Explicit expressions of spin wave functions (original) (raw)

The Schrödinger eigenfunctions for the half-integral spins

Physica A-statistical Mechanics and Its Applications - PHYSICA A, 1999

In this paper we are interested in approaching the problem of the spin from a different point of view. We will show that the spin is neither basically relativistic nor quantum mechanical but reflects just a symmetry property related to the Lie algebra to which it is associated – a Lie algebra that may also be associated with the classical Poisson bracket. The classical approach will be compared with the usual quantum one to stress their formal similarities. With this “classical” representation of the spin by means of phase-space functions we proceed to the usual quantization procedure to derive a Schrödinger equation for the half-integral spin. We then solve this equation to obtain the half-integral spin eigenfunctions. The connection between this approach and that using the Heisenberg matrix calculus will also be worked out.

Quantum Mechanics as a Classical Theory VII: The Classical Spin Eigenfunctions

1995

In this continuation paper the Schr\"odinger equation for the half-integral spin eigenfunctions is obtained and solved. We show that all the properties already derived using the Heisemberg matrix calculation and Pauli's matrices are also obtained in the realm of these analytical functions. We also show that Einstein-Bose condensation for fermions is expected. We then conclude this series of two papers

Unified formulation for helicity and continuous spin fermionic fields

Journal of High Energy Physics

We propose a unified BRST formulation of general massless fermionic fields of arbitrary mixed-symmetry type in d-dimensional Minkowski space. Depending on the value of the real parameter the system describes either helicity fields or continuous spin fields. Starting with the unified formulation we derive a number of equivalent descriptions including the triplet formulation, Fang-Fronsdal-Labastida formulation, light-cone formulation and discuss the unfolded formulation.

UFIFT-HEP-02-16 Continuous Spin Representations of the

2002

We construct Wigner’s continuous spin representations of the Poincaré algebra for massless particles in higher dimensions. The states are labeled both by the length of a space-like translation vector and the Dynkin indices of the short little group SO(d − 3), where d is the space-time dimension. Continuous spin representations are in one-to-one correspondence with representations of the short little group. We also demonstrate how combinations of the bosonic and fermionic representations form supermultiplets of the super-Poincaré algebra. If the light-cone translations are nilpotent, these representations become finite dimensional, but contain zero or negative norm states, and their supersymmetry The Poincaré group is an essential ingredient of relativistic quantum field theories. Its representations in four space-time dimensions were first studied by E. Wigner [1]. Some of its representations describe quantum states found in local field theory: massless particles of fixed helicity a...