Confining quantum field theories
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910006857695232 |
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| author | Metaxas, Dimitrios |
| author_facet | Metaxas, Dimitrios |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01168 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Confining quantum field theories Metaxas, Dimitrios High Energy Physics - Theory 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. |
| title | Confining quantum field theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2409.01168 |