Covariant Derivative of Fermions and All That
Ilya L. Shapiro
Abstract
We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. On top of that, local conformal transformations for a Dirac fermion in curved spacetime are considered and we obtain the expression for the energy-momentum tensor on the cosmological background.
Topics & Concepts
PhysicsCovariant transformationMathematical physicsCovariant derivativeFermionCommutatorTensor (intrinsic definition)Gauge covariant derivativeSpacetimeDirac equationStress–energy tensorConformal mapTheoretical physicsQuantum electrodynamicsQuantum mechanicsGauge theoryExact solutions in general relativityLie algebraSupersymmetric gauge theoryGauge anomalyGeometryLie conformal algebraMathematicsNoncommutative and Quantum Gravity TheoriesCosmology and Gravitation TheoriesRelativity and Gravitational Theory