Consistent quantization of massless fields of any spin and the generalized Maxwell's equations

9th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

Gersten, Alexander^1 ; Moalem, Amnon^1

Department of Physics, Ben Gurion University of the Negev, Beer-Sheva, Israel^1

关键词: any spin;    Four-vector;    Gauge conditions;    Lorentz group;    Massless particles;    Probability current;    Subsidiary condition;    Vector representations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/615/1/012011/pdf
DOI  :  10.1088/1742-6596/615/1/012011

来源: IOP

【 摘 要 】

A simplified formalism of first quantized massless fields of any spin is presented. The angular momentum basis for particles of zero mass and finite spin s of the D(s-1/2,1/2)representation of the Lorentz group is used to describe the wavefunctions. The advantage of the formalism is that by equating to zero the s - 1 components of the wavefunctions, the 2s - 1 subsidiary conditions (needed to eliminate the non-forward and non-backward helicities) are automatically satisfied. Probability currents and Lagrangians are derived allowing a first quantized formalism. A simple procedure is derived for connecting the wavefunctions with potentials and gauge conditions. The spin 1 case is of particular interest and is described with the D(1/2,1/2)vector representation of the well known self-dual representation of the Maxwell's equations. This representation allows us to generalize Maxwell's equations by adding the E0and B0components to the electric and magnetic four-vectors. Restrictions on their existence are discussed.