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## 1 The geometric approach to GWs

*Michele Maggiore*

### in Gravitational Waves: Volume 1: Theory and Experiments

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570745
- eISBN:
- 9780191717666
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570745.003.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations ... More

## Tensors in special relativity

*Ta-Pei Cheng*

### in Relativity, Gravitation and Cosmology: A Basic Introduction

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199573639
- eISBN:
- 9780191722448
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573639.003.0012
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

Tensors in a general coordinate system are introduced. When a tensor is expanded in terms of a set of basis (or inverse basis) vectors, the coefficients of expansion are its contravariant (or ... More

## Conformal Symmetry in Statistical Mechanics

*Hans-Peter Eckle*

### in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780199678839
- eISBN:
- 9780191878589
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199678839.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The core of the exposition of the theory of conformal symmetry in statistical mechanics are the concepts of correlation functions of order parameter fields, whose behaviour under conformal ... More

## THE WEYL ANOMALY AND RENORMALIZATION GROUP

*Kazuo Fujikawa and Hiroshi Suzuki*

### in Path Integrals and Quantum Anomalies

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198529132
- eISBN:
- 9780191712821
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529132.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the quantum anomaly associated with the scale transformation of space-time coordinates, or the transformation generally called the Weyl transformation. In flat space-time, this ... More

## Field Quantization and Vacuum Energy in the Presence of Boundaries

*M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko*

### in Advances in the Casimir Effect

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199238743
- eISBN:
- 9780191716461
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238743.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics

From the standpoint of quantum field theory, the Casimir effect is related to the vacuum polarization that arises in quantization volumes restricted by boundaries or in spaces with nontrivial ... More

## Two-Fluid Hydrodynamics

*VOLOVIK GRIGORY E.*

### in The Universe in a Helium Droplet

- Published in print:
- 2009
- Published Online:
- January 2010
- ISBN:
- 9780199564842
- eISBN:
- 9780191709906
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199564842.003.0005
- Subject:
- Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology

The analog of matter in the background of superfluid vacuum consists of quanta of sound waves (phonons), which form a dilute gas. This gas of quasiparticles represents the so-called normal component ... More

## Advantages and Drawbacks Of Effective Theory

*VOLOVIK GRIGORY E.*

### in The Universe in a Helium Droplet

- Published in print:
- 2009
- Published Online:
- January 2010
- ISBN:
- 9780199564842
- eISBN:
- 9780191709906
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199564842.003.0006
- Subject:
- Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology

The energy momentum tensor for the vacuum field which represents gravity is non-covariant, since the effective gravitational field obeys hydrodynamic equations rather than Einstein equations. ... More

## A Kinetic-Theory Description of Fluids

*Luciano Rezzolla and Olindo Zanotti*

### in Relativistic Hydrodynamics

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780198528906
- eISBN:
- 9780191746505
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528906.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter illustrates how the foundations of the fluid description are rooted in statistical mechanics and in kinetic theory. This approach, which is appropriate for those systems composed of a ... More

## The Einstein equations

*Nathalie Deruelle and Jean-Philippe Uzan*

### in Relativity in Modern Physics

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0044
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter deals with Einstein equations. In the absence of matter there is no gravitational field, and the spacetime which represents this empty universe is Minkowski spacetime. More precisely, if ... More

## The force on a defect

*Adrian P. Sutton*

### in Physics of Elasticity and Crystal Defects

- Published in print:
- 2020
- Published Online:
- August 2020
- ISBN:
- 9780198860785
- eISBN:
- 9780191893001
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198860785.003.0008
- Subject:
- Physics, Condensed Matter Physics / Materials, Crystallography: Physics

This chapter is based on Eshelby’s static energy-momentum tensor which results in an integral expression for the configurational force on a defect. After elucidating the concepts of a configurational ... More

## Matter in curved spacetime

*Nathalie Deruelle and Jean-Philippe Uzan*

### in Relativity in Modern Physics

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0043
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter is concerned with the laws of motion of matter—particles, fluids, or fields—in the presence of an external gravitational field. In accordance with the equivalence principle, this motion ... More

## Fields and matter

*Nathalie Deruelle and Jean-Philippe Uzan*

### in Relativity in Modern Physics

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0026
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the laws of relativistic dynamics for continuous media, namely, the ‘fields’ that mediate interactions in relativistic theories, and also fluids. The concept of field ... More

## The Maxwell equations

*Nathalie Deruelle and Jean-Philippe Uzan*

### in Relativity in Modern Physics

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0030
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents Maxwell equations determining the electromagnetic field created by an ensemble of charges. It also derives these equations from the variational principle. The chapter studies ... More

## The Theory of Special Relativity

*Hanoch Gutfreund and Jürgen Renn*

### in The Formative Years of Relativity: The History and Meaning of Einstein's Princeton Lectures

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691174631
- eISBN:
- 9781400888689
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174631.003.0015
- Subject:
- Physics, History of Physics

This chapter shows how the principle of special relativity and the principle of the constancy of the velocity of light uniquely determine the Lorentz transformation. Unlike in pre-relativity physics, ... More

## Riemann and Einstein

*Moataz H. Emam*

### in Covariant Physics: From Classical Mechanics to General Relativity and Beyond

- Published in print:
- 2021
- Published Online:
- May 2021
- ISBN:
- 9780198864899
- eISBN:
- 9780191897313
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198864899.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

In this chapter we make notions of spatial and spacetime curvature more precise by presenting Riemann’s theory of non-Euclidean spaces. We then construct Einstein’s gravitational field equations and ... More

## Gravitational waves and the radiative field

*Nathalie Deruelle and Jean-Philippe Uzan*

### in Relativity in Modern Physics

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0053
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter turns to the gravitational radiation produced by a system of massive objects. The discussion is confined to the linear approximation of general relativity, which is compared with the ... More

## Energy-based approach to fracture

*Lallit Anand and Sanjay Govindjee*

### in Continuum Mechanics of Solids

- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780198864721
- eISBN:
- 9780191896767
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198864721.003.0027
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter introduces the concept of energy release rates for linear elastic fracture mechanics. The concept of an energy release rate is defined and related to the criteria of Griffith with ... More

## Primordial quantum perturbations

*Nathalie Deruelle and Jean-Philippe Uzan*

### in Relativity in Modern Physics

- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198786399
- eISBN:
- 9780191828669
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0062
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter shows that fluctuations of quantum origin are generated during inflation and that this process supplies initial conditions compatible with the observations. These fluctuations are ... More

## Lagrange formalism in field theory

*Iosif L. Buchbinder and Ilya L. Shapiro*

### in Introduction to Quantum Field Theory with Applications to Quantum Gravity

- Published in print:
- 2021
- Published Online:
- April 2021
- ISBN:
- 9780198838319
- eISBN:
- 9780191874666
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198838319.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter is devoted to a general discussion of classical field theory. It presents the minimum information required about classical fields for the subsequent treatment of quantum theory in the ... More

## Classical Electromagnetism

*Peter Mann*

### in Lagrangian and Hamiltonian Dynamics

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198822370
- eISBN:
- 9780191861253
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198822370.003.0027
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In this chapter, Noether’s theorem as a classical field theory is presented and the properties of variations are again discussed for fields (i.e. field variations, space variations, time variations, ... More

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