"클리퍼드 대수"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
1번째 줄: 1번째 줄:
 
<h5>introduction</h5>
 
<h5>introduction</h5>
  
−
* [[#]]
 
 
* 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.
 
* 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.
  
10번째 줄: 9번째 줄:
 
<h5>spinor</h5>
 
<h5>spinor</h5>
  
−
* consider a representation of [[Clifford algebras and spinors|Clifford algebras]]
 
−
* the elements in this space are called spinors
 
 
* Spinors are classified according to Dirac, Weyl, Majorana and Weyl-Majorana spinors.
 
* Spinors are classified according to Dirac, Weyl, Majorana and Weyl-Majorana spinors.
 
*  applications<br>
 
*  applications<br>
17번째 줄: 14번째 줄:
 
** spin connections
 
** spin connections
 
** the role of spinors in the description of the fundamental interactions between elementary particles
 
** the role of spinors in the description of the fundamental interactions between elementary particles
−
 
−
 
 
−
 
−
 
 
−
 
−
<h5>Pauli spinor</h5>
 
−
 
−
* 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.
 
−
 
−
 
 
−
 
−
 
 
−
 
−
<h5>Dirac matrices</h5>
 
−
 
−
* 16 dimensional real algebra
 
−
* isomorphic to C(E_{3,1}) Clifford algebra of the Minkowski space E_{3,1}
 
−
 
−
* <math>\gamma_{\mu}^2=\epsilon_{\mu}</math>, <math>\gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu}=0</math><math>\epsilon_{0}=1, \epsilon_{i}=-1</math>
 
−
* 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
 
  
 
 
 
 

2012년 3월 5일 (월) 10:43 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
  • 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

 

 

history

 

 

related items

 

 

encyclopedia

 

 

books

 

 

 

expositions
  • 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

 

 

 

question and answers(Math Overflow)

 

 

 

blogs

 

 

experts on the field

 

 

links
원본 주소 "https://wiki.mathnt.net/index.php?title=클리퍼드_대수&oldid=43048"