Cornwell J.F. - Group theory in physics vol 2
ISBN 0-12-189802-4
Techniques of Physics
GROUP THEORV IN PHVSICS
Editors
N. H. MARCH
Department 01 Theoret;cal Chem;stry, University of Oxford,
Oxford, England
Twenty years or so ago group theory could have been regarded merelyas
providing a very valuable tool for the etucidation of the symmetry aspects
of physical problems, but recent developments. particularly in theoretical
high-energy physics, have transformed its role. so that it now occupies a
crucial and indispensable position at the centre of the stage. These develop-
ments have taken physicists increasingly deeper into the fascinating world
cf the pure mathematicians, and have ied to an ever-growing appreciation
cf their achievements. That this recognition is in some respects rather
belated is to a large extent due to the unfortunate fact that much of modern
pure mathematics is written in a style that outsiders find difficult te
penetrate. Consequently one of the main objectives of these two volumes
(and particularly cf the second) has been to help overcome this unnatural
barrier. and to present to theo reti ca I physicists and others the relevant
mathematical deveopments in a form that should be easier to comprehend
and appreciate.
The main ai m of these two volumes has been to previde a thorough and
self-contained account both ot those parts of group theory that have been
found to be most usefui and of their major applications to phys ica I
problems. The treatment starts with the basic concepts and is carried right
through to some of the most significant and recent developments. The
8reas of physics that appear inctude atomic physics. electronic energy
bands in solids, vibrations in molecules and so1ids, and the theory of
elementary particles. No prior knowledge of group theory is assumed, and
fur convenience various relevant algebraic concepts are summarized in
Appendices A and B.
It need hardly be said that the titte that has been chosen for these
volumes, .'Group Theory in Physics", does not jmply that they contai n
8Very appiication of group theoretical ideas to physics. nor that the
mathematical concepts contained within them are strictly restricted to those
of group theory. Some parts of physics. such as nuclear structure theory,
have had 10 be ommed completely. Moreover. even in those areas that have
encouraging. Tile development of semi-simple Lie algebras foUows the
dassic approach of Cartan, wl1ich has the great advantage of betng equaUy
applicable to ali cases. and treatments that are va1id only for restricted types
have been largety neglected. A considerable amount of useful data on
semi-simple lie algebras and groups has been presented in the Appen- dices
some of this having been specially obtained by computer ca1cu1ation.
I would like to thank Dr A. Cant far his valuable eomments on the first
drafts of certain chapters
and Miss L. M. McLean, Mrs J. Kubrycht and Mrs
N. Pacholek far the excel1ence of their typing.
ISBN 0-12-189802-4
Techniques of Physics
GROUP THEORV IN PHVSICS
Editors
N. H. MARCH
Department 01 Theoret;cal Chem;stry, University of Oxford,
Oxford, England
Twenty years or so ago group theory could have been regarded merelyas
providing a very valuable tool for the etucidation of the symmetry aspects
of physical problems, but recent developments. particularly in theoretical
high-energy physics, have transformed its role. so that it now occupies a
crucial and indispensable position at the centre of the stage. These develop-
ments have taken physicists increasingly deeper into the fascinating world
cf the pure mathematicians, and have ied to an ever-growing appreciation
cf their achievements. That this recognition is in some respects rather
belated is to a large extent due to the unfortunate fact that much of modern
pure mathematics is written in a style that outsiders find difficult te
penetrate. Consequently one of the main objectives of these two volumes
(and particularly cf the second) has been to help overcome this unnatural
barrier. and to present to theo reti ca I physicists and others the relevant
mathematical deveopments in a form that should be easier to comprehend
and appreciate.
The main ai m of these two volumes has been to previde a thorough and
self-contained account both ot those parts of group theory that have been
found to be most usefui and of their major applications to phys ica I
problems. The treatment starts with the basic concepts and is carried right
through to some of the most significant and recent developments. The
8reas of physics that appear inctude atomic physics. electronic energy
bands in solids, vibrations in molecules and so1ids, and the theory of
elementary particles. No prior knowledge of group theory is assumed, and
fur convenience various relevant algebraic concepts are summarized in
Appendices A and B.
It need hardly be said that the titte that has been chosen for these
volumes, .'Group Theory in Physics", does not jmply that they contai n
8Very appiication of group theoretical ideas to physics. nor that the
mathematical concepts contained within them are strictly restricted to those
of group theory. Some parts of physics. such as nuclear structure theory,
have had 10 be ommed completely. Moreover. even in those areas that have
encouraging. Tile development of semi-simple Lie algebras foUows the
dassic approach of Cartan, wl1ich has the great advantage of betng equaUy
applicable to ali cases. and treatments that are va1id only for restricted types
have been largety neglected. A considerable amount of useful data on
semi-simple lie algebras and groups has been presented in the Appen- dices
some of this having been specially obtained by computer ca1cu1ation.
I would like to thank Dr A. Cant far his valuable eomments on the first
drafts of certain chapters
and Miss L. M. McLean, Mrs J. Kubrycht and Mrs
N. Pacholek far the excel1ence of their typing.
