A First Course in Loop Quantum Gravity
This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.
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1 Why quantize gravity?
2 Special relativity and electromagnetism
3 Some elements of general relativity
4 Hamiltonian mechanics including constraints and fields
5 YangMills theories
6 Quantum mechanics and elements of quantum field theory
7 General relativity in terms of Ashtekars new variables
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action algebra annihilated Ashtekar black hole called canonical variables Chapter classical clock components compute connection consider construct coordinates covariant derivative curvature curved space-time defined degrees of freedom density diffeomorphism constraint Dirac observables discussed divergences eigenvalues Einstein electromagnetism entropy equations of motion evolution expression field tensor finite flat gauge transformations Gauss given Hamiltonian constraint Hamiltonian formulation holonomy inner product instance interactions introduce Lagrange multipliers Lagrangian loop quantum cosmology loop quantum gravity loop representation Lorentz transformations manifold master constraint matrix Maxwell theory Maxwell’s metric momentum Newton’s parameter particle path integral perturbative Phys physics Planck Poisson bracket problem quantity quantization quantum field theory quantum mechanics quantum operator quantum theory relativity result Rovelli scalar field smeared solution space spatial spin foams spin network symmetry theorem Thiemann triads vacuum vanishes vector potential wavefunctions Yang–Mills theory zero