Abstract
Matrix elements of internal symmetry currents and energy momentum density tensor are constructed in Migdal Polyakov conformal invariant bootstrap field theory. Their 3-point functions satisfy Bethe Salpeter equations which determine any free coefficients that may still occur in the conformal invariant Ansatz. Ward identities are verified for alln-point functions. They imply correct equal time current commutation relations. A proof of generalized unitarity is also given. Various equivalent forms of the propagator bootstrap are discussed. Our algebraic techniques also yield an eigenvalue equation for first order correction to the exactly conformal invariant theory, assuming the latter is Gell-Mann Low large momentum asymptote of a renormalizable finite mass theory.
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References
Migdal, A. A.: Phys. Letters37 B, 98 (1971).
——: Letters37 B, 386 (1971).
Polyakov, A. M.: Zh ETF Pis. Red.12, 538 (1970); — Transl. JETP Letters12, 381 (1970).
Parisi, G., Peliti, L.: Lettere Nuovo Cimento2, 627 (1971).
Mack, G., Todorov, I. T.: IC/71/139, Trieste, Oct. 1971.
Schroer, B.: Lettere Nuovo Cimento2, 867 (1971).
Gell-Mann, M., Low, F. E.: Phys. Rev.95, 1300 (1954). — Wilson, K. G.: Phys. Rev. D3, 1818 (1971).
Symanzik, K.: Commun. math. Phys.23, 49 (1971).
Wess, J. E.: Nuovo Cimento18, 1086 (1960). — Kastrup, H. A.: Ann. Physik7, 388 (1962) and references cited in [11].
Mack, G.: Nucl. Phys. B5, 499 (1968).
—— Salam, A.: Ann. Phys. (N. Y.)53, 174 (1969).
Wilson, K. G.: Phys. Rev.179, 1499 (1969).
Schroer, B.: Fortschr. Physik11, 1 (1963).
Glaser, V., Lehmann, H., Zimmermann, W.: Nuovo Cimento6, 1122 (1957).
Symanzik, K.: J. Math. Phys.1, 249 (1960). In: Lectures in Theoretical physics, Vol. III, ed. W.E. Brittinet al., p. 490. New York: Interscience Publ. 1961. In: Ramakrishnan, A., (Ed.): Symposia on Theoretical Physics, Vol. 3, p. 121. New York: Plenum Press 1967.
—— In: Jaśič, (Ed.): Lectures on High Energy Physics. Zagreb: 1961, New York: Gordon and Breach 1965.
Schwinger, J.: Proc. Natl. Acad. Sci. US44, 956 (1958). — Symanzik, K.: J. Math. Phys.7, 510 (1966).
Hortacsu, M., Seiler, R., Schroer, B.: NYO-3829-80, U. of Pittsburgh, Sept. 1971.
Brandt, R. A.: Ann. Phys.52, 122 (1969).
Symanzik, K.: Lettere Nuovo Cimento3, 734 (1972).
Epstein, H., Glaser, V.: CERN Th. 1156, Geneva, May 1970. — Steinmann, O.: Perturbation expansions in axiomatic field theory. Lecture Notes in Physics, Vol. 11. Berlin-Heidelberg-New York: Springer 1971.
Polyakov, A. M.: Zh ETF59, 542 (1970); — Transl. JETP32, 296 (1971).
Wu, T. T.: Phys. Rev.125, 1436 (1962).
Taylor, J. G.: Suppl. al Nuovo Cimento1, 857 (1963).
Johnson, R. W.: J. Math. Phys.11, 2161 (1970).
Symanzik, K.: Commun. math. Phys.6, 228 (1967).
—— In: Bessis, J. D., (Ed.): Cargèse Lectures in Physics, Vol. 6. New York: Gordon and Breach 1971.
D'Eramo, M., Peliti, L., Parisi, G.: Lettere Nuovo Cimento2, 878 (1971).
Gatto, R.: Riv. Nuovo Cimento1, 514 (1969).
Callan, C. G., Jr., Coleman, S., Jackiw, R.: Ann. Phys.59, 42 (1970).
Speer, E. R.: Generalized Feynman amplitudes. Princeton: Princeton University Press 1969.
Mack, G.: Expansions around canonical dimensions in conformal invariant Quantum field theory II (in preparation).
Bogolubov, N. N., Shirkov, D. V.: Introduction to the theory of quantized fields. § 17.5 New York: Intersc. Publ. 1959.
Veltman, M.: Physica29, 186 (1963).
Pohlmeyer, K.: Commun. math. Phys.12, 204 (1969).
Baker, M., Johnson, K.: Phys. Rev.183, 1292 (1969); D3, 2516 (1971).
Adler, S. L., Bardeen, W. A.: Phys. Rev. D4, 3045 (1971).
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Mack, G., Symanzik, K. Currents, stress tensor and generalized unitarity in conformal invariant quantum field theory. Commun.Math. Phys. 27, 247–281 (1972). https://doi.org/10.1007/BF01645514
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DOI: https://doi.org/10.1007/BF01645514