Quantization of relativistic Fermi-Bose systems with first- and second-order couplings by the compensating functional method

S. T. Ali

Hugo Reinhardt

The third volume in this three-part textbook deals with second quantization and functional integral quantization for Bose and Fermi systems as well as relativistic fields. Other emphases include quantum statistics and Green's functions, as well as their application to the description of multibody systems at finite temperatures.

Edward R. Pike

Xiang‐Gui Li, Shu‐Cun Li

In this work, a high-order numerical method with mass and energy conservation obtained by the operator-compensation (OC) technique is proposed for the coupled Gross–Pitaevskii equations (CGPEs) modelling the spin–orbit-coupled Bose–Einstein condensates. The OC technique is utilized to seek high-order approximations to the first- and the second-order spatial derivatives in the CGPEs, after which a time-dependent semi-discrete system is obtained. Then we obtain a fully discrete scheme by applying the Crank–Nicolson method to discretize this system in time. We theoretically show that the semi-discrete system and the fully discrete scheme conserve both mass and energy on the discrete level. In addition, the stability analysis is discussed for the proposed method. Numerical experiments are given to test accuracy and verify conservative properties. The dynamics of the two-dimensional CGPEs and the effects of the parameters in the CGPEs are simulated.

Gerhard Heber, Adolf Kühnel

Oscar Wallace Greenberg, Albert Messiah

Para-Bose and para-Fermi quantization are schemes of second quantization which generalize the usual Bose and Fermi schemes. The different cases of para-Bose (para-Fermi) quantization are labeled by a positive integer p, which is called the ``order.'' For p = 1, the usual Bose (Fermi) quantization is recovered. The high-p limit of para-Bose (para-Fermi) quantization is studied, and it is shown that, to a large extent, the high-p limit of a para-Bose (para-Fermi) field is a Fermi (Bose) field. The nature of the limit is studied in detail, and a paradox relating to the connection of spin and statistics is resolved.