Confining quantum field theories

TL;DR

This paper proposes a new understanding of quantum confinement through a non-trivial vacuum structure in quantum field theories, with implications for causality, measurement, and consciousness.

Contribution

It introduces a confining vacuum mechanism in quantum field theories that explains confinement and relates it to measurement and consciousness theories.

Findings

Vacuum expectation values tend to zero at large spacelike distances in confined states.

Correlation functions are non-zero only along timelike worldlines, indicating confinement.

The theory remains unitary and Lorentz invariant despite multiple vacua.

Abstract

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.