The Vacuum as a Lagrangian subspace
Por:
Colosi, Daniele, Oeckl, Robert
Publicada:
19 ago 2019
Categoría:
Physics and astronomy (miscellaneous)
Resumen:
We unify and generalize the notions of vacuum and amplitude in linear
quantum field theory in curved spacetime. Crucially, the generalized
notion admits a localization in spacetime regions and on hypersurfaces.
The underlying concept is that of a Lagrangian subspace of the space of
complexified germs of solutions of the equations of motion on
hypersurfaces. Traditional vacua and traditional amplitudes correspond
to the special cases of definite and real Lagrangian subspaces,
respectively. Further, we introduce both infinitesimal and asymptotic
methods for vacuum selection that involve a localized version of Wick
rotation. We provide examples from Klein-Gordon theory in settings
involving different types of regions and hypersurfaces to showcase
generalized vacua and the application of the proposed vacuum selection
methods. A recurrent theme is the occurrence of mixed vacua, where
propagating solutions yield definite Lagrangian subspaces and evanescent
solutions yield real Lagrangian subspaces. The examples cover Minkowski
space, Rindler space, Euclidean space, and de Sitter space. A simple
formula allows for the calculation of expectation values for observables
in the generalized vacua.
Filiaciones:
Colosi, Daniele:
Univ Nacl Autonoma Mexico, Unidad Morelia, Scuela Nacl Studios Super, Morelia 58190, Michoacan, Mexico
Oeckl, Robert:
Univ Nacl Autonoma Mexico, Ctr Ciencias Matemat, Morelia 58190, Michoacan, Mexico
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