A particle that is formed entirely from ethereal, imaginary or neutral components can be difficult to characterize and distinguish from other phenomena. So if there are a lot of these elusive particles in a description then it may be more convenient to group them together and refer to them collectively as a **field**. For example we may vaguely refer to a set of leptonic quarks as an electromagnetic field, or a collection of gravitons as a gravitational field.

## Field Quanta

A **field quantum** is formed by quark-pairs that are out-of-phase anti-particles to each other.

They have no mass, charge, baryon number or lepton number. But they have distinct temperatures and momenta that vary by quark-type. Different sorts of fields are defined by different quark distributions.

Field quanta can be understood as parts or components of photons. Field quanta can move around between Newtonian particles by 'hitching a ride' on any passing photon.

Momentum is conserved. So if a Newtonian particle absorbs or emits a field quantum, then it experiences a force that is proportional to the momentum of the quantum.

The likelihood of an interaction involving the exchange of a field quantum is proportional to the temperature difference between particles. These interactions moderate extreme motions, scatter energy values and cause regression toward mean temperatures, i.e. dispersion. Thermodynamic equilibrium is obtained by field quanta moving about. For a specific case of using $\begin{align} \sf { q \overline{q} } \end{align}$ pairs to obtain thermodynamic viability, take a look at the difference between the core quarks and the coefficients of all quarks in the models of, for example, pions .

We use the symbol $\mathscr{F}$ to denote a field quantum. There are two possible arrangements for any given pair of quarks, that depend on the phase. E.g.

$ℱ \sf{(e)} \equiv$ | $\Huge{ \{ }$ | , | $\Huge{\} }$ |

$\overline{ℱ} \sf{(e)} \equiv$ | $\Huge{ \{ }$ | , | $\Huge{\} }$ |

These two quanta have their momenta pointed in opposite directions. So if one increases, then the other decreases the total momentum of any absorbing particle. Hence, the impressed force has two possibilites; like an attraction or a repulsion, or perhaps a push vs a pull.

These field quanta are components that are combined to make a general description of any physical force. They are used to define larger force-carrying bosons (photons, gravitons and weak quanta …) that then fit into space-time descriptions.

## Dark Quanta

- include pairs of down quarks because Ud is approximately zero

## Atomic Transition Forces

Here is a repertoire of little kicks and torques used to get hydrogen to jump from state to state. These field quanta are generically noted by $\mathscr{F}$. There are no electrochemical quarks in these fields. Energies are typically stated in micro electron-volts. The most important characteristic for classifying these fields is their helicity, $\delta_{z} \,$. The atomic quantum numbers $\, \ell$ and $s$ are also relevant. The letter $Ł$ notes a frequently used collection of quarks that is called the Lamb quantum.

Recall that the internal energy of quark $\sf{z}$ is noted by $U ^{\sf{z}}$. Then a conjugate difference $\; \Delta \hspace{-2px} U^{\sf{Z}}$, and a conjugate mean $\tilde{U}^{\sf{Z}}$, describe the relationship between quarks and anti-quarks

$\begin{align} \Delta \hspace{-2px} U^{\sf{Z}} \equiv \frac{U^{\sf{\overline{z}}} - \, U^{\sf{z}}}{2} \end{align}$ | $\begin{align} \tilde{U}^{\sf{Z}} \equiv \frac{U^{\sf{\overline{z}}} + \, U^{\sf{z}}}{2} \end{align}$ |

Usually we assume that the internal-energies of down-quarks are small enough to be completely negligible. Then we write $\Delta \hspace{-2px} U^{\sf{D}} \! =0$ and $\tilde{U}^{\sf{D}} \! =0$. But the conjugate mean for down quarks, as found from hydrogen observations, is $\; \tilde{U}^{\sf{D}}= -27$ (µeV). Also, we generally make an assumption of conjugate symmetry so that $\Delta \hspace{-2px} U^{\sf{Z}} \! =0$ and $\tilde{U}^{\sf{Z}} \! = U^{\sf{\overline{z}}} = U^{\sf{z}}$. But again, these assumptions are not good enough for hydrogen where the differences shown in the accompanying table provide a more accurate description of fine structure in the spectrum. The energy of $\mathscr{F}$ is also a function of its spin angular momentum quantum number, $s \,$. The constant of proportionality is $\; k_{\sf{spin}} = -91$ (µeV), so the dependence is slight. But for field quanta, quarks and anti-quarks are paired, mass and charge are always absent, and small effects are noticeable. Let $N$ note the quark coefficients of $\mathscr{F}$. Then the internal energy is obtained from a sum of these small terms

$\begin{align} U ( \mathscr{F} ) \; \equiv \; s k_{\sf{spin}} \; + \; N^{\sf{D}} \hspace{1px} \tilde{U}^{\sf{D}} \; + \; \sum_{\zeta =1}^{16} N^{\zeta} \Delta \hspace{-2px} U^{\zeta} \end{align}$

## Core Quarks

The quarks in any excited particle may be parsed into symmetric and anti-symmetric sets. The anti-symmetric $\begin{align} \sf { q \overline{q} } \end{align}$ pairs are viewed as a collection of field quanta, and so are called *field quarks*. The other quarks in the symmetric sets are called **core** quarks. These core quarks are the minimum required to identify a particle and account for its mass. Many quantum-numbers depend on $\Delta n$ not $n$. So for example the charge, baryon-number and lepton-number are all unchanged by any variation in the field of quark/anti-quark pairs. A particle's rest mass is also completely determined by its core quarks.

## Weak Quanta

## Photons

Field quanta may be combined to define a variety of photons that can fit into space-time descriptions.

## Gravitons

The $\sf{ \Gamma ^{\text{D}} }$ graviton carries the force of gravity in the same direction as all the other gravitons. But absorbing one increases the number of down seeds and so too the outer radius. The absorbing particle expands and cools.

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