Mathematical term for physicist's "Lattice Theory"?

In summary, the discussion revolved around the different definitions and structures of lattices in mathematics and physics. It was mentioned that physicists use a "lattice theory" that involves associating elements of a group with the links between nodes of a lattice. However, when looking for a mathematical term for this additional structure, the best resource found was a Wikipedia article on lattices with order and group structures. The conversation also touched on the concept of "lattice field theory" and the differences in terminology between physics and pure mathematics. Ultimately, it was suggested to ask for more information in the physics part of the forum.
  • #1
Stephen Tashi
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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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  • #5
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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  • #6
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.
 
  • #7
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.
 
  • #8
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").
 
  • #9
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.
 

1. What is "Lattice Theory" in physics?

Lattice Theory is a mathematical framework used to study the behavior of physical systems that are made up of discrete, regularly repeating units. It is often used to model the behavior of crystals, magnets, and other physical systems.

2. How is "Lattice Theory" used in physics?

Lattice Theory is used to study the properties of physical systems that have a regular, repeating structure. It allows physicists to make predictions about the behavior of these systems and to understand how they respond to external forces.

3. What are the key concepts in "Lattice Theory"?

The key concepts in Lattice Theory include lattice structures, lattice points, and lattice energy. Lattice structures refer to the regular, repeating arrangement of particles in a physical system. Lattice points are the points where particles are located in the lattice. Lattice energy is the energy associated with the arrangement of particles in the lattice.

4. How does "Lattice Theory" relate to other mathematical concepts in physics?

Lattice Theory is closely related to other mathematical concepts in physics, such as group theory and symmetry. It is also used in statistical mechanics and quantum field theory to study the properties of physical systems at the atomic and subatomic level.

5. What are some real-world applications of "Lattice Theory"?

Lattice Theory has many real-world applications, including the study of crystal structures in materials science, the behavior of magnetic materials, and the properties of polymers. It is also used in fields such as condensed matter physics, solid state physics, and quantum mechanics.

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