Timeline for The commutation relations of photon and gluon?
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12 events
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| Jul 8 at 11:14 | comment | added | Cosmas Zachos | The force equation you write is of classical electrodynamics, not QED, a QFT. QCD is a "pure" (infrared-enslaving) QFT and has no sensible classical limit, on account of confinement. | |
| Jul 8 at 4:13 | comment | added | James | @CosmasZachos is there a formulation of QCD using forces, similar to $\vec F = q (\vec E + \vec v \times \vec B)$, instead of using Lagrangians? E.g. what is the magnitude and direction of the force that a red up quark exerts on a green down quark given their respective position and momentum? | |
| Jun 28 at 6:53 | comment | added | Qin-Tao Song | Yes, in the papers they are light-cone commutators, in Eq.(6) the spacetime coordinate is same. | |
| Jun 27 at 18:13 | comment | added | Cosmas Zachos | But you do realize that light-cone commutators are not equal time ones, no? | |
| Jun 27 at 17:17 | comment | added | Qin-Tao Song | Thanks very much for your comment, Eq. (6) is equal time commutation, and I also find two papers on the gluon commutation relations, they are: doi.org/10.1103/PhysRevD.1.2901; doi.org/10.1103/PhysRevD.8.2736. I am studing those papers now, and it seems that the commutation relations are complicated for gluons. | |
| Jun 27 at 14:36 | comment | added | Cosmas Zachos | Since, the fields decouple for different colors, the analog of (1) is (2), where the color indices a are not summed over. Again, singularities only emerge for canonical momentum involvement, the analog of (6.93a). With the suitable equal time indices inserted, (6) comports with (2). | |
| Jun 26 at 15:00 | comment | added | Cosmas Zachos | I don't have his book, but, indeed, there are no equal time singularities, for the analogous reason there are no φφ ones... The singularities emerge for combinations of a field with its canonical conjugate... | |
| Jun 26 at 14:45 | comment | added | Qin-Tao Song | Thanks very much, Eq.(1) is from Eq.(6.93b) of the book "Field quantization, greiner", what am I interested is the hadronic matrix element of the vector field $A^{\mu} A^{\nu}$, I guess that singularities do not contribute? | |
| Jun 26 at 14:35 | comment | added | Cosmas Zachos | It would be nice if you referenced (1); the ET commutator vanishes because the structure of coefficients of the constituent oscillators lacks the "interesting snag" of canonically conjugate fields. (Practice with scalar QFT first, abelian and non-abelian). The interesting pieces, however, are the ones involving fields and field momenta, which contain the singularities... Do you want an answer for scalar fields, eschewing the irrelevant complexities? | |
| Jun 26 at 13:01 | history | edited | Qin-Tao Song | CC BY-SA 4.0 |
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| Jun 26 at 10:12 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Jun 26 at 9:48 | history | asked | Qin-Tao Song | CC BY-SA 4.0 |