# scalar

## Definitions

• WordNet 3.6
• adj scalar of or relating to a directionless magnitude (such as mass or speed etc.) that is completely specified by its magnitude "scalar quantity"
• adj scalar of or relating to a musical scale "he played some basic scalar patterns on his guitar"
• n scalar a variable quantity that cannot be resolved into components
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Webster's Revised Unabridged Dictionary
• n Scalar (Math) In the quaternion analysis, a quantity that has magnitude, but not direction; -- distinguished from a vector, which has both magnitude and direction.
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Century Dictionary and Cyclopedia
• n scalar In quaternions, a real number, positive or negative, integral, fractional, or surd: but some writers lately extend the meaning so as to include imaginaries. Sir W. R. Hamilton introduced the word with the meaning “a real number”; and it tends to confuse the subject to use a word needed for one purpose to signify something else for which no new word is needed.
• scalar Of the nature of a scalar.
• n scalar In physics, a quantity, such as mass or volume, which has magnitude but not direction.
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Chambers's Twentieth Century Dictionary
• Scalar (math.) in the quaternion analysis, a quantity that has magnitude but not direction
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## Etymology

Chambers's Twentieth Century Dictionary

## Usage

### In news:

Quantum Debuts Scalar LTFS Appliances.
The Scalar 1000 from Advanced Digital Information Corporation (ADIC) is an expandable robotic tape library designed to handle enterprise-level backups.
Soffa, "Compile-Time Techniques for Improving Scalar Access Performance in Parallel Memories," IEEE Transactions on Parallel and Distributed Systems, vol 2, no.
Scalar Network Analysis using USB Power Sensors.
A scalar network analyzer (like the Agilent 8757D) is the most popular instrument used for scalar stimulus-response measurements due to its moderate price, high freq coverage, and fast measurement speed.
The combination of a tracking generator and a spectrum analyzer enables swept scalar frequency-response measurements of active and passive networks.
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### In science:

Let us consider, for example, the simplest case of the scalar ﬁeld when the vector s is replaced by the scalar ﬁeld ϕ.
A String Approximation for Cooper Pair in High-T$_{\bf c}$ superconductivity
Note that since vertices involving only scalar bosons are proportional to scalars, there is no need to deﬁne speciﬁc three or four scalar vertices.
AMEGIC++ 1.0, A Matrix Element Generator In C++
They can be coupled in pairs to form complex scalars which will be the scalars of three chiral N = 1, d=4 multiplets.
Marginal Deformations of N=4 SYM and of its Supersymmetric Orbifold Descendants
Suppose the scalar potential has minima such that condensates or vacuum expectation values of scalars do not vanish.
String Theory or Field Theory?
Indeed, the divergence of this scalar (equivalent here to the Kretschmann scalar) is a standard way in which texts point out the singularity in this spacetime (e.g.
Invariants of the Kerr Vacuum
Eq.(3.37) means that curvature scalar R is no longer a real scalar under this transformation.
Problems on Foundations of General Relativity
The entropic scalar product (15) appears often in the constructions below. (Usually, this becomes the scalar product indeed after the conservation laws are excluded).
Geometry of irreversibility: The film of nonequilibrium states
If g ∈ C k+ℓ+2, ℓ ≥ 0, has constant scalar curvature, then the variation above can be chosen to have the same scalar curvature up to error terms which are o(r ℓ ) in a C k (B (p0 , r)) norm, for smal l r .
KIDs are non-generic
Other important matter ﬁelds that are compatible with homothety are a massless scalar ﬁeld and a scalar ﬁeld with an exponential potential.
Kinematic self-similar solutions in general relativity
We can also consider a massive scalar ﬁeld, where the mass of the scalar ﬁeld has dimension M .
Kinematic self-similar solutions in general relativity
These soft breaking terms consist of gaugino masses, scalar masses, and scalar trilinear couplings.
Bottom-Up Approach to Moduli Dynamics in Heavy Gravitino Scenario : Superpotential, Soft Terms and Sparticle Mass Spectrum
Visible-sector scalars also have supersymmetry-breaking holomorphic terms, including tri-linear and bi-linear ones in scalar ﬁelds (usually called A and B terms, respectively).
Bottom-Up Approach to Moduli Dynamics in Heavy Gravitino Scenario : Superpotential, Soft Terms and Sparticle Mass Spectrum
For k ≥ 0, denote by Hk the Hilbert space induced by smooth rapidly decreasing functions and the scalar product < ·, · >k deﬁned by < f , g >k = < f , (x2 − ∆)k g > , where < ·, · > stands for the usual scalar product in Rd .
Nonequilibrium Central Limit Theorem for a Tagged Particle in Symmetric Simple Exclusion
The change ∂F (r)/∂z being a scalar can then depend only on the two scalars ∇ · g and g 2 . A direct derivation of the differential equation for the free energy shows that these are the three terms required.
Directed polymers and Randomness
We also studied the case of q-stars in the framework of generalized scalar tensor theories, with ωBD a simple polynomial function of the BD scalar.
Q-stars in scalar-tensor gravitational theories
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