In the article "The Lattice Theory of Quark Confinement", by Claudio Rebbi (Scientific American) there is a graphic representing the chromoelectric field. The caption reads:(adsbygoogle = window.adsbygoogle || []).push({});

"Chromoelectric field is a gauge field similar in principle to the electromagnetic field but more complicated mathematically. At every point on a lattice there are three arrows instead of one; they correspond to the color charges of a quark. Moreover, the color guage field affects not only the direction of each arrow but also its length. ..."

Are such lattice calculations considered classical or does one need to bring the full force of the quantized theory?

On a lattice can I assume we can let 2-dimensional arrows represent every "degree of freedom" of the Standard Model Lagrange Density?

If so, how many arrows at a point do we need to account for the "freedom" of both the matter fields and the force fields?

The color force seems to need three arrows, two arrows for the weak force, one arrow for the electric field, a non-interacting Dirac particle needs 4 arrows at each point in a space-time lattice for each Dirac particle?

Lots of arrows? If string theory turns out to be true how many arrows do we need to represent whats going on at a point in a space-time lattice?

Are there relationships among the various arrows which reduces their "freedom"?

If there is a lattice approximation of classical general relativity? Can we represent the physics of general relativity with some number of 2-dimensional arrows at each point in the space-time lattice? (yikes, now the space-time lattice is not fixed?)

Thanks for your thoughts.

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# Standard Model Lagrange Density, 2D vectors, Lattice Theory.

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