The Generalized Capabilities of the Standard Model Lagrangian?

[JohnH]

If the standard model Lagrangian were generalized into what might be called "core capabilities" what would those capabilities be? For example, there are a lot of varying matrices involved in the standard model Lagrangian and we can generalize all of them as the "core capability" of matrix multiplication or, as another example, it has potentials that scale in varying ways with varying relative strengths. It would help me get a better picture of what's going on if I could see the standard model Lagrangian in this generalized form of a "list of things that are happening."

 

[vanhees71]

I've no clue, what "core capability" is. The Lagrangian is not "list of things that are happening" but a compact description of the dynamics of the fields described by the action principle.

 

[JohnH]

Our universe is mostly described by the standard model Lagrangian, but it might be useful to understanding physics to understand the L_sm in a more generalized way. So imagine there are other universes like ours except maybe the relative strengths of forces are different. Perhaps the various masses of particles on their standard model vary. In comparing these universes, one would naturally wonder what is fundamentally the same about them. And all that is aside from the point but in an analgous way, we might look at all the different particles in the standard model, and ask, what about them is the same? If there were an equation that could describe any particle in our universe, what categories of information would that equation need to have?

 

[vanhees71]

As I see it, there is some fundamental basis the SM is built on, and that's the spacetime structure of special relativity (Minkowski space) implying that the quantum theory should be constructed from the unitary (ray) representations of the proper orthochronous Poincare group. Then in practice it has turned out that the (so far) only successful formulation comes from local quantum field theory formulations, i.e., leading to the usual notion of massive and massless fields transforming locally under the Poincare group and then being reduced to the unitary irreducible pieces, each defining a fundamental field/particle. This particularly implies that massless fields/particles with spin $s \geq 1$ are necessarily gauge fields.

The "rest" of the standard model, which is considering the question, what's "the matter content of the universe" then is based on finding the gauge groups and their representations leading to consistent local QFTs describing the observations, and that has been found by an interesting interplay between theory and experiment, and it's very likely not to be finished since the SM most probably does not provide the complete set of fields/particles needed to describe all observations (in terms of the cosmological standard model what is the "dark matter" made of needed to get the amount of "clumping" to form the observed inhomogeneities like the galaxies, galaxy clusters, and so on, as well as an understanding of why the cosmological constant/dark energy density takes the small value it does).

 

[JohnH]

Okay, so simply put, everything is Minkowski spacetime and mass, and ultimately all information--energy, force, quantum spin etc.--can all be boiled down to aspects of those two things. Is this an accurate simplification?

 

[vanhees71]

That's somewhat right as long as you can neglect the gravitational interaction, for which you need general relativity. Even then you need a bit more, i.e., the consideration of the symmetries of Minkowski space and the experiments telling you, how Nature realizes them ;-).

 

[JohnH]

Thank you for the replies.