Search results
Results from the WOW.Com Content Network
The Wiener process is scale-invariant. In physics, mathematics and statistics, 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, and thus represent a universality.
The scale-invariant feature transform (SIFT) is a computer vision algorithm to detect, describe, and match local features in images, invented by David Lowe in 1999. [1] ...
Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is ...
Unlike the random walk, it is scale invariant, meaning that is a Wiener process for any nonzero constant α. The Wiener measure is the probability law on the space of continuous functions g , with g (0) = 0 , induced by the Wiener process.
For example, in D = 4, only g 4 is classically dimensionless, and so the only classically scale-invariant scalar field theory in D = 4 is the massless φ 4 theory. Classical scale invariance, however, normally does not imply quantum scale invariance, because of the renormalization group involved – see the discussion of the beta function below.
A change in scale is called a scale transformation. The renormalization group is intimately related to scale invariance and conformal invariance, symmetries in which a system appears the same at all scales (self-similarity), [a] where under the fixed point of the renormalization group flow the field theory is conformally invariant.
In Lie algebra representations, the group SO(3) is compact and simple of rank 1, and so it has a single independent Casimir element, a quadratic invariant function of the three generators which commutes with all of them.
In quantum field theory, scale invariance is a common and natural symmetry, because any fixed point of the renormalization group is by definition scale invariant. Conformal symmetry is stronger than scale invariance, and one needs additional assumptions [2] to argue that it should appear in nature.