Continuous Groups for Physicists

Continuous Groups for Physicists is written for graduate students as well as researchers working in the field of theoretical physics. The text has been designed uniquely and it balances coverage of advanced and non-standard topics with an equal focus on the basic concepts for a thorough understanding. The book describes the general theory of Lie groups and Lie algebras, the passage between them, and their unitary/ Hermitian representations in the quantum mechanical setting. The four infinite classical families of compact simple Lie groups and their representations are covered in detail. Readers will benefit from the discussions on topics like spinor representations of real orthogonal groups, the Schwinger representation of a group, induced representations, systems of coherent states, real symplectic groups important in quantum mechanics, Wigner's theorem on symmetry operations in quantum mechanics, ray representations of Lie groups, and groups associated with non-relativistic and relativistic space-time. "The theory of groups and group representations is an important part of mathematics with applications in other areas of mathematics as well as in physics. It is basic to the study of symmetries of physical systems. Its mathematical concepts are equally significant in understanding complex physical systems. It offers the necessary tools to describe, for instance, crystal structures, elementary particles with spin, both Galilean symmetric and special relativistic quantum mechanics, the fundamental properties of canonical commutation relations, and spinor representations of orthogonal groups extensively used in quantum field theory. Continuous Groups for Physicists introduces the ideas of continuous groups and their applications to graduate students and researchers in theoretical physics. The book begins with an introduction to groups and group representations in the context of finite groups. This is followed by a chapter on the special algebraic features of the symmetric groups. The authors then present the theory of Lie groups, Lie algebras, and in particular the classical families of compact simple Lie groups and their representations. Several interesting topics not often found in standard physics texts are then presented: the spinor representations of the real orthogonal groups, the real symplectic groups in even dimensions, induced representations, the Schwinger representation concept, the Wigner theorem on symmetry operations in quantum mechanics, and the Euclidean, Galilei, Lorentz, and Poincare groups associated with spacetime. The general methods and notions of quantum mechanics are used as background throughout"-- Provided by publisher