Fermions without Vierbeins in Curved Space-Time

Abstract

A general formulation of spinor fields in Riemannian space-time is given without using vierbeins. The space-time dependence of the Dirac matrices required by the anticommutation relation {γ_μ,γ_ν}=2g_{μν} determines the spin connection. The action is invariant under any local spin base transformations in the 32 parameter group Gl(4,c) and not just under local Lorentz transformations. The Dirac equation and the energy-momentum tensor are computed from the action.

11 pages, latex

References in corpus (2)

• A new form of the Kerr solution
• Quantization of Dirac fields in static spacetime

Cited by in corpus (46)

• Teleparallel Gravity: From Theory to Cosmology
• Equation of State of a Dense and Magnetized Fermion System
• Asymptotic safety of gravity-matter systems
• Leading Log Solution for Inflationary Yukawa
• The Fermion Self-Energy during Inflation
• Bulk Properties of a Fermi Gas in a Magnetic Field
• Quantum gravity and Standard-Model-like fermions
• Chiral fermions in asymptotically safe quantum gravity
• How perturbative is quantum gravity?
• Kermions: quantization of fermions on Kerr space-time
• Fermions in gravity with local spin-base invariance
• $\Lambda (t)$ cosmology induced by a slowly varying Elko field
• On the impact of Majorana masses in gravity-matter systems
• From inflation to recent cosmic acceleration: The fermionic Elko field driving the evolution of the universe
• Global surpluses of spin-base invariant fermions
• Spin-base invariance of Fermions in arbitrary dimensions
• Simulation of the massless Dirac field in 1+1D curved spacetime
• Thermal expectation values of fermions on anti-de Sitter space-time
• Spinor model of a perfect fluid and their applications in Bianchi type-I and FRW models
• Fermionic fields in a four-dimensional Bonnor-Melvin-Lambda space-time
• Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model
• A simpler solution of the non-uniqueness problem of the covariant Dirac theory
• Particle Dark Energy
• The Vierbein Formalism and Energy-Momentum Tensor of Spinors
• A Keck/HIRES Doppler Search for Planets Orbiting Metal-Poor Dwarfs
• Global properties of physically interesting Lorentzian spacetimes
• Tunnelling of Charged Particles from Black Holes
• A new length scale, and modified Einstein-Cartan-Dirac equations for a point mass
• $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the Asymptotically Safe Standard Model
• Einstein-Cartan-Dirac equations in the Newman-Penrose formalism
• Solution of the Dirac equation in a curved space with static metric
• Quantum field theories of relativistic Luttinger fermions
• About the (in)equivalence between holonomic versus non-holonomic theories of gravity
• Gravitational effects on geonium and free electron ${\mathrm{g}}_s$-factor measurements in a Penning trap
• On the Lévy-Leblond-Newton equation and its symmetries: a geometric view
• Implications of nonsymmetric metric theories for particle physics. New interpretation of the Pauli coupling
• Equality of the Hilbert Hamiltonian and the canonical Hamiltonian for gauge theories in a static spacetime
• Fermi Liquids from D-Branes
• Spin chiral current induced by curvature of space-time
• Geometric studies of the interplay between spin and gravity
• Flavour Condensate and the Dark Sector of the Universe
• Klein-Gordon equation for a particles in brane model
• Black hole with a Dirac field in 3+1 dimensions
• Mean-field theory for self-interacting relativistic Luttinger fermions
• Local spin base invariance from a global differential-geometrical point of view
• Klein-Gordon equation for a particle in brane model