PROJECTIVE AND CONFORMAL STRUCTURES IN GENERAL
... between formalism and observation’; its aim is to shed light on the physical implications of any formalism: the possibility of formally defining any physically significant quantity should coincide with the possibility of measuring it in principle; i.e., by means of some idealized measurement procedu ...
... between formalism and observation’; its aim is to shed light on the physical implications of any formalism: the possibility of formally defining any physically significant quantity should coincide with the possibility of measuring it in principle; i.e., by means of some idealized measurement procedu ...
Effective Field Theories, Reductionism and Scientific Explanation
... Standard Model of the electromagnetic, weak, and strong interactions to be an EFT (Meissner, 1992). Nuclear physicists systematically derive low-energy EFTs from quantum chromodynamics (a theory which is part of the Standard Model) to account for the dynamics of protons and neutrons in atomic nuclei ...
... Standard Model of the electromagnetic, weak, and strong interactions to be an EFT (Meissner, 1992). Nuclear physicists systematically derive low-energy EFTs from quantum chromodynamics (a theory which is part of the Standard Model) to account for the dynamics of protons and neutrons in atomic nuclei ...
Math 9 Study Guide Unit 7 Unit 7 - Similarity and Transformations
... Scale factor can be given as a decimal or a fraction. If you are given a diagram with dimensions and the scale factor and asked to draw the scale diagram multiply each dimension by the scale factor to find out the dimensions of the scale (new) diagram. Scale factor can also be expressed as a ratio ( ...
... Scale factor can be given as a decimal or a fraction. If you are given a diagram with dimensions and the scale factor and asked to draw the scale diagram multiply each dimension by the scale factor to find out the dimensions of the scale (new) diagram. Scale factor can also be expressed as a ratio ( ...
Quantum Effects Through a Fractal Theory of Motion
... There is infinity of fractal curves (geodesics) relating to any couple of points (or starting from any point) and applied for any scale. The phenomenon can be easily understood at the level of fractal surfaces, which, in their turn, can be described in terms of fractal distribution of conic points o ...
... There is infinity of fractal curves (geodesics) relating to any couple of points (or starting from any point) and applied for any scale. The phenomenon can be easily understood at the level of fractal surfaces, which, in their turn, can be described in terms of fractal distribution of conic points o ...
Quantum critical states and phase transitions in the presence of non
... (that is T > 0) in equilibrium is always a relevant perturbation at a quantum critical point[15, 16]. In particular there is no sharp distinction between the different phases of the low dimensional systems we consider here at any T > 0. In certain cases it was argued that a non equilibrium drive may ...
... (that is T > 0) in equilibrium is always a relevant perturbation at a quantum critical point[15, 16]. In particular there is no sharp distinction between the different phases of the low dimensional systems we consider here at any T > 0. In certain cases it was argued that a non equilibrium drive may ...
Completeness, Supervenience, and Ontology
... complete (as Laplace pointed out). But no one would suggest because of this that we think of the state at one moment as all that exists: indeed, it is the various different states at different times that the dynamical laws link to one another. To sum up, informational completeness implies a form of ...
... complete (as Laplace pointed out). But no one would suggest because of this that we think of the state at one moment as all that exists: indeed, it is the various different states at different times that the dynamical laws link to one another. To sum up, informational completeness implies a form of ...
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.