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… 
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25 Citations
Background Citations
9
Methods Citations
1

25 Citations

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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…
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