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Regge poles in particle physics, Springer tracts in modern physics
-~ Nuclear Physics B21 (1970) 331. North-Holland Publishing Company
BOOK
REVIEW
P. D. B. COLLINS and E. J. SQUIRES, Regge poles in particle physics, Springer tracts in modern physics, vol. 45 ( S p r i n g e r - V e r l a g , Berlin, 1968, 292 pp. $19.50) Despite the amount of l i t e r a t u r e on Regge t h e o r y and phenomenology t h e r e has been s o m e lack of books t r e a t i n g this t h e o r y in a connected m a n n e r s t a r t i n g f r o m b a s i c p r i n c i p l e s . The p r e s e n t work is an attempt both to r e v i e w the t h e o r y as it stands and to c o m p a r e it to the e x p e r i m e n t a l situation. It is, of c o u r s e , i m p o s s i b l e to t r e a t such a v a s t subject in all its details, s o m e p a r t s have to be t r e a t e d in a m o r e sketchy m a n n e r . The a u t h o r s have solved this p r o b l e m with s u c c e s s and give extensive r e f e r e n c e s for the r e a d e r ' s help. The f i r s t chapter of the book is a r e v i e w of the S - m a t r i x t h e o r y , postulates, s i n g u l a r i t y s t r u c t u r e of the amplitude, d i s p e r s i o n r e l a t i o n s and the M a n d e l s t a m r e p r e s e n t a t i o n . In the second chapter the authors d i s c u s s the p a r t i a l - w a v e amplitude p r o p e r t i e s . Then follows the s t a n d a r d analytic continuation in angular m o m e n t u m leading to the Regge expansion. An objection to t h e s e c h a p t e r s is that t h e r e a r e a n u m b e r of m i s p r i n t s , m o s t of t h e m t r i v i a l but n e v e r t h e l e s s v e r y annoying. As this p a r t of the book obviously a d d r e s s e s itself to the uninitiated, it is p a r t i c u l a r l y i m p o r t a n t that t h e s e e r r o r s a r e c o r r e c t e d in the c o m i n g editions. The t h i r d chapter deals with the p r o b l e m s that a r i s e when one t r i e s to combine the Regge expansion and the M a n d e l s t a m r e p r e s e n t a t i o n . This leads to the C h e w - J o n e s and K h u r i - J o n e s r e p r e s e n t a t i o n s and to the conc e p t s of ' s a t e l l i t e s ' and ' d a u g h t e r s ' . In chapter four spin is introduced using the J a c o b - W i c k helicity f o r m a l i s m . The nature of the J - p l a n e s i n g u l a r i t i e s is investigated in chapter five. Also s u p e r c o n v e r g e n c e r e l a t i o n s a r e d i s c u s s e d h e r e . Chapter six i n t r o d u c e s the b o o t s t r a p hypothesis which is then used for s o m e simple calculations of Regge t r a j e c t o r i e s . Chapter seven deals with F e y n m a n g r a p h s and it is shown that by s u m m i n g up infinite c l a s s e s of such graphs, one can obtain Regge behaviour. The a p p e a r ance of the v a r i o u s J - p l a n e s i n g u l a r i t i e s is also d i s c u s s e d . Roughly the l a s t t h i r d of the book then t r e a t s c o m p a r i s o n s between Regge t h e o r y and e x p e r i m e n t and exhibits in an i m p r e s s i v e way the s u c c e s s of Regge theory. To s u m m a r i z e , this book contains a wealth of useful i n f o r m a t i o n and it will c e r t a i n l y for a long time to come be an indispensable r e f e r e n c e for both t h e o r i s t s and e x p e r i m e n t a l i s t s working in this field. L a r s GISLI~.N
BOOK
REVIEW
P. D. B. COLLINS and E. J. SQUIRES, Regge poles in particle physics, Springer tracts in modern physics, vol. 45 ( S p r i n g e r - V e r l a g , Berlin, 1968, 292 pp. $19.50) Despite the amount of l i t e r a t u r e on Regge t h e o r y and phenomenology t h e r e has been s o m e lack of books t r e a t i n g this t h e o r y in a connected m a n n e r s t a r t i n g f r o m b a s i c p r i n c i p l e s . The p r e s e n t work is an attempt both to r e v i e w the t h e o r y as it stands and to c o m p a r e it to the e x p e r i m e n t a l situation. It is, of c o u r s e , i m p o s s i b l e to t r e a t such a v a s t subject in all its details, s o m e p a r t s have to be t r e a t e d in a m o r e sketchy m a n n e r . The a u t h o r s have solved this p r o b l e m with s u c c e s s and give extensive r e f e r e n c e s for the r e a d e r ' s help. The f i r s t chapter of the book is a r e v i e w of the S - m a t r i x t h e o r y , postulates, s i n g u l a r i t y s t r u c t u r e of the amplitude, d i s p e r s i o n r e l a t i o n s and the M a n d e l s t a m r e p r e s e n t a t i o n . In the second chapter the authors d i s c u s s the p a r t i a l - w a v e amplitude p r o p e r t i e s . Then follows the s t a n d a r d analytic continuation in angular m o m e n t u m leading to the Regge expansion. An objection to t h e s e c h a p t e r s is that t h e r e a r e a n u m b e r of m i s p r i n t s , m o s t of t h e m t r i v i a l but n e v e r t h e l e s s v e r y annoying. As this p a r t of the book obviously a d d r e s s e s itself to the uninitiated, it is p a r t i c u l a r l y i m p o r t a n t that t h e s e e r r o r s a r e c o r r e c t e d in the c o m i n g editions. The t h i r d chapter deals with the p r o b l e m s that a r i s e when one t r i e s to combine the Regge expansion and the M a n d e l s t a m r e p r e s e n t a t i o n . This leads to the C h e w - J o n e s and K h u r i - J o n e s r e p r e s e n t a t i o n s and to the conc e p t s of ' s a t e l l i t e s ' and ' d a u g h t e r s ' . In chapter four spin is introduced using the J a c o b - W i c k helicity f o r m a l i s m . The nature of the J - p l a n e s i n g u l a r i t i e s is investigated in chapter five. Also s u p e r c o n v e r g e n c e r e l a t i o n s a r e d i s c u s s e d h e r e . Chapter six i n t r o d u c e s the b o o t s t r a p hypothesis which is then used for s o m e simple calculations of Regge t r a j e c t o r i e s . Chapter seven deals with F e y n m a n g r a p h s and it is shown that by s u m m i n g up infinite c l a s s e s of such graphs, one can obtain Regge behaviour. The a p p e a r ance of the v a r i o u s J - p l a n e s i n g u l a r i t i e s is also d i s c u s s e d . Roughly the l a s t t h i r d of the book then t r e a t s c o m p a r i s o n s between Regge t h e o r y and e x p e r i m e n t and exhibits in an i m p r e s s i v e way the s u c c e s s of Regge theory. To s u m m a r i z e , this book contains a wealth of useful i n f o r m a t i o n and it will c e r t a i n l y for a long time to come be an indispensable r e f e r e n c e for both t h e o r i s t s and e x p e r i m e n t a l i s t s working in this field. L a r s GISLI~.N