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Quantum field theories in all dimensions

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Abstract

In this paper we exhibit a large class of hermitian scalar field theories satisfying the Wightman axioms. For eachd>0, and each polynomialP, we exhibit a collection of theories which are loosely but legitimately based on aP(ϕ) interaction ind space dimensions. One of the features of the construction is that the Wightmann-point function of each theory is a sum of finitely many integrals associated with “Feynman-like” graphs. Thus, it is in closed form.

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References

  • [GJ] Glimm, J., Jaffe, A.: Quantum Physics. 2nd ed. Berlin, Heidelberg, New York: Springer, 1987

    Google Scholar 

  • [GJ1] Glimm, J., Jaffe, A.: A λ(φ4)2 quantum field theory without cutoffs I. Phys. Rev.176, 1945–1951 (1968)

    Google Scholar 

  • [GJ2] Glimm, J., Jaffe, A.: A λ(φ4)2 quantum field theory without cutoffs II. The field operators and the approximate vacuum. Ann. Math91, 362–401 (1970)

    Google Scholar 

  • [GJ3] Glimm, J., Jaffe, A.: A λ(φ4)2 quantum field theory without cutoffs III. The physical vacuum. Acta. Math125, 204–267 (1970)

    Google Scholar 

  • [GJ4] Glimm, J., Jaffe, A.: A λ(φ4)2 quantum field theory without cutoffs IV. Perturbations of the Hamiltonian. J. Math. Phys.13, 1568–1584 (1972)

    Google Scholar 

  • [GJ5] Glimm, J., Jaffe, A.: Positivity of the λ(φ4)3 Hamiltonian. Fortschr. Phys.21, 327–376 (1973)

    Google Scholar 

  • [GJ6] Glimm, J., Jaffe, A.: A remark on the existence of λ(φ4)4. Phys. Rev. Lett.33, 440–442 (1974)

    Google Scholar 

  • [H] Haag, R.: Local Quantum Physics. Berlin-Heidelberg-New York: Springer, 1993

    Google Scholar 

  • [I] Iagolnitzer, I.: Scattering in Quantum Field theories. Princeton series in Physics, 1992.

  • [IZ] Itzykson, C., Zuber, J.: Quantum Field Theory. New York: McGraw-Hill, 1980

    Google Scholar 

  • [Reh1] K.H.Rehren: Comments on a recent solution to Wightman's axioms. To appear

  • [SW] Streater, R.F., Wightman, A.S.: PCT, Spin and Statistics, and all that. New York: Benjamin, 1964

    Google Scholar 

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  1. Trinity College, CB2 1TQ, Cambridge, England

    C. J. Read

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  1. C. J. Read
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Communicated by D. Brydges

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Read, C.J. Quantum field theories in all dimensions. Commun.Math. Phys. 177, 631–671 (1996). https://doi.org/10.1007/BF02099541

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  • DOI: https://doi.org/10.1007/BF02099541

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