The regularization and determination of the Yang-Mills vacuum wave functional in three dimensions at \(\mathcal{O}(e^2)\). (English) Zbl 1284.81211
Summary: We complete the computation of the Yang-Mills vacuum wave functional in three dimensions at weak coupling with \(\mathcal{O}(e^2)\) precision. We use two different methods to solve the functional Schrödinger equation. One of them generalizes to \(\mathcal{O}(e^2)\) the method followed by B. F. Hatfield at \(\mathcal{O}(e)\) [Phys. Lett. B 147, No. 6, 435–440 (1984)]. The other uses the weak coupling version of the gauge invariant formulation of the Schrödinger equation and the ground-state wave functional followed by D. Karabali, V. P. Nair and A. Yelnikov [ibid. 824, No. 3, 387–414 (2010; Zbl 1196.81178)]. These methods need to be carefully regularized to yield correct results. This is done in this paper with full detail.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
Citations:
Zbl 1196.81178References:
| [1] | Hatfield, B. F., Phys. Lett. B, 147, 435 (1984) |
| [2] | Karabali, D.; Nair, V. P.; Yelnikov, A., Nucl. Phys. B, 824, 387 (2010) · Zbl 1196.81178 |
| [3] | Krug, S.; Pineda, A. |
| [4] | Karabali, D.; Nair, V. P., Nucl. Phys. B, 464, 135 (1996) · Zbl 1004.81521 |
| [5] | Karabali, D.; Nair, V. P., Phys. Lett. B, 379, 141 (1996) |
| [6] | Karabali, D.; Nair, V. P., Int. J. Mod. Phys. A, 12, 1161 (1997) · Zbl 1161.81416 |
| [7] | Karabali, D.; Kim, C.j.; Nair, V. P., Nucl. Phys. B, 524, 661 (1998) · Zbl 1031.81561 |
| [8] | Karabali, D.; Kim, C.j.; Nair, V. P., Phys. Lett. B, 434, 103 (1998) |
| [9] | Symanzik, K., Nucl. Phys. B, 190, 1 (1981) |
| [10] | Luscher, M., Nucl. Phys. B, 254, 52 (1985) |
| [11] | Agarwal, A.; Karabali, D.; Nair, V. P., Nucl. Phys. B, 790, 216 (2008) · Zbl 1151.81358 |
| [12] | Bars, I., Phys. Rev. Lett., 40, 688 (1978) |
| [13] | Freidel, L. |
| [14] | Alexanian, G.; Nair, V. P., Phys. Lett. B, 352, 435 (1995) |
| [15] | Jackiw, R.; Pi, S.-Y., Phys. Lett. B, 368, 131 (1996) |
| [16] | Buchmuller, W.; Philipsen, O., Phys. Lett. B, 397, 112 (1997) |
| [17] | Cornwall, J. M., Phys. Rev. D, 57, 3694 (1998) |
| [18] | Bieletzki, D.; Lessmeier, K.; Philipsen, O.; Schroder, Y., J. High Energy Phys., 1205, 058 (2012) |
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