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The standard model describes the particle's initial zoo into a smaller set. If I am not wrong quarks were proposed as a solution even before being detected. Is there any reason why we could not describe all the particles in the standard model as coming from a still smaller set? (ideally being described by a single generation of particles). Is there any obvious reason from group theory (or something else) that forbids this?

Note: I am not asking about experimental evidence, but rather, on symmetries and lie algebras, which I just started learning, regardless of if it will ever be possible to reach the energies to test it.

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Yes, for example, combining the electroweak and strong interactions as a symmetry-broken phase of a simple gauge theory is the basic idea of Grand Unified Theories (GUT). There are many proposed gauge groups that have some of the properties needed to recover the Standard Model (SM) when their symmetry is broken in a certain way. Even though it is not known as a fact that the SM arises from the broken symmetry of a GUT, there is no known reason it can't be the case, and indeed many researchers actively work on gauge unification.

Further, in supersymmetric (SUSY) field theories, gauge bosons and fermions are all modelled as states of a single type of field. Work on placing the SM in this setting is called the Minimally Supersymmetric Standard Model. Further still, gravitation can be added into the mix with supergravity theories, which arise from the low-energy behaviour of superstring theories.

Sam Playle
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