X-Nico

3 unusual facts about scalar


Scalar-tensor theory

It uses a scalar field of infinite length scale (i.e. long-ranged), so, in the language of Yukawa's theory of nuclear physics, this scalar field is a massless field.

In theoretical physics, a scalar-tensor theory is a theory that includes both a scalar field and a tensor field to represent a certain interaction.

JBD-type theories with short-ranged scalar fields use, according to Yukawa's theory, massive scalar fields.


AltiVec

Unlike SSE2, AltiVec supports a special RGB "pixel" data type, but it does not operate on 64-bit double precision floats, and there is no way to move data directly between scalar and vector registers.

Bayesian multivariate linear regression

Bayesian approach to multivariate linear regression, i.e. linear regression where the predicted outcome is a vector of correlated random variables rather than a single scalar random variable.

Cross product

Oliver Heaviside in England and Josiah Willard Gibbs, a professor at Yale University in Connecticut, also felt that quaternion methods were too cumbersome, often requiring the scalar or vector part of a result to be extracted.

De Sitter invariant special relativity

The reason it is a semidirect product is that, when you rotate, the x-tilt and the y-tilt rotate into each other, since they form a vector and not two scalars.

Fermi–Walker transport

where V is four-velocity, D is the covariant derivative in the Riemannian space, and (,) is scalar product.

IBM OpenDX

The data may be scalar (such as the concentration of a chemical agent in the brain), vector or tensor fields (like the displacement or strain tensor fields when the gear is in action) at different points of the object.

Peter Richard Killeen

Killeen has also developed a theory of learning as causal inference (1981) bringing these together in his paper on the perception of contingency in conditioning: Scalar timing, response bias, and the erasure of memory by reinforcement (Killeen, 1984).

Q-ball

It should be pointed out that while this kind of Q-ball is stable against decay into scalars, it is not stable against decay into fermions if the scalar field \phi has nonzero Yukawa couplings to some fermions.

Raychaudhuri equation

unstable: for example, the world lines of the dust particles in the Gödel solution have vanishing shear, expansion, and acceleration, but constant vorticity just balancing a constant Raychuadhuri scalar due to nonzero vacuum energy ("cosmological constant").

Scalar electrodynamics

The scalar field is charged, and with an appropriate potential, it has the capacity to break the gauge symmetry via the Abelian Higgs mechanism.

Scalar theories of gravitation

Scalar theories of gravitation are field theories of gravitation in which the gravitational field is described using a scalar field, which is required to satisfy some field equation.

Wess–Zumino model

In 1974, Julius Wess and Bruno Zumino studied, using modern terminology, dynamics of a single chiral superfield (composed of a complex scalar and a spinor fermion) whose cubic superpotential leads to a renormalizable theory.

Yang–Mills theory

A way out has been given by Ludvig Faddeev and Victor Popov with the introduction of a ghost field (see Faddeev–Popov ghost) that has the property of being unphysical since, although it agrees with Fermi–Dirac statistics, it is a complex scalar field, which violates the spin-statistics theorem.


see also