# Imaginary quantity

## Definitions

• Webster's Revised Unabridged Dictionary
• Imaginary quantity (Alg) an algebraic expression which involves the impossible operation of taking the square root of a negative quantity; as, √-9 a + b √-1.
• ***

## Usage

### In literature:

Of course it will be understood that the quantities given above are altogether imaginary.
"Personal Recollections of Birmingham and Birmingham Men" by E. Edwards
***

### In science:

This result is valid in the realization where ρf is a real quantity, i.e., the imaginary parts are not resummed in ρf .
The Twofold Way, a Short Disquisition of LEP Physics
The initial expression consists of the real quantities δ ab and f abc and the quantities (A3.1) and (A3.2), of which the ﬁrst is real and the second is imaginary; therefore, it is proportional to iN ′ , where N ′ is the number of fermion loops with an odd number of vertices.
Constructing the light-front QCD Hamiltonian
However, the lattice QCD had diﬃculties in accessing the dynamical quantities in the Minkowski space, because measurements on the lattice can only be carried out for discrete points in imaginary time.
Spectral Change of Hadrons and Chiral Symmetry
One concerns the relation between Euclidean or imaginary time quantities that one evaluates on the lattice and the real time information that one needs to describe various physical phenomena.
Theoretical Conference Summary
But what about the real (dispersive) part of the amplitudes ge and gm , corresponding to J P = 1−? These quantities are determined by deﬁnite dispersion integrals, from the corresponding imaginary parts - over the photon energy (and over the internal momenta of the N N π-system) from threshold to inﬁnity.
Considerations on rescattering effects for threshold photo- and electro-production of $\pi^0$ on deuteron
We ﬁnd that the imaginary parts of the simulated mean quantities for all numbers fermions and anyons are essentially less than their real parts.
Complex Diffusion Monte-Carlo method: tests by the simulations of 2D electron in magnetic field and 2D fermions-anyons in parabolic well
For the imaginary part there are problems with long-distance contributions from K → πγ γ . but the CP-violating quantities are often dominated by direct part.
QCD and Weak Interactions of Light Quarks
Let us observe that the conserved quantity which we obtain may be real even if c is pure imaginary.
Higher Conservation Law for the Multi-Centre Metrics
It is interesting to note that imaginary parts of g and h can induce imaginary values of proton magnetic and electric dipole moments 16 , respectively, which of course are CPT violating quantities.
Some Tests on CPT Invariance
The scale µ is the usual dimensional regularization scale and the quantity iǫ (ǫ > 0) represents an inﬁnitesimal imaginary part which ensures c ausality and, after the integration, determines the correct sign of the imaginary part of the logarithms and dilogarithms.
The NLO multileg working group: summary report
We therefore turn our attention to the v− i part, investigating which contours i ∼ 0 the quantity iǫδi ∼ iǫv+ the imaginary ǫ terms dictate for the integrals.
Perturbative Gravity and Gauge Theory Relations -- A Review
Such a motion is called a bounce* and is useful, for example, in describing vacuum decay.4 In an instanton we can avoid the one remaining source of imaginary quantities, the imaginary time t, by making a coordinate transformation to a real τ = t/i.
Euclidean Maxwell-Einstein Theory
These properties allow one to continue the Euclidean considered quantities into imaginary values of the coordinate τ 7→ it obtaining real functions of the Lorentzian time t.
A review on recent results of the $\zeta$-function regularization procedure in curved spacetime
Therefore, the imaginary (real) part of the ratio of these quantities, measures the sine (cosine) of the phase in Eq. (3).
The use of early data on B --> rho pi decays
Since as noted above, the imaginary part of this quantity determines the area of all unitarity triangles, it is no less fundamental than r and h.
Rare K decay: results and prospects
***