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The algebras of non-relativistic and of classical mechanics are unstablealgebraic structures. Their deformation towards stable structures leads,respectively, to relativity and to quantum mechanics. Likewise, the combinedrelativistic quantum mechanics algebra is also unstable. Its stabilizationrequires the non-commutativity of the space-time coordinates and the existenceof a fundamental length constant. The new relativistic quantum mechanicsalgebra has important consequences on the geometry of space-time, on quantumstochastic calculus and on the construction of quantum fields. Some of theseeffects are studied in this paper.Comment: 36 pages Latex, 1 eps figur

Geometry, stochastic calculus, and quantum fields in a noncommutative space–time