Euclidean axiom

Definitions

  • WordNet 3.6
    • n Euclidean axiom (mathematics) any of five axioms that are generally recognized as the basis for Euclidean geometry
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Usage


In science:

He was able to isolate a crucial property of Euclidean fields (the Markov property) and gave a set of conditions for Euclidean fields, which allow to derive all properties of relativistic quantum fields satisfying Wightman axioms.
Euclidean Field Theory
In fact, at the beginning of the exploitation of Euclidean methods in constructive quantum field theory, Nelson was able to isolate a set of axioms for the Euclidean fields , allowing the reconstruction of the physical theory.
Euclidean Field Theory
Of course, Nelson axioms are more difficult to verify, since they involve properties of the Euclidean fields and not only of the Schwinger functions.
Euclidean Field Theory
Schrader, Axioms for Euclidean Green’s functions, Commun.
Euclidean Field Theory
It follows from the triangle axiom, ρ (O , P ) + ρ (O , Q) ≥ ρ (Q, P ) which is valid for the proper Euclidean geometry.
General relativity extended to non-Riemannian space-time geometry
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