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?

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In most quantum field theories $^{†}$ , 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.

$^{†}$ Some quantum field theories have no Lagrangian formulation, but this doesn't provide a loophole for your problem.

posted about 5 years ago

5y ago

HDE 226868‭

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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?

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