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(1) - Intellectual Archive
(1) - Intellectual Archive

... vacuum to survive not too far above the LHC scale explains away the fine-tuning problem and signals the breakdown of the SM in this region. This conclusion, albeit preliminary, sheds light on the problem of extrapolating field theories in the deep ultraviolet sector, specifically near the Planck sca ...
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RENORMALIZATION AND GAUGE INVARIANCE∗
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... In principle, observed phenomena only require finite field theories for their description anyway, since there is an energy limit to the collisions that can be studied, and if we choose a cutoff Λ , for instance by introducing a lattice with mesh size a = 1/Λ , our theories may well be accurate for a ...
Evolving QCD - Department of Theoretical Physics
Evolving QCD - Department of Theoretical Physics

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... • Everything at a hadron collider (signals, backgrounds, luminosity measurement) involves QCD • Strong coupling is not small: s(MZ)  0.12 and running is important  events have high multiplicity of hard clusters (jets)  each jet has a high multiplicity of hadrons  higher-order perturbative corre ...
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BernTalk

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Seoul National University, Korea, 06/2010, Insuk Yu

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... The existence of the integer quantum Hall effect (IQHE) depends crucially on Anderson localisation, and, conversely, many aspects of the delocalisation transition have been studied in most detail in quantum Hall systems. The following article is intended to provide a introduction to the IQHE from th ...
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Scale invariance



In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilatations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity.In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale.In quantum field theory, scale invariance has an interpretation in terms of particle physics. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved.In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical point, fluctuations occur at all length scales, and thus one should look for an explicitly scale-invariant theory to describe the phenomena. Such theories are scale-invariant statistical field theories, and are formally very similar to scale-invariant quantum field theories.Universality is the observation that widely different microscopic systems can display the same behaviour at a phase transition. Thus phase transitions in many different systems may be described by the same underlying scale-invariant theory.In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.
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