Algebraic and Geometric Structures in Special Relativity

@inproceedings{Giulini2006AlgebraicAG,
  title={Algebraic and Geometric Structures in Special Relativity},
  author={Domenico Giulini},
  year={2006}
}
I review, some of the algebraic and geometric structures that underlie the theory of Special Relativity. This includes a discussion of relativity as a symmetry principle, derivations of the Lorentz group, its composition law, its Lie algebra, comparison with the Galilei group, Einstein synchronization, the lattice of causally and chronologically complete regions in Minkowski space, rigid motion (the Noether-Herglotz theorem), and the geometry of rotating reference frames. Representation… 
View PDF on arXiv
25 Citations
Background Citations
9
Methods Citations
1

25 Citations

Special relativity in the 21st century

This paper, which is meant to be a tribute to Minkowski's geometrical insight, rests on the idea that the basic observed symmetries of spacetime homogeneity and of isotropy of space, which are…

Special relativity in the 21st century *

This paper, which is meant to be a tribute to Minkowski's geometrical insight, rests on the idea that the basic observed symmetries of spacetime homogeneity and of isotropy of space, which are…

A framework for structure-preserving submersions and some theorems in relativistic flows

In this paper we first propose a framework of structure-preserving submersions, which generalises the concept of a Riemannian submersion, and dualises the concept of subgeometry, or…

The hyperbolic theory of special relativity

The book is based largely on the author's researches presented at conferences in the period 1992 onwards. It is a historically based exposition and an extension of the hyperbolic version of special…

On the General Problem of Structure-Preserving Submersions

In this paper we give a general geometrical framework for working with problems that can be described as a structure-preserving submersion defined on a suitable space with a geometrical structure. We…

Theory of a quantum noncanonical field in curved spacetimes

Much attention has been recently devoted to the possibility that quantum gravity effects could lead to departures from special relativity in the form of a deformed Poincare algebra. These proposals…

A modern view of the classical Herglotz-Noether theorem

In this paper we give a new proof, valid for all dimensions, of the classical HerglotzNoether theorem that all rotational shear-free and expansion-free flows (rotational Bornrigid flows) in Minkowski…

Observers and splitting structures in relativistic electrodynamics

TLDR
A relativistic splitting structure is introduced as a means to map fields and equations of electromagnetism from curved four-dimensional space?time to three-dimensional observer?s space, enabling a compact, yet profound analysis of the problems at hand.

Minkowski space-time and hyperbolic geometry

It has become generally recognized that hyperbolic (i.e. Lobachevskian) space can be represented upon one sheet of a two-sheeted cylindrical hyperboloid in Minkowski space-time. This paper aims to…

The singularities as ontological limits of the general relativity

The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big…

References

SHOWING 1-10 OF 71 REFERENCES

Reciprocity Principle and the Lorentz Transformations

By using the principle of relativity, together with the customary assumptions concerning the nature of the space‐time manifold in special relativity, namely, space‐time homogeneity and isotropy of…

Local quantum physics : fields, particles, algebras

This textbook gives a comprehensive account of local quantum physics understood as the synthesis of quantum theory with the principle of locality. Centered on the algebraic approach, it describes…

The logic of causally closed spacetime subsets

The causal structure of spacetime offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non-timelike related with it. We show…

Uniqueness of Simultaneity

  • D. Giulini
  • Mathematics
    The British Journal for the Philosophy of Science
  • 2001
We consider the problem of uniqueness of certain simultaneity structures in flat spacetime. Absolute simultaneity is specifiled to be a non‐trivial equivalence relation which is invariant under the…

Analytic Hyperbolic Geometry: Mathematical Foundations And Applications

This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry. Analytic hyperbolic geometry regulates relativistic mechanics just as analytic Euclidean…

Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics

Preface. Preface to the English Edition. Introduction. 1. Poincare Invariant Nonlinear Scalar Equations. 2. Poincare-Invariant Systems of Nonlinear PDEs. 3. Euclid and Galilei Groups and Nonlinear…

The structure of space-time transformations

LetT be a one-to-one mapping ofn-dimensional space-timeM onto itself. IfT maps light cones onto light cones and dimM≧3, it is shown thatT is, up to a scale factor, an inhomogeneous Lorentz…

Physical holonomy, Thomas precession, and Clifford algebra

After a general discussion of the physical significance of holonomy group transformations, a relation between the transports of Fermi–Walker and Levi–Civita in special relativity is pointed out. A…

Relativistic velocity space, Wigner rotation, and Thomas precession

We develop a relativistic velocity space called rapidity space from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive…

Thomas rotation and the parametrization of the Lorentz transformation group

Two successive pure Lorentz transformations are equivalent to a pure Lorentz transformation preceded by a 3×3 space rotation, called a Thomas rotation. When applied to the gyration of the rotation…
...