Titlebook: Loop Quantum Gravity for the Bewildered; The Self-Dual Approa Sundance Bilson-Thompson Book 2024Latest edition The Editor(s) (if applicable

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First Steps to a Theory of Quantum Gravity,the role and significance of the Barbero-Immirzi parameter is explored. The attempt to find a basis of states for quantum spacetime which satisfy the Hamiltonian, diffeomorphism, and Gauss constraints is used to motivate the choice of loop variables, from which loop quantum gravity gets its name.

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Kinematical Hilbert Space,rvables from these states. A toy model is introduced which illustrates how space may be subdivided into discrete units. This model motivates a dual representation of discrete space in terms of graphs with labelled edges. The model is extended and connected to Penrose’s conception of spin networks, l

Inclement

Dynamics of Spin Networks,ring how these spin networks evolve between initial and final states through a sum-over-geometries (so-called ‘spin foams’). The historical development of these ideas is described. BF theory, the role of a cosmological constant in taming infinities, and the connection to Chern–Simons theory are disc

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Classical GR,er active diffeomorphisms is discussed, motivating the search for a background-independent theory of quantum gravity in later chapters. The geometrical intuition for curvature established in this chapter establishes the basis for exploring gauge fields in the subsequent chapters.

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Quantum Field Theory,y a central role in the loop formulation of quantum gravity, and the dynamics of quantum fields in both the Lagrangian and Hamiltonian frameworks. The concept of self-duality is introduced through the use of bivectors and differential forms.

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