DMCA. Copyrighted Work that you can Claim.

# ðŸ“™ Quantum gravity in 2+1 dimensions by Steven Carlip â€” free epub

## Similar books results

**Quantum Gravity in 2+1 Dimensions free pdf by Steven Carlip**

This timely volume provides a broad survey of (2+1)-dimensional quantum gravity. It emphasises the 'quantum cosmology' of closed universes and the quantum mechanics of the (2+1)-dimensional black hole. It compares and contrasts a variety of approaches, an...

**Space-Time Foliation in Quantum Gravity epub download by Yuki Sato (auth.)**

In this thesis, the author considers quantum gravity to investigate the mysterious origin of our universe and its mechanisms. He and his collaborators have greatly improved the analyticity of two models: causal dynamical triangulations (CDT) and n-DBI gra...

**Towards Quantum Gravity: Proceeding of the XXXV International Winter School on Theoretical Physics Held in Polanica, Poland, 2â€“11 February 1999 download pdf by Giovanni Amelino-Camelia (auth.), Jerzy Kowalski-Glikman (eds.)**

The aim of this book is to give graduate students an overview of quantum gravity but it also covers related topics from astrophysics. Some well-written contributions can serve as an introduction into basic conceptual concepts like time in quantum gravity ...

**Quantum Gravity epub download by Phillip Kaye**

Kiefer (theoretical physics, U. of Cologne) describes the general features that a quantum theory of gravity is expected to show and gives an up-to-date overview of main approaches, including the quantization of Einstein's theory of general relativity and ...

**Approaches to quantum gravity: toward a new understanding of space, time and matter free pdf by Daniele Oriti**

The theory of quantum gravity promises a revolutionary new understanding of gravity and spacetime, valid from microscopic to cosmological distances. Research in this field involves an exciting blend of rigorous mathematics and bold speculations, foundatio...

**Heat Kernel and Quantum Gravity free epub by Ivan G. Avramidi**

This book tackles quantum gravity via the so-called background field method and its effective action functional. The author presents an explicitly covariant and effective technique to calculate the de Witt coefficients and to analyze the Schwinger-de Wit ...

**Quantum Gravity: From Theory to Experimental Search download pdf by D. Giulini**

The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spaceti...

**The pursuit of quantum gravity: Memoirs of Bryce DeWitt from 1946 to 2004 free download by CÃ©cile DeWitt-Morette (auth.)**

1946 is the year Bryce DeWitt entered Harvard graduate school. Quantum Gravity was his goal and remained his goal throughout his lifetime until the very end. The pursuit of Quantum Gravity requires a profound understanding of Quantum Physics and Gravitati...

**Euclidean Quantum Gravity on Manifolds with Boundary epub download by Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone (auth.)**

This book reflects our own struggle to understand the semiclassical behaviour of quantized fields in the presence of boundaries. Along many years, motivated by the problems of quantum cosmology and quantum field theory, we have studied in detail the one-l...

**Community Disaster Recovery and Resiliency: Exploring Global Opportunities and Challenges free epub by DeMond S. Miller, Jason David Rivera**

Once again natureâ€™s fury has taken a toll in pain, suffering, and lives lost. In recognition of the need for a rapid and appropriate response, CRC Press will donate $5 to the American Red Cross for every copy of Community Disaster Recovery and Resiliency:...

**Discourse and Struggle in Minority Language Policy Formation: Corsican Language Policy in the EU Context of Governance (Palgrave Studies in Minority Languages and Communities) pdf free by Jean-Bernard Adrey**

The author presents a new approach to the study of language policy, by focusing on language policy formation and implementation as a dynamic, conflict-laden process involving the interaction of various actors with different motivations and uneven bargaini...

**Visio 2010: Basic, Student Manual pdf free by Axzo Press**

**Braintrust: What Neuroscience Tells Us about Morality pdf free by Patricia S. Churchland**

What is morality? Where does it come from? And why do most of us heed its call most of the time? In Braintrust, neurophilosophy pioneer Patricia Churchland argues that morality originates in the biology of the brain. She describes the "neurobiological pla...

**Diccionario etimolÃ³gico rapanui-espaÃ±ol free download by ComisiÃ³n para la EstructuraciÃ³n de la Lengua Rapanui**

** pdf free by The Economist Group**

**2DArtist Issue 059 November 2010 issue 59 free epub by 3DTotal.com**

**Fighting for human rights epub download by Paul Gready**

In a world that is increasingly disillusioned with formal politics, people are no longer prepared to wait for governments and international institutions to act on human rights concerns. This book identifies activism as a key means of realizing human right...

**Bureaucratic Politics and Foreign Policy pdf free by Morton H. Halperin**

The first edition of Bureaucratic Politics and Foreign Policy is one of the most successful Brookings titles of all time. This thoroughly revised version updates that classic analysis of the role played by the federal bureaucracy --civilian career officia...

**Chemical Test Methods of Analysis pdf free by Zolotov, Ivanov, Amelin**

Chemical analysis moves from laboratory to places where samples to be analysed are located. This trend is aptly termed "on-site analysis". As the dictum says: "from sample transfer to information transfer". Owing to the ever increasing number of samples t...

When tackling difficult problems in physics, one of the most effective strategies is to study them in a domain or context where they appear more tractable. These strategies work best where there is a paucity of experimental data to guide the researcher through the conceptual search spaces where there is more temptation to engage in an excess of speculation. The quantization of gravity remains one of the most, if not the most difficult problem facing theoretical physicists today, and this in spite of much effort devoted to its resolution. Some researchers point to string theory as providing the correct path to quantum gravity, while others believe other less ambitious approaches show the most promise.
In this book, which to some because of its publication date may be somewhat out of date, the author takes a direct approach to quantum gravity in a context where some of its difficulties are still manifest but where computations can be done. Lowering the spatial dimension by one in general relativity gives a theory that has no local degrees of freedom. This may cause some to think that the theory is basically trivial, and deserves no further consideration, but the author reminds the reader that when the spacetime has a fundamental group that is nontrivial, there are a finite number of global degrees of freedom. If the reader is familiar with some of the work that has been done in topological quantum field theory, the absence of physical degrees of freedom does not entail an uninteresting theory (both in physics and mathematics).
Early on in the book, the author gives evidence as to the value in studying gravity in 2+1 dimensions, such as the fact that its point particle solutions are useful in the study of cosmic strings. But physical theories are very dependent on distance, as the discovery of quantum mechanics readily attests to. The cosmic strings the author discusses are entities that exist in the Newtonian limit of the (2+1)-dimensional theory. The physics at this scale (of "large" distances) is to be contrasted with the scales at which quantum gravity is thought to be relevant. Cosmic strings are not meaningful entities at these (very short) distances.
Classical physics is thought to be better understood than the physics of the quantum realm, and so frequently physicists undertake a study of quantum phenomena by first investigating thoroughly what happens in the classical domain. The author does not deviate from this strategy, and early on in the book he takes up the study of the classical solutions of the Einstein field equations for (2+1)-dimensional general relativity. Since the dimension of space has been lowered by 1, one might expect that there would be a plethora of exact solutions to the Einstein field equations or at least ones that are somewhat easier to find than in the usual case. An immediate issue that arises concerns the topology of the manifold, and the author approaches this first asking what three-manifolds will admit Lorentzian metrics and which manifolds admit solutions of the empty space Einstein field equations, i.e. which three-manifolds admit flat Lorentzian metrics. An interesting conclusion resulting from this discussion is that changes in topology are not permitted by the field equations, at least for the case of spatially closed three-dimensional manifolds.
Doing calculations in general relativity while respecting the unity of space and time is extremely difficult, and what is frequently done is to divide spacetime into spatial and temporal directions. One methodology for doing this is the Arnowitt-Deser-Misner (ADM) formalism, which is given detailed treatment in the book. The ADM formalism allows one to use the Hamiltonian formalism in (2+1)-dimensional gravity, and this results in a dynamical system with constraints. The author wants to interpret these constraints using an analog of what is done in a gauge theory, namely to interpret them as generators of infinitesimal gauge transformations, even though gravity is not a gauge theory. He shows explicitly that this can be done with the momentum constraints, but the Hamiltonian constraint is more problematic. This constraint generates diffeomorphisms in the time direction but "on-shell", i.e. subject to the dynamical equations of motion. But the author goes on to how diffeomorphisms can be represented as gauge transformations in (2+1)-dimensional gravity, i.e. in this case the full diffeomorphism group can be replaced by the group of pointwise gauge transformations. This makes the quantization procedure much more straightforward the author says.
And after a few more chapters of studying the classical dynamics of (2+1)-dimensional gravity, the author gets to this quantization using the ADM formalism and the York time-slicing operation (the latter is a procedure wherein spacetime is given a "foliation" by surfaces with constant mean extrinsic curvature). This strategy allows one to reduce (2+1)-dimensional gravity to a purely quantum-mechanical system with a finite number of degrees of freedom. This is astonishing at first glance, and also quite helpful since it allows the author to use the familiar tools of quantum mechanics to quantize gravity. His discussion is interesting not only because of its importance to the subject of quantum gravity, but also because of the presence of various constructions from mathematics, such as the mapping class group and automorphic functions. The presence of these functions is due to the author's choice of a torus for the spatial part of spacetime. The Schrodinger equation then involves a Hamiltonian that can be written in terms of the "Maass Laplacian", the latter of which acts on the automorphic functions. The author however shows that this quantization procedure is not unique, with many choices of Hamiltonian possible, and each of these leading to physically inequivalent theories.
This non-uniqueness in quantization procedures leads the author to consider, based on his study of the classical dynamics of (2+1)-gravity earlier in the book, alternative approaches to quantization. One of these alternatives is the viewing of the classical dynamics in terms of the geometry of flat connections. Rather than studying the evolution of the spatial geometry as done in the ADM formalism, this approach studies the evolution of the entire spacetime, and gives, as the author puts it, a kind of "Heisenberg picture" for the quantum dynamics (as compared with the "Schrodinger picture") of the ADM formalism. The quantization of the space of geometric structures (with nondegenerate metrics) is then carried out, interestingly without any need for a Hamiltonian. He also discusses how to proceed with the assumption of nondegeneracy of the metric, leading to the famous Ashtekar variables so widely used in some research circles in quantum gravity. Further analysis in a more general context, where the canonical quantization procedure of replacing Poisson brackets by commutators is replaced by a general operator algebra of holonomies leads the author to discuss the Nelson/Regge approach to quantization and its "dual": the famous Ashtekar loop representation.

## About book:

## About file:

Security code:

- Series:
**Cambridge monographs on mathematical physics** - Author:
**Steven Carlip** - Year:
**1998** - Publisher:
**Cambridge University Press** - Language:
**English** - ISBN:
**9780521564083,0521564085,0521545889**

- File size:
**14 393 083** - Format:
**pdf**

Security code:

This timely volume provides a broad survey of (2+1)-dimensional quantum gravity. It emphasises the 'quantum cosmology' of closed universes and the quantum mechanics of the (2+1)-dimensional black hole. It compares and contrasts a variety of approaches, an...

In this thesis, the author considers quantum gravity to investigate the mysterious origin of our universe and its mechanisms. He and his collaborators have greatly improved the analyticity of two models: causal dynamical triangulations (CDT) and n-DBI gra...

The aim of this book is to give graduate students an overview of quantum gravity but it also covers related topics from astrophysics. Some well-written contributions can serve as an introduction into basic conceptual concepts like time in quantum gravity ...

Kiefer (theoretical physics, U. of Cologne) describes the general features that a quantum theory of gravity is expected to show and gives an up-to-date overview of main approaches, including the quantization of Einstein's theory of general relativity and ...

The theory of quantum gravity promises a revolutionary new understanding of gravity and spacetime, valid from microscopic to cosmological distances. Research in this field involves an exciting blend of rigorous mathematics and bold speculations, foundatio...

This book tackles quantum gravity via the so-called background field method and its effective action functional. The author presents an explicitly covariant and effective technique to calculate the de Witt coefficients and to analyze the Schwinger-de Wit ...

The relation between quantum theory and the theory of gravitation remains one of the most outstanding unresolved issues of modern physics. According to general expectation, general relativity as well as quantum (field) theory in a fixed background spaceti...

1946 is the year Bryce DeWitt entered Harvard graduate school. Quantum Gravity was his goal and remained his goal throughout his lifetime until the very end. The pursuit of Quantum Gravity requires a profound understanding of Quantum Physics and Gravitati...

This book reflects our own struggle to understand the semiclassical behaviour of quantized fields in the presence of boundaries. Along many years, motivated by the problems of quantum cosmology and quantum field theory, we have studied in detail the one-l...

Once again natureâ€™s fury has taken a toll in pain, suffering, and lives lost. In recognition of the need for a rapid and appropriate response, CRC Press will donate $5 to the American Red Cross for every copy of Community Disaster Recovery and Resiliency:...

The author presents a new approach to the study of language policy, by focusing on language policy formation and implementation as a dynamic, conflict-laden process involving the interaction of various actors with different motivations and uneven bargaini...

What is morality? Where does it come from? And why do most of us heed its call most of the time? In Braintrust, neurophilosophy pioneer Patricia Churchland argues that morality originates in the biology of the brain. She describes the "neurobiological pla...

In a world that is increasingly disillusioned with formal politics, people are no longer prepared to wait for governments and international institutions to act on human rights concerns. This book identifies activism as a key means of realizing human right...

The first edition of Bureaucratic Politics and Foreign Policy is one of the most successful Brookings titles of all time. This thoroughly revised version updates that classic analysis of the role played by the federal bureaucracy --civilian career officia...

Chemical analysis moves from laboratory to places where samples to be analysed are located. This trend is aptly termed "on-site analysis". As the dictum says: "from sample transfer to information transfer". Owing to the ever increasing number of samples t...