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Zuber - Ivariances in Physics and Group Theory.pdf

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M2/International Centre for Fundamental Physics Parcours of Physique Th´eorique Invariances in Physics and Group Theory Jean-Bernard Zuber #$%& '$()#* +,$% -%#$ ./)0/( '$(1)#* ./#) .%/31$ .4$5/%%$6 7318%9 :; +; .%$,&
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  M2/International Centre for Fundamental Physics Parcours of Physique Th´eorique Invariances in Physicsand Group Theory Jean-Bernard Zuber   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  +(1)Q R$#% '$)2/(( R$6% -3L$($ O; R#L($) -)(&0 R#00 +%9)$1 \83(L @EBJ D @EEF @EBF D @EEA @AAG D @EGG @EBC D @EEG @E@@ D @EE@ @AKJ D @EIB =82$ 89 04$ 2/]8) /<08)& 89 L)83U 04$8)6 2$(0#8(($1 #( 04$ 9#)&0 U/)0 89 04$&$ (80$&    i Foreword The following notes cover the content of the course “Invariances in Physique and GroupTheory” given in the fall 2013. Additional lectures were given during the week of “pr´erentr´ee”on the SO(3), SU(2), SL(2, C ) groups, see below Chap. 0.Chapters 1 to 5 also contain, in sections in smaller characters and Appendices, additionaldetails that are not treated in the oral course. General bibliography ã  [BC] N.N. Bogolioubov et D.V. Chirkov,  Introduction `a la th´eorie quantique des champs  ,Dunod. ã  [BDm] J.D. Bjorken and S. Drell:  Relativistic Quantum Mechanics  , McGraw Hill. ã  [BDf] J.D. Bjorken and S. Drell:  Relativistic Quantum Fields  , McGraw Hill. ã  [Bo] N. Bourbaki,  Groupes et Alg`ebres de Lie  , Chap. 1-9, Hermann 1960-1983. ã  [Bu] D. Bump,  Lie groups  , Series “Graduate Texts in Mathematics”, vol.  225 , Springer2004. ã  [DFMS] P. Di Francesco, P. Mathieu and D. S´en´echal,  Conformal Field Theory  , Springer, ã  [DNF] B. Doubrovine, S. Novikov et A. Fomenko,  G´eom´etrie contemporaine  , 3 volumes,´Editions de Moscou 1982, reprinted in english by Springer. ã  [FH] W. Fulton and J. Harris,  Representation Theory  , Springer. ã  [Gi] R. Gilmore,  Lie groups, Lie algebras and some of their applications  , Wiley. ã  [Ha] M. Hamermesh,  Group theory and its applications to physical problems  , Addison-Wesley ã  [IZ] C. Itzykson et J.-B. Zuber,  Quantum Field Theory  , McGraw Hill 1980; Dover 2006. ã  [Ki] A.A. Kirillov,  Elements of the theory of representations  , Springer. ã  [LL] L. Landau et E. Lifschitz,  Th´eorie du Champ , Editions Mir, Moscou ou  The Classical Theory of Fields  , Pergamon Pr. ã  [M] A. Messiah,  M´ecanique Quantique  , 2 tomes, Dunod. ã  [OR] L. O’ Raifeartaigh,  Group structure of gauge theories  , Cambridge Univ. Pr. 1986. ã  [PS] M. Peskin and D.V. Schroeder,  An Introduction to Quantum Field Theory  , AddisonWesley.  ii ã  [Po] L.S. Pontryagin,  Topological Groups  , Gordon and Breach, 1966. ã  [St] S. Sternberg,  Group theory and physics  , Cambridge University Press. ã  [W] H. Weyl,  Classical groups  , Princeton University Press. ã  [Wf] S. Weinberg,  The Quantum Theory of Fields  , vol. 1, 2 and 3, Cambridge UniversityPress. ã  [Wg] S. Weinberg,  Gravitation and Cosmology  , John Wiley & Sons. ã  [Wi] E. Wigner,  Group Theory and its Applications to Quantum Mechanics  . Academ. Pr.1959. ã  [Z-J] J. Zinn-Justin,  Quantum Field Theory and Critical Phenomena  , Oxford Univ. Pr.
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