Generalized field quantization and statistics of elementary particles

S. Kamefuchi

Iwo Białynicki‐Birula

S. Kamefuchi, J. A. STRATHDEE

Gordon McCabe

The purpose of this paper is to elucidate the concept of an elementary particle in the first-quantized Standard Model. The emphasis is upon the mathematical structures involved, rather than numerical computations. After the general concepts and philosophical outlook are introduced in the opening section, Section 2 addresses the question of what a free elementary particle is, paying particular attention to the relationships between the configuration representation and momentum representation. Section 3 deals with gauge fields, Section 4 deals with interactions between particles and gauge fields, Section 5 deals with composite systems, and Section 6 deals with the representation of Baryons, Mesons, and Hadrons. Section 7 addresses the interpretational question of whether an elementary particle has only one intrinsic state, and Section 8 attempts to elucidate what an interacting elementary particle is in the Standard Model.

Edwin Langmann A

We present further remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. The identities involve two eCS Hamiltonians with arbitrary and, in general, different particle numbers N and M, and a particular function of N + M variables arising as anyon correlation function of N particles and M anti-particles. In addition to identities obtained from anyons with the same statistics parameter λ, we also obtain “dual ” relations involving “mixed” correlation functions of anyons with two different statistics parameters λ and 1/λ. We also give alternative, elementary proofs of these identities by direct computations.

H. S. Green

A method of field quantization is investigated which is more general than the usual methods of quantization in accordance with Bose of Fermi statistics, though these are included in the scheme. The commutation properties and matrix representations of the quantized field amplitudes are determined, and the energy levels of the field are derived in the usual way. It is shown that spin-half fields can be quantized in such a way that an arbitrary finite number of particles can exist in each eigenstate. With the generalized statistics, the interchange of two particles of the same kind may or may not be physically significant, according to the type of interaction by means of which they are created or annihilated. Physical consequences of the assumption that there are particles which obey the generalized statistics are briefly examined.