 
Summary: THE ROLE OF THE MODULAR PAIRS IN THE CATEGORY OF COMPLETE
ORTHOMODULAR LATTICE
D. AERTS
Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B1050 Brussel,
Belgium
and
C. PIRON
Department of TheoreticaIPhysics, University of Geneva, CH1211 Geneva 4,
Switzerland
ABSTRACT. We study the modular pairs of a complete orthomodular lattice i.e. a CROC. We
propose the concept of mmorphism as a mapping which preserves the lattice structure, the ortho
gonality and the property to be a modular pair. We give a characterization of the mmorphisms in
the case of the complex ttilbert space to justify this concept.
INTRODUCTION
There are many formulations of quantum physics, the Hilbertspace formulation, the phasespace
formulation, the C*algebra formulation, etc. All these formulations are equivalent and which one
to choose for formulating and solving a particular problem depends on the nature of the problem
at hand. It is thus important to be able to formulate the problem in terms independent of this
choice. In pure mathematics we encounter the same situation. For example in algebraic geometry
we like to define the objects independent of the coordinate field. This kind of difficulty was
