Abstract
Covariant perturbation methods, developed over a quarter century ago, have since then dominated dynamical calculations in quantum field theory. Marvelously successful results can be achieved with some problems (especially in electrodynamics); but in many other contexts the technique yields no information. When the coupling constant is large, perturbation theory is useless. Even for weak coupling there remain phenomena, apparently of physical interest, which cannot easily be seen in the perturbative expansion; for example spontaneous symmetry violation, bound states, entrapment of various excitations. These cooperative, coherent effects can only be exposed by approximation procedures which do not rely on analyticity or regularity in the coupling constant. Such approximations are widely used in quantum mechanics (one does not find the properties of a complex atom or nucleus in the Born series!) and it is profitable to extend them to relativistic quantum field theory.
This work is supported in part through funds provided by the Atomic Energy Commission under Contract AT(11–1)-3069.
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References
Colleagues include S. Coleman, J. Cornwall, L. Dolan, J. Goldstone, J. Kuti, L. Jacobs, K. Johnson, H. Politzer, R. Root, H. Schnitzer, E. Tomboulis, S. Weinberg.
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Jackiw, R. (1975). Quantum Mechanical Approximations in Quantum Field Theory. In: Perlmutter, A., Widmayer, S.M. (eds) Theories and Experiments in High-Energy Physics. Studies in the Natural Sciences. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-4464-3_12
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