Spin
and Spinors| Spin
and Spinors |
In General > s.a. spin
models; spinors in field theory; types
of particles [electron].
* Idea: Spinors are elements of vector spaces carrying spinor representations
of the rotation group, where a 2
rotation
is –1.
* Interpretation: Spinors
themselves cannot have a physical interpretation, but bilinear products of
spinors and complex conjugate spinors can (e.g., a
4D null vector can be seen as a tensor product of an SL(2,C)
spinor
and its complex conjugate); They can however have geometrical interpretations
as generalized geometrical objects.
* Kähler spinors: Polynomials of differential forms.
* Applications: Spinors
are natural in quantum mechanics, but they are also very useful in classical
theories; Witten's proof of the positive energy theorem, spinorial
decomposition
of the curvature tensor, principal null directions of Weyl tensors.
Types and Related Topics > s.a. 2-spinors;
4-spinors; Pin Group; spin
structure.
* ELKO spinors: "Eigenspinoren
des Ladungskonjugationsoperators", or dual-helicity eigenspinors of the charge
conjugation operator.
@ General references: Trautman ln(87) [Dirac and Chevalley]; Goncharov IJMPA(94)
[real]; van Nieuwenhuizen & Waldron PLB(96)
[Euclidean]; Hamilton JMP(97)
[hypercomplex numbers]; Faber FBS(01)ht/99 [topological
fermions]; Friedman & Russo FP(01)
[geometry, Jordan triples and spin factors]; Rodrigues JMP(04)mp/02 [Dirac-Hestenes
spinors]; Miralles & Pozo JMP(06)
[unified description
of different types]; Poplawski a0710 [covariant
derivatives].
@ Kähler spinors: Becher & Joos ZPC(82)
[lattice]; Bullinaria
AP(86);
Jourjine PRD(87)
[quantization]; Shimono PTP(90)
[and lattice gravity]; Borstnik & Nielsen ht/99-in,
PRD(00)ht/99, ht/00;
Jourjine a0805.
@ ELKO spinors: da
Rocha
& Rodrigues MPLA(06)mp/05
[and Lounesto classification]; Böhmer AdP(06)gq [and
Einstein-Cartan theory], AdP(07)gq [in
curved spacetime, coupled Einstein-ELKO fields]; da Rocha & Hoff da Silva JMP(07)-a0711,
IJMPA(09)-a0903 [and
Dirac spinors], IJGMP(09)-a0901 [and
gravity].
> Other topics: see deformation
quantization; inertia; lie
derivatives.
Spinor Irreducible Representations
* Pattern: (repeats itself mod
4)
| SO(3,1) | SO(5,1) | SO(7,1) | SO(9,1) |
| SO(2) | SO(4) | SO(6) | SO(8) |
| 2 each | Pseudoreal | 2 each | Real |
| (L & R) | (equivalent to its c.c. but not real) | (L & R) |
main page – abbreviations – journals – comments – other
sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 15
sep 2009