Abstract
We give a special form of the Osterwalder-Schrader axioms in terms of conditions on a functional integral S{f} = ∫eiϕ(f)dμ. This yields a simple, self-contained construction of a Hamiltonian H, a relativistic, local boson quantum field Φ, and a Feynman-Kac formula to study perturbations H + Φ of H.
Supported in part by the National Science Foundation under Grant PHY7 6-17191.
Supported in part by the National Science Foundation under Grant PHY75-21212.
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References
R. P. Feynman, Rev. Mod. Phys. 20, 367–387 (1948); M. Kac, Probability and Related Topics in Physical Sciences, Interscience, 1959; K. Symanzik, Euclidean quantum field theory, in Local Quantum Field Theory, R. Jost (ed.), Academic Press, 1969; E. Nelson, J. Funct. Anal. 12, 97-112 (1973); K. Osterwalder and R. Schrader, Commun. Math. Phys. 31, 83-112 (1973) and 42, 281-305 (1975).
J. Glimm and A. Jaffe, Quantum Field Models, in Statistical Mechanics, C. DeWitt and R. Stora (eds.), 1970 Les Houches Lectures, Gordon and Breach Science Publishers, New York, 1971.
J. Fröhlich, Helv. Phys. Acta 47, 265–306 (1974); Adv. Math., to appear; Ann. de l’ Inst H. Poincaré 22, 271-317 (1974); Ann. Phys. 97, 1-54 (1976); G. Hegerfeldt, Commun. Math. Phys. 35, 155 (1974); F. Guerra, L. Rosen and B. Simon, Ann. Math. 101, 111-259 (1975); A. Klein and L. Landau, J. Funct. Anal. 20, 44-82 (1973); A. Klein, preprint; H. Borchers and J. Yngvason, preprint; J. Challifour, preprint; D. Uhlenbrock, preprint.
I. Gelfand and N. Vilenkin, Generalized Functions, Vol. 4, Academic Press, 1964.
J. Glimm and A. Jaffe, Commun. Math. Phys. 44, 293–320 (1975), footnote page 297.
W. Driessler and J. Fröhlich, preprint.
T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, 1966, formula (3.43), page 282.
Ibid., Theorem 3. 13, page 459.
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© 1977 Plenum Press, New York
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Glimm, J., Jaffe, A. (1977). Functional Integral Methods in Quantum Field Theory. In: Lévy, M., Mitter, P. (eds) New Developments in Quantum Field Theory and Statistical Mechanics Cargèse 1976. Nato Advanced Study Institutes Series, vol 26. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8918-1_2
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DOI: https://doi.org/10.1007/978-1-4615-8918-1_2
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