On the Lorentz-Invariance of the Dyson Series in Theories with Derivative Couplings
DOI:
https://doi.org/10.15407/ujpe66.11.945Keywords:
quantum field theory, canonical quantization, Dyson series, Wick’s theoremAbstract
We study the Dyson series for the S-matrix, when the interaction depends on derivatives of the fields. We concentrate on two particular examples: the scalar electrodynamics and the renormalized ф4 theory. By using Wick’s theorem, we eventually give evidence that the Lorentz invariance is satisfied, and the usual Feynman rules can be applied to the interaction Lagrangian.
References
F. Rohrlich. Quantum electrodynamics of charged particles without spin. Phys. Rev. 80, 666 (1950).
https://doi.org/10.1103/PhysRev.80.666
W. Greiner, J. Reinhardt. Field Quantization (Springer, 1996) [ISBN: 978-3-642-61485-9].
https://doi.org/10.1007/978-3-642-61485-9
C. Itzykson, J.B. Zuber. Quantum Field Theory (McGraw-Hill, 1980) [ISBN 10: 0070320713, ISBN 13: 9780070320710].
P.T. Matthews. The application of Dyson's methods to meson interactions. Phys. Rev. 76, 684 (1949); Erratum ibid. 1489.
https://doi.org/10.1103/PhysRev.76.684.2
T.D. Lee, C.N. Yang. Theory of charged vector mesons interacting with the electromagnetic field. Phys. Rev. 128, 885 (1962).
https://doi.org/10.1103/PhysRev.128.885
Y. Nambu. On Lagrangian and Hamiltonian formalism. Progr. Theor. Phys. 7 (2), 131 (1952).
https://doi.org/10.1143/ptp/7.2.131
K. Nishilima. On Lagrangian formalism. Progr. Theor. Phys. 8 (4), 401 (1952).
https://doi.org/10.1143/ptp/8.4.401
A.D. Sukhanov. On the interaction Hamiltonian in quantum field theory. JETP 14 (6), 1361 (1962).
A.D. Sukhanov. The connection between operators in the Heisenberg and interaction representations in local quantum field theory. JETP 20 (4), 881 (1965) 881.
V.P. Pavlov, G.A. Tavluev. Interaction Hamiltonian in quantum field theory. Theor. Math. Phys. 9 (1), 993 (1971).
https://doi.org/10.1007/BF01036027
R.L. Ingraham. Canonical commutation relations for renormalized fields. Nucl. Phys. B 13, 113 (1969).
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