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http://bomber0.myid.net/ (토론)님의 2012년 3월 5일 (월) 10:37 판
introduction
- #
- Clifford algebras may be thought of as quantizations (cf. quantization (physics), Quantum group) of the exterior algebra, in the same way that the Weyl algebra is a quantization of the symmetric algebra.
spinor
- consider a representation of Clifford algebras
- the elements in this space are called spinors
- Spinors are classified according to Dirac, Weyl, Majorana and Weyl-Majorana spinors.
- applications
- spinor bundles
- spin connections
- the role of spinors in the description of the fundamental interactions between elementary particles
Pauli spinor
- 8-dimensional real algebra
- isomorphic to C(E_{3}) Clifford algebra of the Euclidean space E_{3}
- http://en.wikipedia.org/wiki/Spinors_in_three_dimensions
- spinor = a vector in two-dimensional space over complex number field
- Hermitian dot product is given on the vector space
- the space of spinors is a projective representation of the orthogonal group.
Dirac matrices
- 16 dimensional real algebra
- isomorphic to C(E_{3,1}) Clifford algebra of the Minkowski space E_{3,1}
- \(\gamma_{\mu}^2=\epsilon_{\mu}\), \(\gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu}=0\)\(\epsilon_{0}=1, \epsilon_{i}=-1\)
- there exists unique four dimensional representation of a Clifford algebra
- projective representation of the Lorentz group
- universal covering of the Lorentz group H=SL(2,\mathbb{C}) also acts on it
history
- Schrodinger equation
- Pauli equation
- Dirac equation
- spin system and Pauli exclusion principle
- spin structures and spinor fields
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
expositions
- Lachièze-Rey, Marc. 2009. “Spin and Clifford Algebras, an Introduction”. Advances in Applied Clifford Algebras 19 (3-4): 687-720. doi:10.1007/s00006-009-0187-y.
- [1]http://www.math.ucla.edu/~vsv/papers/ch5.pdf
- Frescura, F. A. M. 1981. “Geometric interpretation of the Pauli spinor”. American Journal of Physics 49: 152. doi:10.1119/1.12548.
- Vivarelli, Maria Dina. 1984. “Development of spinor descriptions of rotational mechanics from Euler’s rigid body displacement theorem”. Celestial Mechanics 32 (3월): 193-207. doi:10.1007/BF01236599.
- Coquereaux, Robert. 2005. “Clifford algebras, spinors and fundamental interactions : Twenty Years After”. arXiv:math-ph/0509040 (9월 19). http://arxiv.org/abs/math-ph/0509040.
articles
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
- http://math.stackexchange.com/search?q=
- http://math.stackexchange.com/search?q=
- http://physics.stackexchange.com/search?q=
- http://physics.stackexchange.com/search?q=
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field