Is there any relation between weak and strong fields, similar to electric and magnetic fields?

Question

Is it possible to unify the strong, weak, electric and magnetic field just by Maxwellian type equations? (Maxwell by adding a small change - unified electric and magnetic field, then Einstein's equations - use it to create special and general theory of relativity, now maybe all we need is a little more change to unify all fields,) When $B$ and $E$ are known magnetic and electric fields, then $W$ and $S$ are weak and strong fields, what are their units?

This post imported from StackExchange Physics at 2014-03-24 03:48 (UCT), posted by SE-user unifiedator

Comments

I dont understand your question, Perhaps you are referring to the standard model.

This post imported from StackExchange Physics at 2014-03-24 03:48 (UCT), posted by SE-user Prathyush

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You've got some catching up to do! Look up "Yang-Mills Theory". From Wiki: Yang–Mills theory seeks to describe the behavior of elementary particles using these non-Abelian Lie groups and is at the core of the unification of the Weak and Electromagnetic force (i.e. U(1) × SU(2)) as well as Quantum Chromodynamics, the theory of the Strong force (based on SU(3)). Thus it forms the basis of our current understanding of particle physics, the Standard Model.

This post imported from StackExchange Physics at 2014-03-24 03:48 (UCT), posted by SE-user Alfred Centauri

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What do you mean by "strong field" and "weak field" ...? This question looks very confused to me.

This post imported from StackExchange Physics at 2014-03-24 03:48 (UCT), posted by SE-user Dilaton

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What Alfred Centauri said. The weak and strong theories are generalisations of ordinary electromagnetism. So for the strong force their are chromo-electric and chromo-magnetic fields (actually eight of each) and for the weak force there are weak-electric and weak-magnetic fields (actually three of each). These follow a close analogy to ordinary E&M (although the theories are much more complicated). It is less common to work with the electric & magnetic fields than the vector potentials for technical reasons, but they exist.

This post imported from StackExchange Physics at 2014-03-24 03:48 (UCT), posted by SE-user Michael Brown

Answer 1

I'm guessing at what you're asking - ignore this answer if I've misunderstood you.

Maxwell's equations describe the classical behaviour of electromagnetism. They can only do this because the EM forces are long range so at macroscopic distances they behave classically. By contrast, the weak and strong forces are short range and cease to act over anything like the classical limit of distance. There is no classical approximation to describe the weak and strong forces, so there is no analogy to Maxwell's equation.

Above the electroweak transition the electroweak force will become long range. Whether there is some classical limit in the spirit of the Maxwell's equations is a good question and I don't know the answer. I would guess that there is no such limit for the strong force even about the EW transition because the force will still be confined.

This post imported from StackExchange Physics at 2014-03-24 03:48 (UCT), posted by SE-user John Rennie

Comments

At high enough temperature and energy density, the strong force stops confining. This plays a role in the standard stories of the early universe.

This post imported from StackExchange Physics at 2014-03-24 03:48 (UCT), posted by SE-user user1504

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Ah yes, as in the quark gluon plasma. I bet there's still no (useful) classic long distance description though.

This post imported from StackExchange Physics at 2014-03-24 03:48 (UCT), posted by SE-user John Rennie

Answer 2

Depends on what you mean by "unify" If you just mean "describe", then it's simple. We have the Standard Model with it's exceedingly simple Lagrangian Density formed by adding Yang - Mills & Dirac fields to Klein - Gordon fields.

$${\mathcal L} = - {1 \over 4}{F^{\mu\nu }}{F_{\mu \nu }} + i\overline \psi \not\nabla \psi + \overline \psi \phi \psi + \mbox{h.c.} + {\left| {\nabla \phi } \right|^2} - V(\phi )$$

Here, it is easy to identify the Yang Mills field for gluons et al, the Dirac Fields for the quwarks et al, the Klein - Gordon for the Higgs, a scalar field.

If you mean "unify" in the sense of grand unification and such, then it's a bit more complicated.

Grand Unification

Refers to the unification (meaning: having a simple group as the gauge group, as opposed to the Standard Model whose gauge group is $SU(3)\times SU(2)\times U(1)$; yet describe the Standard Model, since it's experimentally verified to a pretty high degree).

Examples include

• "$SU(5)$ GUT" Gauge group $SU(5)$

• "$SO(10)$ GUT", or $\operatorname{Spin}(10)$ GUT Gauge group $\mathrm{Spin(10)}$

• $E(6)$ GUT Gauge group $E(6)$.

Theories of Everything

Better than GUTs; unify (quantised) gravity too. Examples include string-theory.