Hilbert space structure in quantum gravity: an algebraic perspective

Understand

If quantum gravity respects the principles of quantum mechanics, suitably generalized, it may be that a more viable approach to the theory is through identifying the relevant quantum structures rather than by quantizing classical spacetime.

• This viewpoint is supported by difficulties of such quantization, and by the apparent lack of a fundamental role for locality.
• In finite or discrete quantum systems, important structure is provided by tensor factorizations of the Hilbert space.
• However, even in local quantum field theory properties of the generic type III von Neumann algebras and of long range gauge fields indicate that factorization of the Hilbert space is problematic.