Could there be something like the Higgs field which gives particles their energy in a similar way to how the Higgs boson gives particles their mass?
First of all, in no way do I have advanced knowledge of particle physics, quantum mechanics, or any other necessary scientific concept for a full understanding of this question. Secondly, this is purely hypothetical; I am a writer looking to explore fictional concepts that are guided by science, not strictly within its realm.
Could there be something like the Higgs field which gives particles their energy in a similar way to how the Higgs boson gives particles their mass? What conditions would there need to be for the existence of this field? Could it exist without changing existing, fundamental laws? Keep in mind that, as it's fiction, new processes can exist to allow it. I understand that the Higgs boson does not literally give particles mass; i.e: there aren't Higgs bosons clustered around particles and making them massive.
I'm guessing there's something fundamentally wrong with this question (meaning my understanding of energy and mass) that makes it unanswerable or difficult to answer directly. If you can find a way around it, hats off to you! And thanks very much to anyone who answers at all. Again, I really have no idea what I'm talking about, so feel free to brush the question off as complete nonsense.
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In most quantum field theories$^{\dagger}$, we have a quantity called the Lagrangian, from which we can derive information about the behavior of our system. It consists of a number of terms representing different quantum fields. Now, we are mathematically forbidden from naively adding mass terms by something called a gauge symmetry. However, it turns out that we can add in a particular type of quantum field that breaks that symmetry and implicitly contains the mass terms we need. This field is the Higgs field. Though a more detailed discussion of this is beyond our scope here, el duderino wrote an excellent introduction on the Higgs field in an answer to a different question, and these notes give a couple interesting examples of adding in the Higgs.
Why, then, won't your proposal work? Well, there's no such thing as an "energy term" in the Lagrangian. It's not a property associated with a quantum field; rather, it's a property of each particle associated with that field. Therefore, it doesn't really make sense - mathematically or physically - to talk about energy terms or an energy analog of the Higgs.
$^{\dagger}$Some quantum field theories have no Lagrangian formulation, but this doesn't provide a loophole for your problem.
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