*Nathalie Deruelle and Jean-Philippe Uzan*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198786399.003.0040
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter begins by examining p-forms and the exterior product, as well as the dual of a p-form. Meanwhile, the exterior derivative is an operator, denoted d, which acts on a p-form to give a (p + ...
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This chapter begins by examining p-forms and the exterior product, as well as the dual of a p-form. Meanwhile, the exterior derivative is an operator, denoted d, which acts on a p-form to give a (p + 1)-form. It possesses the following defining properties: if f is a 0-form, df(t) = t f (where t is a vector of Eₙ), which coincides with the definition of differential 1-forms. Moreover, d(α + β) = dα + dβ, where α and β are forms of the same degree. Moreover, the exterior calculus can be used to obtain a compact and elegant formulation of Maxwell’s equations.Less

This chapter begins by examining *p*-forms and the exterior product, as well as the dual of a *p*-form. Meanwhile, the exterior derivative is an operator, denoted d, which acts on a *p*-form to give a (*p* + 1)-form. It possesses the following defining properties: if *f* is a 0-form, d*f(t*) = *t f* (where *t* is a vector of *E*ₙ), which coincides with the definition of differential 1-forms. Moreover, d(*α* + *β*) = d*α* + d*β*, where *α* and *β* are forms of the same degree. Moreover, the exterior calculus can be used to obtain a compact and elegant formulation of Maxwell’s equations.

*Moataz H. Emam*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198864899.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

This book is an introduction to the modern methods of the general theory of relativity, tensor calculus, space time geometry, the classical theory of fields, and a variety of theoretical physics ...
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This book is an introduction to the modern methods of the general theory of relativity, tensor calculus, space time geometry, the classical theory of fields, and a variety of theoretical physics oriented topics rarely discussed at the level of the intended reader (mid-college physics major). It does so from the point of view of the so-called principle of covariance; a symmetry that underlies most of physics, including such familiar branches as Newtonian mechanics and electricity and magnetism. The book is written from a minimalist perspective, providing the reader with only the most basic of notions; just enough to be able to read, and hopefully comprehend, modern research papers on these subjects. In addition, it provides a (hopefully short) preparation for the student to be able to conduct research in a variety of topics in theoretical physics; with particular emphasis on physics in curved spacetime backgrounds. The hope is that students with a minimal mathematical background in calculus and only some introductory courses in physics may be able to study this book and benefit from it.Less

This book is an introduction to the modern methods of the general theory of relativity, tensor calculus, space time geometry, the classical theory of fields, and a variety of theoretical physics oriented topics rarely discussed at the level of the intended reader (mid-college physics major). It does so from the point of view of the so-called principle of covariance; a symmetry that underlies most of physics, including such familiar branches as Newtonian mechanics and electricity and magnetism. The book is written from a minimalist perspective, providing the reader with only the most basic of notions; just enough to be able to read, and hopefully comprehend, modern research papers on these subjects. In addition, it provides a (hopefully short) preparation for the student to be able to conduct research in a variety of topics in theoretical physics; with particular emphasis on physics in curved spacetime backgrounds. The hope is that students with a minimal mathematical background in calculus and only some introductory courses in physics may be able to study this book and benefit from it.

*Moataz H. Emam*

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198864899.003.0009
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

In this chapter we present the modern theory of differential forms and see how it applies to the classical fields studied in the previous chapter. We apply the theory to Maxwell fields as well as to ...
More

In this chapter we present the modern theory of differential forms and see how it applies to the classical fields studied in the previous chapter. We apply the theory to Maxwell fields as well as to Cartan’s formulation of general relativity. A discussion of the generalized Stokes theorem is given.Less

In this chapter we present the modern theory of differential forms and see how it applies to the classical fields studied in the previous chapter. We apply the theory to Maxwell fields as well as to Cartan’s formulation of general relativity. A discussion of the generalized Stokes theorem is given.