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Qmechanic ♦
Qmechanic ♦
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Background

  • The standard model of particle physics is entirely determined by writing down its Lagrangian or, equivalently, writing down the corresponding system of PDEs.
  • Every set of PDEs has a corresponding set of "continuous symmetries" (essentially continuous changes of variables). The well-known (non-discrete) symmetries of the standard model are examples of these.
  • There are tools for computing all the symmetries of a given set of PDEs (or at least for generating constraining relationships between the symmetries). One source for these tools is Applications of Lie Groups to Partial Differential Equations by Peter J. Olver.

Question

Have the above-mentioned symmetry-finding techniques been applied to the standard model as a whole? Or even to part of it? In other words, do we know all of the symmetries of the standard model or some part of it? We obviously know some because the standard model was built to have them, but my question is whether the existence of other symmetries has been ruled out. Should the answer be affirmative, I would appreciate a reference to relevant literature.

Background

  • The standard model of particle physics is entirely determined by writing down its Lagrangian or, equivalently, writing down the corresponding system of PDEs.
  • Every set of PDEs has a corresponding set of "continuous symmetries" (essentially continuous changes of variables). The well-known (non-discrete) symmetries of the standard model are examples of these.
  • There are tools for computing all the symmetries of a given set of PDEs (or at least for generating constraining relationships between the symmetries). One source for these tools is Applications of Lie Groups to Partial Differential Equations by Peter J. Olver.

Question

Have the above-mentioned symmetry-finding techniques been applied to the standard model as a whole? Or even to part of it? In other words, do we know all of the symmetries of the standard model or some part of it? We obviously know some because the standard model was built to have them, but my question is whether the existence of other symmetries has been ruled out. Should the answer be affirmative, I would appreciate a reference to relevant literature.

Background

  • The standard model of particle physics is entirely determined by writing down its Lagrangian or, equivalently, writing down the corresponding system of PDEs.
  • Every set of PDEs has a corresponding set of "continuous symmetries" (essentially continuous changes of variables). The well-known (non-discrete) symmetries of the standard model are examples of these.
  • There are tools for computing all the symmetries of a given set of PDEs (or at least for generating constraining relationships between the symmetries). One source for these tools is Applications of Lie Groups to Partial Differential Equations by Peter J. Olver.

Question

Have the above-mentioned symmetry-finding techniques been applied to the standard model as a whole? Or even to part of it? In other words, do we know all of the symmetries of the standard model or some part of it? We obviously know some because the standard model was built to have them, but my question is whether the existence of other symmetries has been ruled out.

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William Wright
William Wright
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Have all the symmetries of the standard model of particle physics been found?

Background

  • The standard model of particle physics is entirely determined by writing down its Lagrangian or, equivalently, writing down the corresponding system of PDEs.
  • Every set of PDEs has a corresponding set of "continuous symmetries" (essentially continuous changes of variables). The well-known (non-discrete) symmetries of the standard model are examples of these.
  • There are tools for computing all the symmetries of a given set of PDEs (or at least for generating constraining relationships between the symmetries). One source for these tools is Applications of Lie Groups to Partial Differential Equations by Peter J. Olver.

Question

Have the above-mentioned symmetry-finding techniques been applied to the standard model as a whole? Or even to part of it? In other words, do we know all of the symmetries of the standard model or some part of it? We obviously know some because the standard model was built to have them, but my question is whether the existence of other symmetries has been ruled out. Should the answer be affirmative, I would appreciate a reference to relevant literature.