Physics

Free particle

Jovan Stosic October 24, 2022

In physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy varies. In classical physics, this means the particle is present in a “field-free” space. In quantum mechanics, it means the particle is in a region of uniform potential, usually set to zero in the region of interest since the potential can be arbitrarily set to zero at any point in space.

https://en.wikipedia.org/wiki/Free_particle

Gluon

Jovan Stosic September 21, 2022

There are eight remaining independent color states, which correspond to the “eight types” or “eight colors” of gluons. Because states can be mixed together as discussed above, there are many ways of presenting these states, which are known as the “color octet”. One commonly used list is:[8]{\displaystyle (r{\bar {b}}+b{\bar {r}})/{\sqrt {2}}}(r{\bar {b}}+b{\bar {r}})/{\sqrt {2}}      {\displaystyle -i(r{\bar {b}}-b{\bar {r}})/{\sqrt {2}}}-i(r{\bar {b}}-b{\bar {r}})/{\sqrt {2}}{\displaystyle (r{\bar {g}}+g{\bar {r}})/{\sqrt {2}}}(r{\bar {g}}+g{\bar {r}})/{\sqrt {2}}{\displaystyle -i(r{\bar {g}}-g{\bar {r}})/{\sqrt {2}}}-i(r{\bar {g}}-g{\bar {r}})/{\sqrt {2}}{\displaystyle (b{\bar {g}}+g{\bar {b}})/{\sqrt {2}}}(b{\bar {g}}+g{\bar {b}})/{\sqrt {2}}{\displaystyle -i(b{\bar {g}}-g{\bar {b}})/{\sqrt {2}}}-i(b{\bar {g}}-g{\bar {b}})/{\sqrt {2}}{\displaystyle (r{\bar {r}}-b{\bar {b}})/{\sqrt {2}}}(r{\bar {r}}-b{\bar {b}})/{\sqrt {2}}{\displaystyle (r{\bar {r}}+b{\bar {b}}-2g{\bar {g}})/{\sqrt {6}}.}(r{\bar {r}}+b{\bar {b}}-2g{\bar {g}})/{\sqrt {6}}.

These are equivalent to the Gell-Mann matrices. The critical feature of these particular eight states is that they are linearly independent, and also independent of the singlet state, hence 32 − 1 or 23. There is no way to add any combination of these states to produce any other, and it is also impossible to add them to make rr, gg, or bb[9] the forbidden singlet state. There are many other possible choices, but all are mathematically equivalent, at least equally complicated, and give the same physical results.

https://en.wikipedia.org/wiki/Gluon#:~:text=A%20gluon%20(%2F%CB%88%C9%A1l,such%20as%20protons%20and%20neutrons.