Springer Tracts in Modern Physics, Volume 60 by Professor Dr. J. Wess (auth.)

By Professor Dr. J. Wess (auth.)

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As we shall see in the next lecture the attempt to do so establishes a very beautiful connection between this definition of PCAC and Weinberg's 'phenomenological Lagrangian' formalism. 54 M. Weinstein: 4. Phenomenological Lagrangians I would now like to discuss the way in which one derives the consequences of a symmetry of the Goldstone type. A really detailed treatment of this point is given in a paper written by Roger Dashen and myself [2]. I would like, however, to use this lecture in order to familiarize you with the most important aspects of our results.

Throughout our discussion we shall alternate between a discussion of the idea of an approximate S U ( 2 ) | U(2) symmetry for the strong interactions and that of an approximate S U(3)| S U(3) symmetry. The difference will lie primarily in whether or not we are considering predictions for processes involving the strange-pseudo scalar mesons. We shall therefore adopt the typical convention of letting the symbols V~(x) and A~(x) (~= 1, 2 .... 8) stand for the eight vector and axialvector currents encountered in the theory of the weak and electromagnetic interactions.

2. The G o l d b e r g e r - T r e i m a n R e l a t i o n . . . . . . . . . . . 3. S y m m e t r i e s - C o n v e n t i o n a l vs. G o l d s t o n e Basic A s s u m p t i o n s . . . . . 4. P h e n o m e n o l o g i c a l L a g r a n g i a n s . . . . . . . . . . . 5. B e y o n d the Z e r o t h A p p r o x i m a t i o n . . . . . . . . . . 6. S U ( 3 ) | S U(3) a n d W e a k a n d E l e c t r o m a g n e t i c Processes . . . . . . References .

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