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Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory
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Group Theory in Physics (Hardcover)
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Group Theory in Physics (Hardcover)
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Group theory studies that has been considered by physicists as a
very valuable tool for the clarification of the symmetry aspects of
physical problems. The book intents to describe in detail the most
important fundamental ideas of the group theory, its significant
developments and various applications in: Hamiltonian systems,
nonlinear systems, thermo-fluid dynamics, quantum mechanics and
solid-state physics. In particular, different applications of Lie's
group theory to the above said fields are shown.The examination of
the exact solutions of nonlinear equations takes an important place
in physics. One of the noteworthy and efficient methods for gaining
solutions of systems of nonlinear differential equations is the
classical symmetries method, also called Lie's group analysis. This
method is employed for the constructions of solutions for the
magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM)
fluid over a porous shrinking wall, for the boundary layer
equations for the Sisko fluid, and for a two-dimensional, unsteady
flow and heat transfer of a viscous fluid over a surface in the
presence of variable suction/injection. Another interesting
application about the design of Lie's group integrators of
multibody system dynamics is presented. The quantum behavior of a
physical system is a natural consequence of its symmetries. Hence,
it is a fundamental to study the invariants of symmetry groups of
them. In particular, invariant bilinear forms are very important
for quantum physics, because these forms provide the link between
mathematical description and experimental observations. The group
theoretical analysis of the electronic and vibrational structure of
the trimethine cyanine dye molecules is described. Other example of
application of the group theory in the quantum mechanics is the
establishment of a method for the description of an interacting
spin-0 particle. The electronic energy band structure is a basic
theory in condensed matter physics and can be used to study many
physical properties of crystal materials. Here are presented a
general method to unfold energy bands of supercell calculations to
a primitive Brillouin zone and the results of the symmetry
classification of the electron energy bands in graphene and
silicene. The band degeneracy at high symmetry points or the
existence of energy gaps, usually reflect the symmetry of the
crystal, and this property is analyzed by considering
two-dimensional (2D)-hexagonal lattices.
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