Group Theory webbook - literature

Predrag Cvitanović publications


Predrag Cvitanović (Nordita Jan 1984)
might still be available from Nordita; please enquire with the secretary in charge of preprints. It is a cute little book with hand drawn birdtracks, of sentimental use only - its entire contents are incorporated into this webbook.

  Group theory for Feynman diagrams in non-Abelian gauge theories
Predrag Cvitanović
Phys. Rev. D14, 1536 (1976) - SLAC-PUB-1663 (November 1975)
citations on INSPIRE, Google Scholar
A useful initial introduction into diagramatic techniques for classical and exceptional Lie algebras; superceeded by this webbook, but contains interesting material (counting of invariants, graphs, etc.,) not included in the webbook.

  Negative dimensions and E_7 symmetry
Predrag Cvitanović
Nucl. Phys. B188, 373 (1981) - 4 citations in 22 years?
Julia and Cremer (Nucl. Phys. B159, 141 (1979)) extended supergravities coincide with the E_7 family row of my Magic Triangle, so in a rush of optimism that there might be an application of my theory of invariance groups, I published a derivation of the E_7 row. As the cogniscenti find birtracks difficult to follow, in this paper I translateded birdtracks into (for me unintelligable) conventional tensorial notation, and published the derivation without a single diagram. The Magic Triangle, introduced in the Oxford preprint (below) is published for the first time here, as well as the intriguing "negative dimensional" relation between SO(4) and E_7 families.

  Spinors in negative dimensions
P. Cvitanović and A.D. Kennedy
Phys. Scripta 26, 5 (1982) - Citations on SPIRES
computer implementation - Alexander Kryukov's computer Lie algebra programs (29 Sept 99)
Only scanned version of preprint available, from KEK Library

  Diagrammatic Young projection operators for U(n)
J. Math. Phys. 46, 043501 (2005)
Henriette Elvang, Predrag Cvitanović and Anthony D. Kennedy
hep-th/0307186, (rejected by Phys. Rev. D and Nucl. Phys. B editors without refereeing)
We utilize a diagrammatic notation for invariant tensors to construct the Young projection operators for the irreducible representations of the unitary group, and show that all U(n) invariant scalars can be constructed and evaluated diagrammatically.

  Tracks, Lie's, and Exceptional Magic
Predrag Cvitanović
in B. Julia, P. Moussa and P. Vanhove, eds., Number Theory and Physics, Les Houches 2003 Spring School (Springer, New York 2007)
Les Houches 2003 lecture: a brief overview of the birdtrack derivation of the Magic Triangle.

  Classical and exceptional Lie algebras as invariance algebras
Predrag Cvitanović
Oxford preprint 40/77 (June, 1977 - unpublished) - 4.1MB pdf file Citations on SPIRES
The initial draft of my construction of exceptional Lie algebras; mostly of historical interest, superceeded by this webbook. Contains some material not yet included in the webbook.


  Sums of Wigner coefficients and their graphical representation
I. B. Levinson
Proceed. Physical-Technical Inst. Acad. Sci. Lithuanian SSR 2 (1956) 17-30.
Appears to be the first paper with group-theoretic diagramatic notation

  The two Magic Triangles are distinctly different
B. L. Julia
There is no known relation between Julia's extended supergravities Magic Triangle and Cvitanović's Magic Triangle.


For a list of software, see
Christoph Schweigert
A. N. Schellekens
A Computer Program for QCD Colour Factor Calculations (ResearchIndex)
  Cvit package