# Algebra in Applied Math

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• Aug 12th 2007, 07:15 AM
DivideBy0
When you are self-studying, do you just pick a topic/book which takes your fancy, or is there a sorta list you like to follow?
• Aug 13th 2007, 05:16 PM
Rebesques
Quote:

do you just pick a topic/book which takes your fancy, or is there a sorta list you like to follow?

Let's just say there are some books that are a must!
• Aug 13th 2007, 07:51 PM
ThePerfectHacker
How is Field Theory used in Quatum Field Theory? What possible connection do they have except for having the same name. Can someone give an example.
• Aug 14th 2007, 06:12 AM
topsquark
Quote:

Originally Posted by ThePerfectHacker
How is Field Theory used in Quatum Field Theory? What possible connection do they have except for having the same name. Can someone give an example.

QFT typically works with groups rather than fields. A "field" in QFT is simply a name we (Physicists) give to something we don't know how to otherwise describe. A field appears to permeate all space at all times. Fields have energy and momentum, interact with other fields, and obey certain rigid physical laws. The structure of these laws is more or less the same, the differences being mainly the strength of the interactions and the symmetries of the group structure that apply to the field. Classical field theory started with the description of the electric field, then of the magnetic field. The concept explained how a charged particle could react to the presence of another particle without touching: action at a distance. A "quantum" field is of a similar nature.

That being said, the similarity of the terms is basically a coincidence. However I have heard of some of the more Mathematical treatments of Feynman diagrams referring to things like "vertex algebras" which my poor understanding takes to be the particular algebra that the field variables obey in specific Feynman diagrams. Does the Mathematics of the field variables create a (Mathematically defined) field? I've never heard of such, but then I can't follow the Math at that level to be able to tell you for sure.

-Dan
• Aug 23rd 2007, 02:49 AM
albi
Algebra and physics
As it was noted before group theory is used in theoretical physics.

Lie groups and algebras are used in classical electrodynamics, quantum electrodynamics and relativity theory (Lorentz group). Group theory is also used in solid state physics for investigating symmetries of crystals.

Algebra can also have more practical application. I heard it is used in cryptography and signal processing (quaternions).

I have found also that link: Group Theory and Physics, maybe it will interest you. I don't have time for reading that because I'm at work recenty ;)
• Aug 23rd 2007, 04:38 AM
topsquark
Quote:

Originally Posted by albi
Lie groups and algebras are used in classical electrodynamics, quantum electrodynamics and relativity theory (Lorentz group).

Actually, it's the Poincare group that's used in relativity (as it is applied to QFT, anyway.)

-Dan
• Aug 23rd 2007, 05:09 AM
albi
Quote:

Originally Posted by topsquark
Actually, it's the Poincare group that's used in relativity (as it is applied to QFT, anyway.)

-Dan

Lorentz group is subgroup of Poincare group, so I didn't made an error ;)

Nevertheless my knowlege in this matter is not deep :P
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