Groupprops:Guided tour for physicists
This article is a guided tour to Groupprops
This is a first-person article written by: Vipul
First-person articles give opinions of their authors, as long as these opinions are broadly endorsed by the wiki
This guided tour is for physics students, or physicists, who may be interested in group theory from the following viewpoints:
- To clarify, or revise, their knowledge of general group theory terms
- To find out whether groups of certain orders or satisfying certain conditions exist. This may be for finite groups or Lie groups
- To understand the linear representations of a particular group
- To understand topics that lie in the fringes of group theory, such as the theory of quantum groups
This wiki is primarily meant as a group theory information source and is thus not designed in a way that may be suitable for physicists. Thus, for instance, much of the header information, templates used, categorization, definition and other formatting, are designed from a group theory perspective. However, people interested in physics can also make good use of the wiki, and some suggestions on how to use this wiki are given below.
Checking out basic definitions and facts
From what I understand, a lot of physics uses mathematical language and results, but many of these results, may not be defined and explored to the same depth in the physics classroom, which is keener on getting ahead with the particular physical situation at hand. A backyard to check out definitions and proofs could be helpful. Definitional problems could arise in the following ways:
- Some definitions may be omitted in physics classrooms, because one is expected to have picked them up in lower-level math, even though they are not always a part of lower-level math. For instance, the notion of external direct product of groups is something at the periphery of a first course in algebra, and may not be covered by the instructor; however, direct products are used all the time in physics.
- Certain kinds of applications in physics/physical chemistry may involve a mathematical concept used only in a particular way, and thus, to simplify matters, they may give this narrower definition to avoid confusion. Thus, some physics texts may directly plunge into the definition of a Lie group without an explicit definition of group (this is an exaggerated example, of course). Some of them may restrict attention to nice objects which arise in physics and tacitly ignore certain extra assumptions that need to be placed to ensure that all objects are nice. This may create confusion when hopping between one part of the subject and the next, when what's nice gets changed. In such a situation, a mathematical reference point can be helpful.
- Sometimes there are niggly little mathematical lemmas or results that are used in physics texts (or that are quoted for reference and analogy) and the proofs of these are not supplied. Groupprops can be a convenient place to check out the proofs.
Currently not a good resources
The group theory wiki is currently far from a good resource for physicists. This is not surprising, since the editing and organization of the wiki has not had active large-scale involvement of people with a physics perspective. An improved physics perspective would at the least involve more survey articles about how ideas in group theory correlate with physics, both at the basic and advanced level. It may also result in a restructuring of articles.