Derivation and BRST Quantization of Models for Spinning Relativistic Particles
Doctoral thesis, 1993
This thesis deals with the construction of models for spinning relativistic particles and their covariant quantization within a BRST framework. In the first part the ideas and methods which constitute the background to the papers are reviewed, and a summary of the main results obtained therein is given. The second part consists of the papers.
In paper I a BRST quantization of a particular model describing free massless relativistic particles of arbitrary spin is performed. It is a pseudoclassical gauge model in which the spin variables are odd Grassmann numbers. The gauge group for a spin-N/2 particle is an O(N) extended supersymmetrized reparametrization group. The BRST condition is solved in detail, and explicit covariant wave equations are derived for any integer and half-integer spin.
In paper II a method to construct manifestly Lorentz covariant models for relativistic spinning particles is introduced. The models are characterized by the choice of covariant spin variables and constraints. The constraints are extracted at the quantum level from the Bargmann-Wigner conditions on the Pauli-Lubanski operator together with consistency conditions. Several models in which the internal variables transform as Lorentz vectors are derived and analysed.
The procedure mentioned above is used in paper III to derive new classes of models for spinning particles in which the internal variables transform as Lorentz spinors. Models for massless and massive particles of arbitrary spin are constructed. The corresponding Lagrangians and their local invariances are explicitly given.
Finally in paper IV, the classical and quantum theory of the spinning conformal particle is presented. This is a model with manifestly O(2,4) (conformal) invariance, and it describes both massive and massless particles of arbitrary spin depending on the projection to Minkowski space. Both an ordinary BRST quantization and an extended one including the antiBRST symmetry is performed. It is shown that the antiBRST invariance is necessary to ensure ghost decoupling and make the quantization of the model consistent.