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Operational Spacetime

Part of the Fundamental Theories of Physics Book Series (volume 163)

DOI: 10.1007/978-1-4419-0898-8

ISBN: 978-1-4419-0897-1

Publisher: Springer New York - Springer Journals

Oct 23, 2009

1 - 10 of 13 Chapters

LitStream

Chapter 1Introduction and Orientation

Saller, Heinrich

Pages: 1 –15

[Einstein’s theory of general relativity identifies spacetime curvature with a gravitational interaction. The theory is formulated primarily in a geometrical language, while the group-theoretical concepts remain more in the background. In an operational spacetime approach, the hierarchy will be...
LitStream

Chapter 2Einstein’s Gravity

Saller, Heinrich

Pages: 17 –28

[In this chapter, Einstein’s gravity with the identification of the curvature of a Riemannian manifold as a geometrical concept and interaction as a physical one is shortly exemplified by Schwarzschild–Kruskal spacetime and by some properties of Friedmann spacetimes with Robertson–Walker metrics....
LitStream

Chapter 3Riemannian Manifolds

Saller, Heinrich

Pages: 29 –80

[In this chapter, general structures of differential manifolds are given, especially the operational aspects of Riemannian manifolds. Manifolds as such are rather amorphous structures. Physically important and manifold-characterizing are the operation groups, they are parametrizing. A Riemannian...
LitStream

Chapter 4Mass Points

Saller, Heinrich

Pages: 81 –92

[A dynamics is a representation of spacetime operations. A nonrelativistic mass point dynamics is a representation of the time translations. The equations of motion, of second order in time for position as basic observable and of first order for the position-momentum pair, express the Lie algebra...
LitStream

Chapter 5Quantum Mechanics

Saller, Heinrich

Pages: 93 –110

[It is not really a good strategy to follow the historical development of classical theory to quantum theory by “quantizing” a classical theory. Quantum theory is not only the change of a government; it is even the change of the constitution. ]
LitStream

Chapter 6Quantum Fields of Flat Spacetime

Saller, Heinrich

Pages: 111 –145

[Spacetime theories are field theories as conceptionally initiated by Faraday and first formulated by Maxwell. Charged or neutral mass points with orbits \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
LitStream

Chapter 7External and Internal Operations

Saller, Heinrich

Pages: 147 –171

[Basic physical theories involve both external or spacetimelike and internal or chargelike degrees of freedom in complex representation vector spaces that are acted on, respectively, by operations from the Poincaré group, i.e., by Lorentz transformations and spacetime translations, and by...
LitStream

Chapter 8Relativities and Homogeneous Spaces

Saller, Heinrich

Pages: 173 –200

[This chapter discusses the dichotomy and connection of external and internal operations in real four-dimensional electroweak spacetime \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Chapter 9Representation Coeffficients

Saller, Heinrich

Pages: 201 –253

[Internal chargelike (“vertical”) operations come from compact groups, e.g., hypercharge U(1), isospin SU(2), and color SU(3). In the electroweak and strong standard model, they are implemented as gauge transformations that, via gauge fields in covariant derivatives, accompany the translations...
LitStream

Chapter 10Convolutions and Product Representations

Saller, Heinrich

Pages: 255 –276

[The Feynman integrals in special relativistic quantum field theories involve convolutions of energy-momentum distributions. The on-shell parts for translation representations give product representation coefficients of the Poincaré group, i.e., energy-momentum distributions for free states...

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