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Polarization-less quantization of free field theories

Oct 18
Group Seminar
4:00 pm o'clock to 5:30 pm o'clock
Dr. Suzanne Lanery (Centro de Ciencias Matematicas UNAM, Campus Morelia)
SR 02.729

The phase space of a classical free field theory is a
symplectic vector space V. Choosing a complex structure (polarization)
turns V into a complex Hilbert space H, and the Fock space built on H
provides a quantization of V. When V is finite-dimensional, the Fock
representations built from different polarizations are equivalent (as a
consequence of the Stone-von Neumann theorem), but this is no longer
true in the infinite-dimensional case.
By constructing the state space of a quantum field theory as a
projective limit of simpler building blocs (truncations), it is possible
to lift the Stone-von Neumann theorem to the infinite-dimensional case.
Carefully selecting a "dense" collection of truncations yields a quantum
state space which is at the same time universal (it encompasses at once
all "reasonable" Fock spaces, and supports arbitrarily good
implementations of all bounded linear symplectomorphisms of V) and
constructive (all states can be constructed in a systematic way, in
contrast eg. to generic algebraic states).