Weak anticommutation relations and amalgams of Grassmann algebras

The Clifford algebra constructed on a given linear space with a symmetric bilinear form is considered along with the family of its Grassmann subalgebras generated by all possible isotropic subspaces. The amalgam (i.e., the inductive limit) of this family is described. As an application, a modification of the canonical anticommutation relations (CAR) is examined. The modification is such that the conventional CAR are imposed only on pairs of space vectors that are orthogonal with respect to the form mentioned above, and each of the vectors is isotropic.