Fermions in the space-time R×S3

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Abstract
Quantum field theories on the surface of a four‐dimensional sphere are considered. The Hamiltonian is rotation invariant and its eigenvalues are discrete. Scalar, vector, and spinorial functions on S3 are discussed. The most general Lagrangians for Dirac, Weyl, and Majorana fermions are derived. They are different from the ones in existing literature. The wave functions and propagator are obtained and formulas for matrix elements involving spinors are presented. The discrete symmetries—parity, charge conjugation, and time reversal—are described. The Lagrangian in R×S3 transforms in a nontrivial way under these. Finally, the fermionic Lagrangian is rederived using the tetrad formalism, and conformal transformations are discussed. This leads to a generalization of the formalism to a time‐dependent radius of curvature. As a particular case, a new Lagrangian for de Sitter space is obtained, which, however, is not invariant under the full de Sitter group.