Theory of Many - Boson Systems.

Richard David Etters

Richard David Etters

Xiao-Gang Wen

The last few chapters have discussed many-boson theory and many-fermion theory because nature has many-boson systems and many-fermion systems. Do many-boson/many-fermion theories describe all the systems in nature? The answer is no. Nature also has photons. Although photons are bosons, they cannot be described by the local bosonic theory discussed in Chapter 3. Photons are described by a non-local quantum theory which is called U(1) gauge theory. This chapter discusses U(1) gauge theory as well as Z_2 gauge theory on lattice. It stresses the non-localness in their Hilbert space. The gapless photonic, as well as the ‘electric’ and the ‘magnetic’ excitations are studied. The chapter also discusses the confinement phase transition in those gauge theories, and a duality between U(1) gauge theory and XY model in 1+2 dimensions.

U. Balucani, F. Barocchi, V. Tognetti

The many-time Green's-function theory for a damped boson system subjected to an external time-dependent excitation is presented. The damping is properly taken into account by means of a generalized form of the Senitzky-Haken theory of a boson system interacting with a heat bath. The theory leads to a hierarchy of equations for the Green's functions of the system, which are averaged over the heat-bath variables and which take into account the damping of the various boson modes. Two examples for a ferromagnetic magnon system coupled by an anharmonic interaction are given.

Felix Jiun-Horn Lee

Qi-Jun Zeng, Ze Cheng, Jianhui Yuan

Within the framework of the theory of q-deformed bosons, we investigate the problem of fluctuations of a q-deformed boson system, and obtain the general result for thermodynamic fluctuations of such a system. Especially, for the system of a q-deformed boson gas, we get the expressions for the fluctuations of internal energy U and particle number N, and the correlation of the fluctuations of the two physical quantities above. Further numerical calculation shows that the fluctuations of such a q-deformed boson gas have some interesting features. We consider that this work may provide much insight into the theory of q bosons, and may also be useful for the further study of a concrete q-deformed boson gas.