Modern canonical quantum general relativity / Thomas Thiemann.
Thiemann, Thomas.| Call Number | 530.12 |
| Author | Thiemann, Thomas, author. |
| Title | Modern canonical quantum general relativity / Thomas Thiemann. |
| Physical Description | 1 online resource (xxvi, 819 pages) : digital, PDF file(s). |
| Series | Cambridge monographs on mathematical physics |
| Notes | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| Contents | Defining quantum gravity -- Classical Hamiltonian formulation of general relativity -- The problem of time, locality, and the interpretation of quantum mechanics -- The programme of canonical quantisation -- The new canonical variables of Ashtekar for general relativity -- Foundations of modern canonical quantum general relativity --Step I : the holonomy-flux algebra -- Step II : quantum algebra -- Step III : representation theory -- Step IV : (1) implementation and solution of the kinematical constraints -- Step IV (2) : impelementation and solution of the Hamiltonian constraint -- Step V : semiclassical analysis -- Physical applications -- Extension to standard matter -- Kinematical geometrical operators -- Spin foam models -- Quantum black hole physics -- Applications to particle physics and quantum cosmology -- Loop quantum gravity phenomenology -- Mathematical tools and their connection to physics -- Tools from general topology -- Differential, Riemannian, symplectic, and complex geometry -- Semianalytic category -- Elements of fibre bundle theory -- Holonomies on non-trivial fibre bundles -- Geometric quantisation -- The Dirac algorithm for field theories with constraints -- Tools from measure theory -- Key results from functional analysis -- Elementary introduction to Gel'fand theory for Abelian C*-algebras -- Bohr compactification of the real line -- Operator *-algebras and spectral theorem -- Refined algebraic quantisation (RAQ) and direct integral decomposition (DID) -- Basics of harmonic analysis on compact Lie groups -- Spin-network functions for SU (2) -- + Functional analytic description of classical connection dynamics. |
| Summary | Modern physics rests on two fundamental building blocks: general relativity and quantum theory. General relativity is a geometric interpretation of gravity while quantum theory governs the microscopic behaviour of matter. Since matter is described by quantum theory which in turn couples to geometry, we need a quantum theory of gravity. In order to construct quantum gravity one must reformulate quantum theory on a background independent way. Modern Canonical Quantum General Relativity provides a complete treatise of the canonical quantisation of general relativity. The focus is on detailing the conceptual and mathematical framework, on describing physical applications and on summarising the status of this programme in its most popular incarnation, called loop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book, which therefore can be read by graduate students with basic knowledge of quantum field theory or general relativity. |
| Subject | QUANTUM THEORY. GENERAL RELATIVITY (PHYSICS) |
| Multimedia |
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$a Defining quantum gravity -- Classical Hamiltonian formulation of general relativity -- The problem of time, locality, and the interpretation of quantum mechanics -- The programme of canonical quantisation -- The new canonical variables of Ashtekar for general relativity -- Foundations of modern canonical quantum general relativity --Step I : the holonomy-flux algebra -- Step II : quantum algebra -- Step III : representation theory -- Step IV : (1) implementation and solution of the kinematical constraints -- Step IV (2) : impelementation and solution of the Hamiltonian constraint -- Step V : semiclassical analysis -- Physical applications -- Extension to standard matter -- Kinematical geometrical operators -- Spin foam models -- Quantum black hole physics -- Applications to particle physics and quantum cosmology -- Loop quantum gravity phenomenology -- Mathematical tools and their connection to physics -- Tools from general topology -- Differential, Riemannian, symplectic, and complex geometry -- Semianalytic category -- Elements of fibre bundle theory -- Holonomies on non-trivial fibre bundles -- Geometric quantisation -- The Dirac algorithm for field theories with constraints -- Tools from measure theory -- Key results from functional analysis -- Elementary introduction to Gel'fand theory for Abelian C*-algebras -- Bohr compactification of the real line -- Operator *-algebras and spectral theorem -- Refined algebraic quantisation (RAQ) and direct integral decomposition (DID) -- Basics of harmonic analysis on compact Lie groups -- Spin-network functions for SU (2) -- + Functional analytic description of classical connection dynamics.
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$a Modern physics rests on two fundamental building blocks: general relativity and quantum theory. General relativity is a geometric interpretation of gravity while quantum theory governs the microscopic behaviour of matter. Since matter is described by quantum theory which in turn couples to geometry, we need a quantum theory of gravity. In order to construct quantum gravity one must reformulate quantum theory on a background independent way. Modern Canonical Quantum General Relativity provides a complete treatise of the canonical quantisation of general relativity. The focus is on detailing the conceptual and mathematical framework, on describing physical applications and on summarising the status of this programme in its most popular incarnation, called loop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book, which therefore can be read by graduate students with basic knowledge of quantum field theory or general relativity.
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| Summary | Modern physics rests on two fundamental building blocks: general relativity and quantum theory. General relativity is a geometric interpretation of gravity while quantum theory governs the microscopic behaviour of matter. Since matter is described by quantum theory which in turn couples to geometry, we need a quantum theory of gravity. In order to construct quantum gravity one must reformulate quantum theory on a background independent way. Modern Canonical Quantum General Relativity provides a complete treatise of the canonical quantisation of general relativity. The focus is on detailing the conceptual and mathematical framework, on describing physical applications and on summarising the status of this programme in its most popular incarnation, called loop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book, which therefore can be read by graduate students with basic knowledge of quantum field theory or general relativity. |
| Notes | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| Contents | Defining quantum gravity -- Classical Hamiltonian formulation of general relativity -- The problem of time, locality, and the interpretation of quantum mechanics -- The programme of canonical quantisation -- The new canonical variables of Ashtekar for general relativity -- Foundations of modern canonical quantum general relativity --Step I : the holonomy-flux algebra -- Step II : quantum algebra -- Step III : representation theory -- Step IV : (1) implementation and solution of the kinematical constraints -- Step IV (2) : impelementation and solution of the Hamiltonian constraint -- Step V : semiclassical analysis -- Physical applications -- Extension to standard matter -- Kinematical geometrical operators -- Spin foam models -- Quantum black hole physics -- Applications to particle physics and quantum cosmology -- Loop quantum gravity phenomenology -- Mathematical tools and their connection to physics -- Tools from general topology -- Differential, Riemannian, symplectic, and complex geometry -- Semianalytic category -- Elements of fibre bundle theory -- Holonomies on non-trivial fibre bundles -- Geometric quantisation -- The Dirac algorithm for field theories with constraints -- Tools from measure theory -- Key results from functional analysis -- Elementary introduction to Gel'fand theory for Abelian C*-algebras -- Bohr compactification of the real line -- Operator *-algebras and spectral theorem -- Refined algebraic quantisation (RAQ) and direct integral decomposition (DID) -- Basics of harmonic analysis on compact Lie groups -- Spin-network functions for SU (2) -- + Functional analytic description of classical connection dynamics. |
| Subject | QUANTUM THEORY. GENERAL RELATIVITY (PHYSICS) |
| Multimedia |