15:54
Multiparavector Subspaces of C?n: Theorems and Applicationse representations of such entities, for example by modeling spacetime vectors by paravectors (sums of scalars and vectors). This contribution explores the geometry of subspaces generated by paravectors of .?., the Clifford algebra of . -dimensional Euclidean space, and its applications to physical phenomena.作者: 外形 時間: 2025-3-29 21:43
Electron Scattering in the Spacetime Algebrandependent of spin, we can provide manifestly spin-independent results. Spin basis states are not needed, and we do no spin sums, instead dealing with the spin orientation directly. We perform some example calculations for single electron scattering and briefly discuss more complicated cases in QED.作者: fibula 時間: 2025-3-30 00:38 作者: CLOT 時間: 2025-3-30 05:44 作者: 死貓他燒焦 時間: 2025-3-30 08:15
Beyond Method and Towards Accountability,ucture is Clifford rather than Grassmann. This double Clifford algebra, however, has limitations. These are taken care of by extending the double algebra to a Kaluza-Klein space associated with the given spacetime, where a canonical connection and interior covariant derivative immediately arise.作者: GUISE 時間: 2025-3-30 15:11
A Pythagorean Metric in Relativityinternal degree of freedom of the particle. As a result, the rest energy, which is . (i.e., independent of frame), is regarded as twice the amount of the . of the particle. This accounts for the acronym ..作者: aesthetician 時間: 2025-3-30 16:50
