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

Two quarks, no mass

no charge

no baryon or lepton number

We use the symbol $\mathscr{F}$ to denote a **field quantum** formed by quark-pairs that are out-of-phase anti-particles to each other.

two out-of-phase possibilities for each quark pair, one increases and one decreases the momentum of an absorbing particle, i.e. an attractive or repulive force can be associated with each momentum carrying field-quantum, $\mathscr{F}$ .

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

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

These field quanta are the smallest components that are combined to make a general description of any physical force.

These field quanta are combined into larger bosons that fit into our space-time descriptions; photons, gravitons and weak quanta …

## Photons

## Gravitons

## Weak Quanta

## Fields and Equilibrium

We can make a description of how particle P attains dynamic equilibrium by considering that P is surrounded by an enormous field of photons. Equilibrium is achieved through interactions between P and these photons. The field concept is vague enough so that we can assume there is some chance that any kind of photon will be absorbed or emitted. Then statistical constraints on these chances specify (temperature dependent) interactions with P. These interactions moderate extreme motions, scatter energy values and cause regression toward mean temperatures. Energy and momentum can also be shuffled around between P and other large particles.

More specifically let particle $\sf{P}$ be described by a historically ordered chain of events $\Psi$ and consider some pair of events $\sf{P}_{ \it{i}}$ and $\sf{P}_{ \it{f}}$ from the sequence

$\Psi ^{\sf{P}} = \left( \, \sf{P}_{1}, \sf{P}_{2}, \sf{P}_{3} \ \ldots \ \sf{P}_{ \it{i}} \ \ldots \ \sf{P}_{ \it{f}} \ \ldots \, \right)$

Let $\sf{P}_{ \it{i}}$ mark the absorption of $\sf{\gamma}$ a photon such that $\sf{P}_{ \it{i} \sf{\, -1}} +\sf{\gamma} \to \sf{P}_{ \it{i}}$. And let $\sf{P}_{ \it{f}}$ note the emission of $\sf{\gamma^{\prime}}$ a different photon $\sf{P}_{ \it{f}} \to \sf{P}_{ \it{f} \sf{\, +1}} + \sf{\gamma^{\prime}}$. The differing quark content of the two photons is drawn from the surrounding $\begin{align} \sf { q \overline{q} } \end{align}$ field such that

$\begin{align} \sf{P}_{ \it{f}} - \sf{P}_{ \it{i} } \ \ \leftrightarrow \ \ \frac{ \it{N}^{\, \sf{E}} }{2} \sf{e} \overline{\sf{e}} + \frac{ \it{N}^{\, \sf{M}} }{2} \sf{m} \overline{\sf{m}} + \ldots \end{align}$

Then the interaction, and the approach to equilibrium, is precisely specified by the seed coefficients $\ \it{N}^{\, \sf{E}}$, $\it{N}^{\, \sf{M}}$ etc. 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 .