Hybrid Geometrodynamics: A Hamiltonian description of classical gravity
coupled to quantum matter
- URL: http://arxiv.org/abs/2307.00922v2
- Date: Wed, 14 Feb 2024 22:39:55 GMT
- Title: Hybrid Geometrodynamics: A Hamiltonian description of classical gravity
coupled to quantum matter
- Authors: J. L. Alonso, C. Bouthelier-Madre, J. Clemente-Gallardo, D.
Mart\'inez-Crespo
- Abstract summary: We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where gravity is described by a Quantum Field Theory in Curved Spacetime.
In our approach there is no non-dynamic background structure, apart from the manifold of events, and the gravitational and quantum degrees of freedom have their dynamics inextricably coupled.
An important feature of this work is the use of Gaussian measures over the space of matter fields and of Hida distributions to define a common superspace to all possible Hilbert spaces with different measures, to properly characterize the Schrodinger wave functional picture of QFT in
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We generalize the Hamiltonian picture of General Relativity coupled to
classical matter, known as geometrodynamics, to the case where such matter is
described by a Quantum Field Theory in Curved Spacetime, but gravity is still
described by a classical metric tensor field over a spatial hypersurface and
its associated momentum. Thus, in our approach there is no non-dynamic
background structure, apart from the manifold of events, and the gravitational
and quantum degrees of freedom have their dynamics inextricably coupled. Given
the Hamiltonian natureof the framework, we work with the generators of
hypersurface deformations over the manifold of quantum states. The construction
relies heavily on the differential geometry of a fibration of the set of
quantum states over the set of gravitational variables. An important feature of
this work is the use of Gaussian measures over the space of matter fields and
of Hida distributions to define a common superspace to all possible Hilbert
spaces with different measures, to properly characterize the Schrodinger wave
functional picture of QFT in curved spacetime. This allows us to relate states
within different Hilbert spaces in the case of vacuum states or measures that
depend on the gravitational degrees of freedom, as the ones associated to
Ashtekar's complex structure. This is achieved through the inclusion of a
quantum Hermitian connection for the fibration, which will have profound
physical implications. The most remarkable physical features of the
construction are norm conservation of the quantum state (even if the total
dynamics are non-unitary), the clear identification of the hybrid conserved
quantities and the description of a dynamical backreaction of quantum matter on
geometry and vice versa, which shall modify the physical properties the
gravitational field would have in the absence of backreaction.
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