1202.1846 (Alejandro Corichi et al.)

Effective constrained polymeric theories and their continuum limit    [PDF]

Alejandro Corichi, Tatjana Vukasinac

The classical limit of polymer quantum theories yields a one parameter family
of `effective' theories labeled by \lambda. Here we consider such families for
constrained theories and pose the problem of taking the `continuum limit',
\lambda -> 0. We put forward criteria for such question to be well posed, and
propose a concrete strategy based in the definition of appropriately
constructed Dirac observables. We analyze two models in detail, namely a
constrained oscillator and a cosmological model arising from loop quantum
cosmology. For both these models we show that the program can indeed be
completed, provided one makes a particular choice of \lambda-dependent internal
time with respect to which the dynamics is described and compared. We show that
the limiting theories exist and discuss the corresponding limit. These results
might shed some light in the problem of defining a renormalization group
approach, and its associated continuum limit, for quantum constrained systems.

View original: http://arxiv.org/abs/1202.1846