Ground-Lineage Compatibility

Record: DEF-RENORM-GLC
Source: Definition II.1.

Short definition

Ground-lineage compatibility says that the observable coarse-graining map and the selected Hilbert-space carrier map act identically on vectors generated from the distinguished carrier state:

What it means

The theory may hand us two pieces of data: an observable map and a selected carrier map . GLC is the interface equation that says they represent the same scale arrow. It is stronger than agreement of one expectation value and different from complete positivity.

Example

If , GLC forces . Thus the observable prescription descends to the declared represented carrier.

Scope

GLC does not imply Dirichlet covariance, common-refinement descent, SNC, or a continuum limit.

Read source manuscript. Research manuscript — not peer reviewed.