"클리퍼드 대수"의 두 판 사이의 차이

2012년 3월 5일 (월) 10:37 판

#
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.

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

\(\gamma_{\mu}^2=\epsilon_{\mu}\), \(\gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu}=0\)\(\epsilon_{0}=1, \epsilon_{i}=-1\)
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

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.

@@ 2번째 줄: / 2번째 줄: @@
 * [[#]]
-* quadratic space <math>(V,Q)</math>
-* Q : non-degenerate quadratic form, defines a symmetric bilinear form <math><x,y></math>
-*  Clifford algebra : associative algebra generated by vectors in V with relations<br>
-** <math>v^2=Q(v)</math>
-** <math>vw+wv=2<w,v></math>
 * 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.