“Van der Waerden notation”的意思、由来-开放百科全书

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Van der Waerden notation

释义

Dotted indices
Hatted indices
See also
Notes
References

In theoretical physics, van der Waerden notation^[1]^[2] refers to the usage of two-component spinors (Weyl spinors) in four spacetime dimensions. This is standard in twistor theory and supersymmetry. It is named after Bartel Leendert van der Waerden.

Dotted indices

Undotted indices (chiral indices)

Spinors with lower undotted indices have a left-handed chiralty, and are called chiral indices.

Dotted indices (anti-chiral indices)

Spinors with raised dotted indices, plus an overbar on the symbol (not index), are right-handed, and called anti-chiral indices.

Without the indices, i.e. "index free notation", an overbar is retained on right-handed spinor, since ambiguity arises between chiralty when no index is indicated.

Hatted indices

Indices which have hats are called Dirac indices, and are the set of dotted and undotted, or chiral and anti-chiral, indices. For example, if

then a spinor in the chiral basis is represented as

where

In this notation the Dirac adjoint (also called the Dirac conjugate) is

Notes

1. ^{{cite journal|title=Spinoranalyse|author=Van der Waerden B.L.|journal=Nachr. Ges. Wiss. Göttingen Math.-Phys.|volume=1929|year=1929|pages=100–109}}
2. ^{{cite journal|title=Geometry of two-component Spinors|author=Veblen O.|journal=Proc. Natl. Acad. Sci. USA|volume=19|year=1933|pages=462–474|doi=10.1073/pnas.19.4.462 |bibcode = 1933PNAS...19..462V |pmc=1086023}}

References

[https://web.archive.org/web/20160920000629/https://terpconnect.umd.edu/~wdlinch3/MyNotes/07.04.30.14.30.RTGSpin.pdf Spinors in physics]
{{citation|author= P. Labelle|title=Supersymmetry|year = 2010|publisher = Demystified series, McGraw-Hill (USA)|isbn=978-0-07-163641-4}}
{{citation|last1 = Hurley|first1=D.J.|last2 = Vandyck|first2=M.A.|title=Geometry, Spinors and Applications|year = 2000|publisher = Springer |isbn=1-85233-223-9}}
{{citation|last1 = Penrose|first1=R.|last2 = Rindler|first2=W.|title=Spinors and Space–Time|year = 1984|publisher = Cambridge University Press|volume=Vol. 1|isbn=0-521-24527-3}}
{{citation|last1 = Budinich|first1=P.|last2 = Trautman|first2=A.|title=The Spinorial Chessboard|year = 1988|publisher = Springer-Verlag|isbn=0-387-19078-3}}

3 : Quantum field theory|Spinors|Mathematical notation

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Dotted indices

Hatted indices

See also

Notes

References