Proca's equations were known to Wolfgang Pauli who mentioned the equations in his Nobel address, and they were also known to Yukawa, Wentzel, Taketani, Sakata, Kemmer, Heitler, and Fröhlich who appreciated the content of Proca's equations for developing a theory of the atomic nuclei in Nuclear Physics.

Yukawa also worked on the theory of K-capture, in which a low energy electron is absorbed by the nucleus, after its initial prediction by G. C. Wick.

The screened 1 / r function is often encountered in physics as a screened Coulomb potential, also called a " Yukawa potential ".

In particle physics, a Yukawa potential ( also called a screened Coulomb potential ) is a potential of the form

The Yukawa interaction is also used in the Standard Model to describe the coupling between the Higgs field and massless quark and lepton fields ( i. e., the fundamental fermion particles ).

It's also possible to have a Yukawa interaction between a scalar and a Majorana field.

Yukawa is a Japanese surname, but is also applied to proper nouns.

* In 2000, solo violinist Diana Yukawa recorded " Sukiyaki " on her bestselling debut album ( known as Elegy in the UK and La Campanella in Japan ).

Figure 1: A comparison of Yukawa potentials where g = 1 and with various values for m.

Yukawa called his carrier particle the meson, from mesos, the Greek word for intermediate, because its predicted mass was between that of the electron and that of the proton, which has about 1, 836 times the mass of the electron.

A detailed presentation of the Higgs mechanism is given in the article on the Yukawa interaction, illustrating how it further gives mass to fermions.

Yukawa couplings are not constants and their properties change depending on the energy scale at which they are measured, this is known as running of the constants.

The solution to both these problems comes from the Higgs mechanism, which involves scalar fields ( the number of which depend on the exact form of Higgs mechanism ) which ( to give the briefest possible description ) are " absorbed " by the massive bosons as degrees of freedom, and which couple to the fermions via Yukawa coupling to create what looks like mass terms.

The strong interactions were then ( incorrectly ) understood in the mid-1950s, to be mediated by the pi-mesons, the particles predicted by Hideki Yukawa in 1935, based on his profound reflections concerning the reciprocal connection between the mass of any force-mediating particle and the range of the force it mediates.

Another kind of fifth force, which arises in Kaluza-Klein theory, where the universe has extra dimensions, or in supergravity or string theory is the Yukawa force, which is transmitted by a light scalar field ( i. e. a scalar field with a long Compton wavelength, which determines the range ).

Figure 2: A " long-range " comparison of Yukawa and Coulomb potentials ' strengths where g = 1.

where is the color gauge coupling ( which is a function of and associated with asymptotic freedom ) and is the Yukawa coupling.

This length scale would be the distance where a Yukawa force is mediated by the weak vector bosons.

where are 3 × 3 matrices of Yukawa couplings, with the ij term giving the coupling of the generations i and j.

Yukawa had originally named his particle the " mesotron ", but he was corrected by the physicist Werner Heisenberg ( whose father was a professor of Greek at the University of Munich ).

Among the dead are singer Kyu Sakamoto and the father of violinist Diana Yukawa.

* three from Japan ( Iwao Ogawa, Shinichiro Tomonaga, Hideki Yukawa )

* Yukawa Institute for Theoretical Physics, a research institute in the field of theoretical physics, attached to Kyoto University in Japan

* Yukawa Station, a train station in Nachikatsuura, Higashimuro District, Wakayama Prefecture, Japan

The easiest way to understand that the Yukawa potential is associated with a massive field is by examining its Fourier transform.

The Yukawa interaction couples the fermion field to the meson field with the coupling term

An obvious possibility is some kind of " Yukawa coupling " ( see below ) between the fermion field ψ and the Higgs field Φ, with unknown couplings ', which after symmetry-breaking ( more precisely: after expansion of the Lagrange density around a suitable ground state ) again results in the original mass terms, which are now, however ( i. e. by introduction of the Higgs field ) written in a gauge-invariant way.

This equation describes how the Yukawa coupling changes with energy scale.

If two fermions interact through a Yukawa interaction with Yukawa particle mass, the potential between the two particles, known as the Yukawa potential, will be:

In fact, the Yukawa interaction involving a scalar and a Dirac spinor can be thought of as a Yukawa interaction involving a scalar with two Majorana spinors of the same mass.

may contain a self interaction or interaction with other fields, like a Yukawa interaction.

In particular, since has weak isospin ½ like the Higgs field H, and χ has weak isospin 0, the mass parameter M can be generated from Yukawa interactions with the Higgs field,

But within the standard model, the right-handed neutrino does not exist, so even with a Yukawa coupling neutrinos remain massless.

From theoretical considerations, Hideki Yukawa in 1934 predicted the existence and the approximate mass of the " meson " as the carrier of the nuclear force that holds atomic nuclei together.

Following the discovery of the pion, Yukawa was awarded the 1949 Nobel Prize in Physics for his predictions.

In 1935 Hideki Yukawa proposed the first significant theory of the strong force to explain how the nucleus holds together.

In the Yukawa interaction a virtual particle, later called a meson, mediated a force between all nucleons, including protons and neutrons.

However, the nuclear force acts only over relatively short ranges ( a few nucleon diameters ), since it follows an exponentially decaying Yukawa potential which makes it insignificant at longer distances.

* January 23 – Hideki Yukawa, Japanese physicist, Nobel Prize laureate ( d. 1981 )

* September 8 – Hideki Yukawa, Japanese physicist, Nobel Prize laureate ( b. 1907 )

; Hideki Yukawa ( member of the Japanese academy of Sciences, director of the Institute of Basic Research at the University of Kyoto ): for outstanding merits in the development of theoretical physics.

* In the Standard Model of elementary particles, a scalar Higgs field is used to give the leptons and massive vector bosons their mass, via a combination of the Yukawa interaction and the spontaneous symmetry breaking.

Essentially, they are looking for signs that the Yukawa interaction is kicking in at a certain length.

Later important contributors to twentieth century mathematical physics include: Satyendra Nath Bose, Julian Schwinger, Sin-Itiro Tomonaga, Richard Feynman, Freeman Dyson, Hideki Yukawa, Roger Penrose, Stephen Hawking, Edward Witten, and Rudolf Haag.

Yukawa was born in Tokyo and grew up in Kyoto.

Yukawa became the first chairman of Yukawa Institute for Theoretical Physics in 1953.

Solo violinist Diana Yukawa ( ダイアナ湯川 ) is a relative of Hideki Yukawa.

Note that this potential has the same form as the Yukawa potential.

Pions were postulated by Hideki Yukawa as mediators of the residual strong force, which binds the nucleus together.