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Fixed some typos.
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Moguntius
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Two things here:

1.) When you are constructing "gravity" (whether it be GR, or Einstein-Cartan theory, or any extension that may include torsion but not non-metricity) and want to include spinor/fermionic fields it is advisable to pass to the double cover of the Poincaré group, i.e. the "Poincaré-Pin-group" or whatever you want to call it, that is the semi-direct product of the translations and the Pin group of the signature with which you are working.(In fact it suffices to use the connected component of the identity of the Pin group (so $SL(2, \mathbb{C})$ when you are working in 1+3 dimensions) because that is sufficient for gauge theories as all other components can be "reached" by multiplying with a "constant" group element).

2.) If you want to reproduce "ordinary" GR rather than starting with gauging the whole Poincaré-Pin-group and then "artificially" imposing the condition for the torsion to vanish you can simply start with the orthochronous Spin group (or the proper, orthochronous Lorentz group ofif you do not want/need to pass to the double cover) and then you will never find a connexion with torsion as a solution of your field equations.

As to answer your question: While you are correct that neither gravity (in the sense of GR being quantised) nor the standard model of particle physics are UV-complete, there is a difference between them: the standard model of particle physics is perturbatively renormalisable while gravity is not$^1$. Furthermore, I suspect that the expected corrections to say scattering angles one would receive by adding a form of quantised gravity are negligible for the energies at which we can probe physics at the moment.


$^1$ That is at first glance. There are some people that think that gravity might by asymptotically safe and therefore one would only need to fix a finite amount of couplings to "determine" how gravity works at high energies. While there is some evidence that this might be true for GR it has thus far not been rigourously proven.

Two things here:

1.) When you are constructing "gravity" (whether it be GR, or Einstein-Cartan theory, or any extension that may include torsion but not non-metricity) and want to include spinor/fermionic fields it is advisable to pass to the double cover of the Poincaré group, i.e. the "Poincaré-Pin-group" or whatever you want to call it, that is the semi-direct product of the translations and the Pin group of the signature with which you are working.(In fact it suffices to use the connected component of the identity of the Pin group (so $SL(2, \mathbb{C})$ when you are working in 1+3 dimensions) because that is sufficient for gauge theories as all other components can be "reached" by multiplying with a "constant" group element).

2.) If you want to reproduce "ordinary" GR rather than starting with gauging the whole Poincaré and then "artificially" imposing the condition for the torsion to vanish you can simply start with the orthochronous Spin group (or the proper, orthochronous Lorentz group of you do not want/need to pass to the double cover) and then you will never find a connexion with torsion as a solution of your field equations.

As to answer your question: While you are correct that neither gravity (in the sense of GR being quantised) nor the standard model of particle physics are UV-complete, there is a difference between them: the standard model of particle physics is perturbatively renormalisable while gravity is not$^1$. Furthermore, I suspect that the expected corrections to say scattering angles one would receive by adding a form of quantised gravity are negligible for the energies at which we can probe physics at the moment.


$^1$ That is at first glance. There are some people that think that gravity might by asymptotically safe and therefore one would only need to fix a finite amount of couplings to "determine" how gravity works at high energies. While there is some evidence that this might be true for GR it has thus far not been rigourously proven.

Two things here:

1.) When you are constructing "gravity" (whether it be GR, or Einstein-Cartan theory, or any extension that may include torsion but not non-metricity) and want to include spinor/fermionic fields it is advisable to pass to the double cover of the Poincaré group, i.e. the "Poincaré-Pin-group" or whatever you want to call it, that is the semi-direct product of the translations and the Pin group of the signature with which you are working.(In fact it suffices to use the connected component of the identity of the Pin group (so $SL(2, \mathbb{C})$ when you are working in 1+3 dimensions) because that is sufficient for gauge theories as all other components can be "reached" by multiplying with a "constant" group element).

2.) If you want to reproduce "ordinary" GR rather than starting with gauging the whole Poincaré-Pin-group and then "artificially" imposing the condition for the torsion to vanish you can simply start with the orthochronous Spin group (or the proper, orthochronous Lorentz group if you do not want/need to pass to the double cover) and then you will never find a connexion with torsion as a solution of your field equations.

As to answer your question: While you are correct that neither gravity (in the sense of GR being quantised) nor the standard model of particle physics are UV-complete, there is a difference between them: the standard model of particle physics is perturbatively renormalisable while gravity is not$^1$. Furthermore, I suspect that the expected corrections to say scattering angles one would receive by adding a form of quantised gravity are negligible for the energies at which we can probe physics at the moment.


$^1$ That is at first glance. There are some people that think that gravity might by asymptotically safe and therefore one would only need to fix a finite amount of couplings to "determine" how gravity works at high energies. While there is some evidence that this might be true for GR it has thus far not been rigourously proven.

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Moguntius
  • 357
  • 1
  • 10

Two things here:

1.) When you are constructing "gravity" (whether it be GR, or Einstein-Cartan theory, or any extension that may include torsion but not non-metricity) and want to include spinor/fermionic fields it is advisable to pass to the double cover of the Poincaré group, i.e. the "Poincaré-Pin-group" or whatever you want to call it, that is the semi-direct product of the translations and the Pin group of the signature with which you are working.(In fact it suffices to use the connected component of the identity of the Pin group (so $SL(2, \mathbb{C})$ when you are working in 1+3 dimensions) because that is sufficient for gauge theories as all other components can be "reached" by multiplying with a "constant" group element).

2.) If you want to reproduce "ordinary" GR rather than starting with gauging the whole Poincaré and then "artificially" imposing the condition for the torsion to vanish you can simply start with the orthochronous Spin group (or the proper, orthochronous Lorentz group of you do not want/need to pass to the double cover) and then you will never find a connexion with torsion as a solution of your field equations.

As to answer your question: While you are correct that neither gravity (in the sense of GR being quantised) nor the standard model of particle physics are UV-complete, there is a difference between them: the standard model of particle physics is perturbatively renormalisable while gravity is not$^1$. Furthermore, I suspect that the expected corrections to say scattering angles one would receive by adding a form of quantised gravity are negligible for the energies at which we can probe physics at the moment.


$^1$ That is at first glance. There are some people that think that gravity might by asymptotically safe and therefore one would only need to fix a finite amount of couplings to "determine" how gravity works at high energies. While there is some evidence that this might be true for GR it has thus far not been rigourously proven.