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The linearly polarized Gowdy $T^3$ model is paradigmatic for studyingtechnical and conceptual issues in the quest for a quantum theory of gravitysince, after a suitable and almost complete gauge fixing, it becomes an exactlysoluble midisuperspace model. Recently, a new quantization of the model,possessing desired features such as a unitary implementation of the gauge groupand of the time evolution, has been put forward and proven to be essentiallyunique. An appropriate setting for making contact with other approaches tocanonical quantum gravity is provided by the Schr\"odinger representation,where states are functionals on the configuration space of the theory. Here weconstruct this functional description, analyze the time evolution in thiscontext and show that it is also unitary when restricted to physical states,i.e. states which are solutions to the remaining constraint of the theory.

Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics