# 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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