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First Steps to a Theory of Quantum Gravity
This chapter covers the attempt to quantise general relativity, through a reformulation in terms of the Ashtekar variables. These are introduced, and...
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Kinematical Hilbert Space
This chapter covers the conceptual structure of spacetime in terms of loop states, as well as the formulation of operators which extract physical...
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Expanding on Classical GR
This chapter covers the reformulation of classical general relativity in both the Lagrangian and Hamiltonian frameworks. In the first case this...
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Dynamics of Spin Networks
This chapter covers the dynamics of quantum spacetime, utilising networks labelled with spin representations to describe kinematical states, and...
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Quantum Field Theory
This chapter covers the essentials of quantum field theory. Topics discussed include the curvature of gauge fields and the definition of the...
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Introduction
This chapter covers the historical basis of the quest for a theory of quantum gravity. The discussion includes the development of quantum theory in...
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Classical GR
This chapter covers the essential aspects of classical general relativity, such as probing spacetime curvature with parallel transport of vectors,...
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Discussion
This chapter covers several common objections to loop quantum gravity, and addresses them one-by-one to build a clear picture of the true state of...
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Applications
This chapter covers the application of loop quantum gravity to the study of black hole entropy, as well as the large-scale evolution of spacetime...
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Weak Interactions
Non-covalent interactions dominate soft matter, and have been particularly difficult to model theoretically. Given their importance in supramolecular...
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Molecules
In this chapter, we will review some applications of the topological tools in the understanding of the structure, bonding and properties of...
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Motion of Particles
In this chapter, we will explore how to describe the position and momentum of a particle in quantum mechanics, and how we set up its Schrödinger...
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Entanglement
In this chapter, we will find out how we can apply quantum mechanics to more than one system. In doing so, we encounter what is truly strange in...
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Operators
In this chapter, we recall the material from the previous chapters and summarise how vectors and operators play different roles in quantum mechanics....
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Lorentzian Addition of Velocities
In Sect. 3.5 , we have shown how velocities are added in classical mechanics. By adding velocities, we mean the...
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Waves and Light
Light plays a central role in special relativity. The reason for this will become clear in the course of this book.
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The Lorentz Transformation: Applications
In possession of the Lorentz transformation
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Radiation Emission and Scattering
Topics The radiation field. Multipole expansion. Electric dipole radiation. Magnetic dipole radiation. Basic equations of this chapter: Fields in the...
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Basics of Electrostatics
Topics. The electric charge. The electric field. The superposition principle. Gauss’s law. Symmetry considerations. The electric field of simple...