How Are Math and Science Interconnected?

[Matterwave]

How are they related? Can you derive one from another, or are they separate fields of study?

 

[waht]

QED, and QCD and QFD are theories based on QFT.

 

[diazona]

QFT = "Quantum Field Theory" sort of a general term for any theory which involves a field (something defined at every point in space and time) that is acted on with quantum operators.
QED = "Quantum Electrodynamics" which is one example of a quantum field theory, where the fields are the electric and magnetic fields that arise from electrical charges and currents.
QCD = "Quantum Chromodynamics" which is another example of a quantum field theory, where the field comes from the "color charges" on quarks (and gluons I suppose).

 

[malawi_glenn]

One can say something about the relation QED vs. QCD, QED is based on the invariance of a local phase transformation of the fields according to the group U(1). One starts with a free lagrangian of fermions (no interactions) and by demanding this local invariance, one has to include interactions. This is called a Gauge Theory, and QCD is also a gauge theory, but with SU(3) group for the local phase transformations.

In order to stody QED and QCD, one has to study QFT first. And very very often, QED is assumed to be know in quite detail before you attempt to learn QCD. You can think of QFT as the analogy with the Schrödinger equation in QM. In Schrödinger equation, the potential is unknown, and you can use potentials to fit a known phenomenon. Examples: The Hydrogen Atom, use a Coulomb potential. For semiconductors, use a step potential. Etc. In Quantum Field theory, you do in a similar way, you include the fields, fermions and/or boson fields, and interaction terms, and then you start to calculate observables and see if they fit with experiments. Also, one would like to have underlying symmetries, like these local phase transformations.

 

[Matterwave]

Ok, thanks. :)