2024/09/02 by Dimitrios Metaxas, Metaxas, Dimitrios
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2409.01168
openalex publication_date 2024/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is widely believed, and axiomatically postulated in mathematical quantum field theory, that the vacuum is a unique vector state. The recent solution of the quantum Yang-Mills theory of the strong interaction revealed the presence of two vacua and a mixed quantum state. The second, confining vacuum, is an eigenstate of an auxiliary field, with a non-zero eigenvalue, as opposed to the zero eigenstate of the perturbative vacuum, and provides a new mechanism of scale generation. I show that this non-trivial vacuum structure implies confinement, in the sense that vacuum expectation values between states separated at large, space-like distances, tend to zero, whereas in ordinary quantum theories with a unique vacuum, they are known to satisfy the cluster decomposition principle, and tend to free, asymptotic states, at large separations. 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.