Abstract
Constrained systems in quantum field theories call for a careful study of diverse classes of constraints and consistency checks over their temporal evolution. Here we study the functional structure of the free electromagnetic and pure Yang–Mills fields on the front-form coordinates with the null-plane gauge condition. It is seen that in this framework, we can deal with strictu sensu physical fields.
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References
Dirac P.A.M.: Forms of relativistic dynamics. Rev. Mod. Phys. 21, 392–399 (1949)
Steinhardt P.J.: Problems of quantization in the infinite momentum frame. Ann. Phys. 128, 425–447 (1980)
Rohrlich F.: Theory of photons and electrons on null planes. Acta Phys. Aust. Suppl. VIII 277, 87–106 (1971)
Neville R.A., Rohrlich F.: Quantum field theory of null planes. Nuo. Cim. A 1, 625–644 (1971)
Ten Eyck J.H., Rohrlich F.: Equivalence of null plane and conventional quantum electrodynamics. Phys. Rev. D 9, 2237–2245 (1974)
Casana R., Pimentel B.M., Zambrano G.E.R.: The Schwinger model on the null-plane. Int. J. Mod. Phys. E 16, 2993–2997 (2007)
Casana, R., Pimentel, B.M., Zambrano, G.E.R.: SQED 4 and QED 4 on the null-plane. arXiv: 0803-2677 [hep-th]
Casana, R., Pimentel, B.M., Zambrano, G.E.R.: Scalar QCD 4 on the null-plane. arXiv: 0808-2217 [hep-th]
Sundermeyer K.: Constrained Dynamics, Lectures Notes in Physics, vol. 169. Springer, New York (1982)
Srivastava, P.P.: Perspectives of light front quantized field theory: some new results. Invited article for: Saga of Field Theory. From Points to Strings, ed., A. N. Mitra, Indian National Science Academy (INSA), New Delhi. hep-ph/9908492
Srivastava P.P.: Light front quantized Schwinger model and theta-vacua. Mod. Phys. Lett. A 13, 1223–1233 (1998)
Srivastava P.P.: Light front quantized chiral Schwinger model and its vacuum structure. Phys. Lett. B 448, 68–75 (1999)
Brodsky S.J., Pauli H., Pinsky S.S.: Quantum chromodynamics and other field theories on the light cone. Phys. Rep. 301, 299–486 (1998)
Pauli H., Brodsky S.J.: Discretized light cone quantization: solution to a field theory in one space one time dimensions. Phys. Rev. D 32, 2001–2013 (1985)
Maskawa T., Yamawaki K.: The problem of P + = 0 mode in the null plane field theory and Dirac’s method of quantization. Prog. Theor. Phys. 56, 270–283 (1976)
Robertson D.G.: On spontaneous symmetry breaking in discretized light cone field theory. Phys. Rev. D 47, 2549–2553 (1993)
Pritchard D.J., Stirling W.J.: QCD calculations in the light cone gauge. 1. Nucl. Phys. B 165, 237–268 (1980)
Cursi G., Furmanski W., Petronzio R.: Evolution of parton densities beyond leading order: the nonsinglet case. Nucl. Phys. B 175, 27–92 (1980)
Morara M., Soldati R., McCartor G.: Consistent perturbative light-front formulation of Yang–Mills theories. AIP Conf. Proc. 494, 284–290 (1999)
Chakrabarti A., Darzens C.: Comment on the null-plane gauge. Phys. Rev. D 9, 2484–2488 (1974)
Mandelstam S.: Light cone superspace and the ultraviolet finiteness of the N = 4 model. Nucl. Phys. B 213, 149–168 (1983)
Leibbrandt G.: The light cone gauge in Yang–Mills theory. Phys. Rev. D 29, 1699–1708 (1984)
Capper D.M., Jones D.R.T., Suzuki A.T.: The light cone gauge at two loops: the scalar anomalous dimension. Z. Phys. C 29, 585–596 (1985)
Smith A.: Light cone formulation on N = 2 Yang–Mills. Nucl. Phys. B 261, 285–296 (1985)
Capper D.M., Jones D.R.T., Litvak M.J.: The triangle anomaly in the light cone gauge. Z. Phys. C 32, 221–226 (1986)
Pimentel B.M., Suzuki A.T.: The light cone gauge and the principal value prescription. Phys. Rev. D 42, 2115–2119 (1990)
Pimentel B.M., Suzuki A.T.: Causal prescription for the light cone gauge. Mod. Phys. Lett. A 6, 2649–2654 (1991)
Tomboulis E.: Quantization of the Yang–Mills field in the null-plane frame. Phys. Rev. D 8, 2736–2740 (1973)
Casana R., Pimentel B.M., Zambrano G.E.R.: Hamiltonian formulation of the Yang–Mills field on the null-plane. Nucl. Phys. B (Proc. Suppl.) 199, 219–222 (2010)
Senjanovic, P.: Path integral quantization of field theories with second class constraints. Ann. Phys. 100, 227–261 (1976) Erratum by Miao, Y.-G., Ann. Phys. 209, 248 (1991)
Faddeev L.D., Popov V.N.: Feynman diagrams for the Yang–Mills field. Phys. Lett. B 25, 29–30 (1967)
DeWitt B.S.: Quantum theory of gravity. 1. The canonical theory. Phys. Rev. 160, 1113–1148 (1967)
Suzuki A.T., Sales J.H.O.: Light-front gauge propagator reexamined. Nucl. Phys. A 725, 139–148 (2003)
Suzuki A.T., Sales J.H.O.: Surveillance on the light-front gauge-fixing Lagrangians. Mod. Phys. Lett. A 19, 1925–1932 (2004)
Suzuki A.T., Sales J.H.O.: Quantum gauge boson propagators in the light-front. Mod. Phys. Lett. A 19, 2831–2844 (2004)
Kummer W.: Eichtransformation und Quantelung des freien elektromagnetischen Feldes. Acta Phys. Aust. 14, 149–161 (1961)
Arnowitt R.L., Fickler S.I.: Quantization of the Yang–Mills field. Phys. Rev. 127, 1821–1829 (1962)
Suzuki A.T.: One-loop three-gluon vertex and power counting in the light-cone-gauge. Z. Phys. C 38, 595–601 (1988)
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Pimentel, B.M., Suzuki, A.T. & Zambrano, G.E.R. Functional Analysis for Gauge Fields on the Front-Form and the Light-Cone Gauge. Few-Body Syst 52, 437–442 (2012). https://doi.org/10.1007/s00601-011-0263-4
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DOI: https://doi.org/10.1007/s00601-011-0263-4