Mathematical term for physicist's "Lattice Theory"?

[Stephen Tashi]

TL;DR

Lattices are studied in mathematics. What physicists call a "lattice theory" uses the mathematical object that is a lattice, but involves other things, such as associating elements of a group with the links between nodes of a lattice. Is there a mathematical term for the study of lattices with this additional structure?

Lattices are studied in mathematics. What physicists call a "lattice theory" uses the mathematical object that is a lattice, but it involves other things, such as associating elements of a group with the links between nodes of a lattice. Is there a mathematical term for lattices with this additional structure?

 

[jedishrfu]

Best I can find is this wiki article. However, it may lead you to what you're looking for until @fresh_42 replies.

https://en.wikipedia.org/wiki/Lattice_(order)

 

[Office_Shredder]

This sounds more like this lattice to me

https://en.m.wikipedia.org/wiki/Lattice_(group)

 

[Stephen Tashi]

Best I can find is this wiki article. However, it may lead you to what you're looking for until @fresh_42 replies.

https://en.wikipedia.org/wiki/Lattice_(order)

I want the math name for the structures in the physical theory: https://en.wikipedia.org/wiki/Lattice_field_theory

 

[Office_Shredder]

Just click the links in your article telling you what the lattices are and it will take you to the link I posted after two clicks.

The mathematical term for it is a lattice.

 

[Stephen Tashi]

Just click the links in your article telling you what the lattices are and it will take you to the link I posted after two clicks.

The mathematical term for it is a lattice.

Yes, but a mathematical "lattice" does not have all the structure associated with the physical theory.

 

[Office_Shredder]

A mathematical lattice is a group, which is generated by the edges between adjacent nodes. Isn't that what you wanted? Maybe I don't understand the structure.

 

[Stephen Tashi]

A mathematical lattice is a group, which is generated by the edges between adjacent nodes. Isn't that what you wanted? Maybe I don't understand the structure.

Apparently the physical concept of a "lattice field theory" includes the concept of a physical "field" (as in "force field" etc. as opposed to the mathematical concept of an algebraic "field").

 

[nuuskur]

Could you provide some articles/literature, where such additional structure is studied?

Something to do with lattice gauge theory, mayhaps?

 

[Stephen Tashi]

Could you provide some articles/literature, where such additional structure is studied?

I'm not familiar with the physics literature. It's a vocabulary question. My curiosity is motivated only by seeing the terminology "lattice theory" used in posts about physics on the forum. Physics terminology often doesn't match the terminology of pure mathematics. For example, a "vector field" in physics isn't identical to a "vector space" or an (algebraic) field in mathematics.

 

[Office_Shredder]

I understand now. Yeah it seems like someone needs to describe the structure you are talking about or an expert needs to come to this thread. I think the special stuff is not what you said in your first post, unless I am missing something.

You might have more luck asking this in the physics part of the forum.