A Simple Lagrangian Formalism for Fermi-Dirac Quantization

Philip Broadbridge, C. A. Hurst

C. A. Hurst

A. J. K�lnay, G. J. Ruggeri

J. S. de Wet

It is shown that Fermi-Dirac quantization by the procedure of Heisenberg and Pauli cannot be carried out for tensor wave equations. Since the general wave equations for particles with integral spin are tensor equations, it follows that for these integral spin equations Fermi-Dirac quantization cannot be carried out. During the course of the discussion it appears that for equations derived from Lagrangians which are nonlinear in the derivatives of the functions, Fermi-Dirac quantization cannot be carried out. Since the Heisenberg-Pauli theory applies only to nonlinear Lagrangians, a special discussion of linear Lagrangians (linear in the derivatives of the functions) is given. It is shown how equations derived from such Lagrangians can be put into Hamiltonian form. Lagrangians of this type occur for the equations for half-odd spin.

Alberto Zannoni

An english translation of the original work of Enrico Fermi on the quantization of the monoatomic ideal gas, is given in this paper. Fermi introduced here for the first time the statistical law obeyed by most of the particles in nature: Fermi-Dirac statistics. The formalism that he used is based on the quantization of the monoatomic ideal gas in a harmonic trap. This trappping configuration is similar to that used in current experiments on trapped Fermi gases.

Nikolai Andreevich Tyurin