REVIEW 2 cited by
Quantum (Matrix) Geometry and Quasi-Coherent States
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and allows to extract the underlying classical space without requiring the limit of large matrices or representation theory. The approach is based on the previously introduced concept of quasi-coherent states. In particular, a concept of quantum K\"ahler geometry arises naturally, which includes the well-known quantized coadjoint orbits such as the fuzzy sphere $S^2_N$ and fuzzy $\mathbb{C} P^n_N$. A quantization map for quantum K\"ahler geometries is established. Some examples of quantum geometries which are not K\"ahler are identified, including the minimal fuzzy torus.
Forward citations
Cited by 2 Pith papers
-
Quantization of Algebraic Varieties Defined by Casimir Polynomials via Matrix Regularization: Fuzzy $S^7$ and Beyond
A weak matrix regularization of any single-Casimir level set of a compact semisimple Lie algebra is built from reducible representations whose coadjoint orbits densely fill the variety, with fuzzy S^7 worked out explicitly.
-
Minimal covariant quantum space-time
The minimal covariant quantum space-time M^{1,3}_0 is shown to be a quantized twistor space, an S2 bundle over a k=-1 FLRW space-time, with localized quasi-coherent states.
Discussion (0). Continue with ORCID to comment.