The most general representation of spin operators via boson operators

Charles Paul Enz

Vitor Rocha Vieira, Pedro D Sacramento

We consider a spin coherent states description of a general quantum spin system. It is shown that it is possible to use the spin-1/2 representation to study the general spin-J case. We identify the 1/2 spinor components as the homogeneous coordinates of the projective space associated to the complex variable that labels the coherent states and establish a relation between the two-component spinor and the bosonic Schwinger representation of a spin operator. We rewrite the equations of motion, obtained from the path integral for the evolution operator or partition function, in terms of the 1/2 spinor and define the effective Hamiltonian of its evolution.

Pedro de M. Rios, Eldar Straume

Alexander J. Silenko

Abstract Zitterbewegung of massive and massless scalar bosons and a massive Proca (spin-1) boson is analyzed. The equations describing the evolution of the velocity and position of the scalar boson in the generalized Feshbach–Villars representation and the corresponding equations for the massive Proca particle in the Sakata–Taketani representation are equivalent to each other and to the well-known equations for the Dirac particle. However, Zitterbewegung does not appear in the Foldy–Wouthuysen representation. Since the position and velocity operators in the Foldy–Wouthuysen representation and their transforms to other representations are the quantum-mechanical counterparts of the corresponding classical variables, Zitterbewegung is not observable.

H. J. Hilhorst

Yang Liu, Jia‐Wei Mei, Rong Yu +3 more

Spin-wave theory provides a quasiparticle description of excitation spectra in quantum spin systems. In this theory, the spin operators are usually bosonized by the Holstein-Primakoff transformation or the Dyson-Maleev transformation. In practical calculations, the bosonized Hamiltonian has to be truncated, and thus the resulting excitation spectra depend on the choice of bosonic representation. Here, we introduce a generalized Holstein-Primakoff transformation that continuously interpolates between the conventional Holstein-Primakoff and Dyson-Maleev transformations through a single parameter. The formulation naturally extends to the SU(N) algebra and provides a flexible framework for optimizing bosonic truncations beyond harmonic order. As an application, we investigate the spin-1 bilinear-biquadratic model on the square lattice. By combining the generalized Holstein-Primakoff transformation with continuous similarity transformations, we obtain excitation spectra in excellent agreement with tensor-network calculations. Our results demonstrate that optimizing the bosonic representation substantially reduces truncation errors and provides quantitatively reliable descriptions of both quasiparticle dispersions and multi-boson continua.