Abstract
The concepts of four-momentum, mass, energy and linear momentum of a single particle are introduced and then extended to a system of particles. The principle of conservation of four-momentum is stated in its most general form, before specific aspects of it are considered. As an application, a derivation of the Doppler effect, alternative to that given in Chap. 5, is presented. Applications to particle physics are then considered, by discussing elastic and inelastic collisions, with a detailed treatment of Compton and inverse Compton scatterings. Finally the concepts of four-force and force measured by an observer is introduced for a single non-isolated particle.
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Notes
- 1.
- 2.
Max Planck (1858–1947): German physicist, 1918 Nobel Prize in Physics, famous for having introduced the concept of energy quantum, via the constant bearing his name [cf. Eq. (9.25) ], which was the prelude to quantum mechanics. Planck supported Albert Einstein as soon as 1905, recognizing immediately the importance of relativity and contributing to its diffusion in Germany.
- 3.
If quantum effects are to be taken into account, a second intrinsic dynamical quantity must be considered: the photon’s spin (cf. Sect. 10.7).
- 4.
Let us recall that hypersurface stands for a surface of dimension 4 − 1 = 3. It is actually a three-dimensional volume; hypersurfaces will be discussed in details in Chap. 16.
- 5.
Cf. Sect. 9.3.2.
- 6.
Stanley Mandelstam: Theoretician physicist born in South Africa in 1928; he made his career in Birmingham (United Kingdom) and then of the University of California in Berkeley. He introduced the variables bearing his name in 1958 (Mandelstam 1958), in order to study the interaction of pions with atomic nuclei.
- 7.
In Chap. 10, we will introduce a particular comoving observer: the barycentric observer or centre-of-mass observer. However, in the present problem, a generic comoving observer is sufficient.
- 8.
Arthur H. Compton (1892–1962): American physicist, 1927 Nobel Prize in Physics for the discovery of the effect bearing his name. During the Second World War, he was responsible of the “Metallurgical Laboratory” in Chicago—the cover name for facilities producing the uranium and the plutonium of the first atomic bombs.
- 9.
One says that a galaxy has an active nucleus when it harbours in its core a supermassive black hole in the vicinity of which a relativistic jet is emitted, as we shall discuss in more details in Sect. 21.7.1.
- 10.
Synchrotron radiation will be studied in Sect. 20.4.
- 11.
The name Bevatron stems from the abbreviation BeV for billion of electronvolts ; today BeV has been replaced by the international abbreviation GeV.
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Gourgoulhon, É. (2013). Energy and Momentum. In: Special Relativity in General Frames. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37276-6_9
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