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Seminars
Constraints, confinement, and the vacuum state in quantum field theory. Connections with the conceptual problems of consciousness and measurement.
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Europe/Athens
Description
I describe the formalism, Feynman rules, and combinatorics that constrain a scalar field to propagate "classically", in tree diagrams, either by itself, or interacting with other purely quantum fields. Examples are given with the quartic and the cubic scalar interaction in four and six spacetime dimensions respectively, and possible generalizations and applications are discussed. When the constraint of Gauss's law is enforced in this way in the non-Abelian gauge theory, a second, confining vacuum emerges, which is an eigenstate of an auxiliary field, with a non-zero eigenvalue, and non-zero (positive) energy density, as opposed to the zero eigenstate of the perturbative vacuum. This is a new mechanism of scale generation.
The modification of the postulate of the uniqueness of the vacuum in axiomatic quantum field theory is described, since the cluster decomposition property does not hold. Instead, in a confined state, the correlation functions are zero at spacelike distances larger than the scale of the theory. Accordingly, they can be non-zero only along a timelike worldline (with an associated spacelike width). The theory is by construction unitary and Lorentz invariant, but the different vacua give a direct sum decomposition. Implications on determinism and causality, and generalizations of the confinement mechanism for theories with other symmetries and interactions are discussed.
I argue that confinement (in the generalized sense) is a necessary (certainly not sufficient) condition for proposed theories of a conscious state. Also, I discuss the relation with the measurement postulate of quantum mechanics (when the "observer" is merely a detector). I argue that confinement (in the strong interaction) is an important mechanism (similar to and possibly along with decoherence) for the measurement process.
Videoconference via https://us02web.zoom.us/j/82249348474
