Topological quantum field theory and quantum gravity

Abstract

This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same result as the continuum partition functions evaluated using zeta-function regularisation. Some implications for more physical models are discussed. In the second part, the gauge gravity action is written using a particularly simple matrix technique. The coupling to scalar, fermion and Yang-Mills fields is reviewed, with some small additions. A sum over histories quantisation of the gauge gravity theory in 2+1 dimensions is then carried out for a particular class of triangulations of the three-sphere. The preliminary stage of the Hamiltonian analysis for the (3+1)-dimensional gauge gravity theory is undertaken.

University of Nottingham PhD thesis (2014)

References in corpus (7)

• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• Cosmology with torsion: An alternative to cosmic inflation
• Holonomy Spin Foam Models: Definition and Coarse Graining
• Fermions in three-dimensional spinfoam quantum gravity