Fermions in Loop Quantum Cosmology and the Role of Parity
arXiv:0806.2821 · doi:10.1088/0264-9381/25/19/195006
Abstract
Fermions play a special role in homogeneous models of quantum cosmology because the exclusion principle prevents them from forming sizable matter contributions. They can thus describe the matter ingredients only truly microscopically and it is not possible to avoid strong quantum regimes by positing a large matter content. Moreover, possible parity violating effects are important especially in loop quantum cosmology whose basic object is a difference equation for the wave function of the universe defined on a discrete space of triads. The two orientations of a triad are interchanged by a parity transformation, which leaves the difference equation invariant for ordinary matter. Here, we revisit and extend loop quantum cosmology by introducing fermions and the gravitational torsion they imply, which renders the parity issue non-trivial. A treatable locally rotationally symmetric Bianchi model is introduced which clearly shows the role of parity. General wave functions cannot be parity-even or odd, and parity violating effects in matter influence the microscopic big bang transition which replaces the classical singularity in loop quantum cosmology.
arXiv comment17 pages
References in corpus (44)
- Quantum Nature of the Big Bang
- Absence of Singularity in Loop Quantum Cosmology
- Real Ashtekar Variables for Lorentzian Signature Space-times
- Quantum Spin Dynamics (QSD)
- Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
- Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
- Loop Quantum Cosmology
- QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
- Real and complex connections for canonical gravity
- Loop quantum cosmology of k=1 FRW models
- Isotropic Loop Quantum Cosmology
- Loop Quantum Dynamics of the Schwarzschild Interior
- Effective Equations of Motion for Quantum Systems
- Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories
- Homogeneous Loop Quantum Cosmology
- Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
- Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations
- Loop Quantum Cosmology IV: Discrete Time Evolution
- Dynamical Initial Conditions in Quantum Cosmology
- Loop Quantum Cosmology I: Kinematics
- Fermions in Ashtekar-Barbero Connections Formalism for Arbitrary Values of the Immirzi Parameter
- Loop quantum cosmology and inhomogeneities
- Large scale effective theory for cosmological bounces
- Lattice refining loop quantum cosmology, anisotropic models and stability
- Homogeneous Loop Quantum Cosmology: The Role of the Spin Connection
- Quantum Gravity and Higher Curvature Actions
- Dynamical coherent states and physical solutions of quantum cosmological bounces
- Singularities and Quantum Gravity
- Canonical Gravity with Fermions
- Fermions in Quantum Gravity
- Immirzi parameter and fermions with non-minimal coupling
- Initial Conditions for a Universe
- Supersymmetric Quantum Cosmology --- Shaken not stirred
- Wave functions for the Schwarschild black hole interior
- The Dark Side of a Patchwork Universe
- Effective action and decoherence by fermions in quantum cosmology
- Holst Actions for Supergravity Theories
- On the Configuration Spaces of Homogeneous Loop Quantum Cosmology and Loop Quantum Gravity
- Numerical solutions to lattice-refined models in loop quantum cosmology
- Numerical techniques for solving the quantum constraint equation of generic lattice-refined models in loop quantum cosmology
- Loop Quantization of Polarized Gowdy Model on : Kinematical States and Constraint Operators
- Gravity Induced Chiral Condensate Formation and the Cosmological Constant
- Self-Dual Action for Fermionic Fields and Gravitation
- A fine tuning free resolution of the cosmological constant problem
Cited by in corpus (21)
- Loop quantum cosmology of Bianchi I models
- Loop quantum cosmology of Bianchi type IX models
- Loop quantum cosmology of Bianchi type II models
- Interaction of the Barbero--Immirzi Field with Matter and Pseudo-Scalar Perturbations
- Barbero-Immirzi field in canonical formalism of pure gravity
- Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter
- Spinfoam fermions
- Fermi-bounce Cosmology and scale invariant power-spectrum
- Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
- Interpretation of the triad orientations in loop quantum cosmology
- Observational consequences of Bianchi I spacetimes in loop quantum cosmology
- Coherent states for FLRW space-times in loop quantum gravity
- Fermions in Hybrid Loop Quantum Cosmology
- Fermion spins in loop quantum gravity
- Loop Quantum Gravity and Cosmology: A dynamical introduction
- A pilot study on canonical gravity with mass dimension one fermions
- Fermion coupling to loop quantum gravity: canonical formulation
- Matter in Loop Quantum Gravity
- Kinematics of arbitrary spin matter fields in loop quantum gravity
- Big bounce as scattering of wave function at big crunch
- On the Generalized Einstein-Cartan Action with Fermions