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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 represe...
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#2: Post edited
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HDE 226868
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2020-06-02T20:39:04Z (almost 4 years ago)
Fixed formatting and changed link to Codidact post - we might have to do link editing manually for a lot of posts.
<p>In most quantum field theories<sup>1</sup>, 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 naïvely adding mass terms by something called a <em>gauge symmetry</em>. 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, <a href="https://worldbuilding.stackexchange.com/a/165984/627">el duderino wrote an excellent introduction on the Higgs field</a> in an answer to a different question, and <a href="https://www.theorie.physik.uni-muenchen.de/lsfrey/teaching/archiv/sose_09/rng/higgs_mechanism.pdf" rel="nofollow noreferrer">these notes</a> give a couple interesting examples of adding in the Higgs.</p><p>Why, then, won't your proposal work? Well, <a href="https://physics.stackexchange.com/a/129955/56299">there's no such thing as an "energy term"</a> 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.</p><hr><p><sup>1</sup>Some quantum field theories <a href="https://physics.stackexchange.com/a/3501/56299">have no Lagrangian formulation</a>, but this doesn't provide a loophole for your problem.</p>
- <p>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 <em>gauge symmetry</em>. 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, <a href="https://speculative-science.codidact.com/questions/259519#answer-259540">el duderino wrote an excellent introduction on the Higgs field</a> in an answer to a different question, and <a href="https://www.theorie.physik.uni-muenchen.de/lsfrey/teaching/archiv/sose_09/rng/higgs_mechanism.pdf" rel="nofollow noreferrer">these notes</a> give a couple interesting examples of adding in the Higgs.</p>
- <p>Why, then, won't your proposal work? Well, <a href="https://physics.stackexchange.com/a/129955/56299">there's no such thing as an "energy term"</a> 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.</p>
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- <p>$^{\dagger}$Some quantum field theories <a href="https://physics.stackexchange.com/a/3501/56299">have no Lagrangian formulation</a>, but this doesn't provide a loophole for your problem.</p>
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System
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2020-06-01T14:13:59Z (almost 4 years ago)
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