Determinism in Free Bosons
It is shown how to map the quantum states of a system of free Bose particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group.
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arXiv subjects
Gerard 't Hooft
Publications and source records attributed to Gerard 't Hooft.
Monopoles, Instantons and Confinement
We review the physics of topological objects in QCD. Topics include: solitons, vortices, magnetic monopoles, instantons, (effective theories of) confinement.
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Determinism and Dissipation in Quantum Gravity, Erice lecture
Without invalidating quantum mechanics as a principle underlying the dynamics of a fundamental theory, it is possible to ask for even more basic dynamical laws that may yield quantum mechanics as the machinery needed for its statistical analysis. In conventional systems such as the Standard Model for quarks and leptons, this would lead to hidden variable theories, which are known to be plagued by problems such as non-locality. But Planck scale physics is so different from field theories in some flat background space-time that here the converse may be the case: we speculate that causality and locality can only be restored by postulating a deterministic underlying theory. A price to be paid may be that the underlying theory exhibits dissipation of information.
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The Holographic Principle
After a pedagogical overview of the present status of High-Energy Physics, some problems concerning physics at the Planck scale are formulated, and an introduction is given to a notion that became known as ``the holographic principle" in Planck scale physics, which is arrived at by studying quantum mechanical features of black holes.
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The Physics of Instantons in the pseudoscalar and vector meson mixing
When the theory of Quantum Chromodynamics was introduced, it was to explain the observed phenomena of quark confinement and scaling. It was then discovered that the emergence of instantons is an essential consequence of this theory. This led to unanticipated explanations not only for the anomalously high masses of the $η$ and the $η'$ particles, but also for the remarkable differences that had been observed in the mixing angles for the pseudoscalar mesons and the vector mesons.
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Quantum Gravity as a Dissipative Deterministic System
It is argued that the so-called holographic principle will obstruct attempts to produce physically realistic models for the unification of general relativity with quantum mechanics, unless determinism in the latter is restored. The notion of time in GR is so different from the usual one in elementary particle physics that we believe that certain versions of hidden variable theories can -- and must -- be revived. A completely natural procedure is proposed, in which the dissipation of information plays an essential role. Unlike earlier attempts, it allows us to use strictly continuous and differentiable classical field theories as a starting point (although discrete variables, leading to fermionic degrees of freedom, are also welcome), and we show how an effective Hilbert space of quantum states naturally emerges when one attempts to describe the solutions statistically. Our theory removes some of the mysteries of the holographic principle; apparently non-local features are to be expected when the quantum degrees of freedom of the world are projected onto a lower-dimensional black hole horizon. Various examples and models illustrate the points we wish to make, notably a model showing that massless, non interacting neutrinos are deterministic.
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The Glorious Days of Physics - Renormalization of Gauge theories
This is an account of the author's recollections of the turbulent days preceding the establishment of the Standard Model as an accurate description of all known elementary particles and forces.
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Topological Aspects of Quantum Chromodynamics
Absolute confinement of its color charges is a natural property of gauge theories such as quantum chromodynamics. On the one hand, it can be attributed to the existence of color-magnetic monopoles, a topological feature of the theory, but one can also maintain that all non-Abelian gauge theories confine. It is illustrated how ``confinement'' works in the SU(2) sector of the Standard Model, and why for example the electron and its neutrino can be viewed as SU(2)-hadronic bound states rather than a gauge doublet. The mechanism called `Abelian projection' then puts the Abelian sector of any gauge theory on a separate footing.
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Counting planar diagrams with various restrictions
Explicit expressions are considered for the generating functions concerning the number of planar diagrams with given numbers of 3- and 4-point vertices. It is observed that planar renormalization theory requires diagrams with restrictions, in the sense that one wishes to omit `tadpole' inserions and `seagull' insertions; at a later stage also self-energy insertions are to be removed, and finally also the dressed 3-point inserions and the dressed 4-point insertions. Diagrams with such restrictions can all be counted exactly. This results in various critical lines in the $λ$-$g$ plane, where $λ$ and $g$ are effective zero-dimensional coupling constants. These lines can be localized exactly.
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Canonical Quantization of Gravitating Point Particles in 2+1 Dimensions
A formalism previously introduced by the author using tesselated Cauchy surfaces is applied to define a quantized version of gravitating point particles in 2+1 dimensions. We observe that this is the first model whose quantum version automatically discretizes time. But also spacelike distances are discretized in a very special way.
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