Mathematical term for physicist's "Lattice Theory"?

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Discussion Overview

The discussion revolves around the mathematical terminology related to "lattice theory" as used in physics, particularly in the context of lattice field theory. Participants explore the relationship between mathematical lattices and their application in physical theories, examining the additional structures that may be involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that while physicists refer to "lattice theory," it involves more than just the mathematical concept of a lattice, suggesting a need for a specific mathematical term that encompasses this additional structure.
  • Others provide links to articles on mathematical lattices, indicating that the term "lattice" is commonly used, but may not fully capture the complexity of the structures in physical theories.
  • One participant mentions that a mathematical lattice can be viewed as a group generated by edges between nodes, questioning if this aligns with the desired structure.
  • Another participant highlights the distinction between the physical concept of a "field" in lattice field theory and the mathematical notion of an algebraic field, emphasizing the differences in terminology between physics and pure mathematics.
  • There is a request for literature or articles that discuss the additional structures associated with lattice gauge theory.
  • Some participants express uncertainty about the specific structures being discussed and suggest that further expertise may be needed to clarify the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific mathematical term that corresponds to the structures in lattice field theory. There are multiple competing views regarding the relationship between mathematical lattices and their physical counterparts, indicating ongoing uncertainty and debate.

Contextual Notes

Participants acknowledge that the terminology used in physics may not align with that of pure mathematics, which could lead to confusion. The discussion reflects a lack of clarity regarding the additional structures present in lattice theories as applied in physics.

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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?
 
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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.
 
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Office_Shredder said:
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.
 
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.
 
Office_Shredder said:
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").
 
Could you provide some articles/literature, where such additional structure is studied?

Something to do with lattice gauge theory, mayhaps?
 
  • #10
nuuskur said:
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.
 
  • #11
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.
 

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