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Lorentz covariance of the \(\lambda (\varphi^ 4)_ 2\) quantum field theory. (English) Zbl 0194.29003


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quantum theory
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[1] Glimm, J., Jaffe, A.: A {\(\lambda\)}4 quantum field theory without cutoffs I. Phys. Rev.176, 1945 (1968). · Zbl 0177.28203 · doi:10.1103/PhysRev.176.1945
[2] —- —- Singular perturbations of self adjoint operators. Comm. Pure Appl. Math.22, 401 (1969). · Zbl 0167.42804 · doi:10.1002/cpa.3160220305
[3] —- —- The {\(\lambda\)}(4)2 quantum field theory without cutoffs II. The field operators and the approximate vacuum. Ann. Math.91, 362 (1970). · Zbl 0191.27005 · doi:10.2307/1970582
[4] – – The {\(\lambda\)}(4)2 quantum field theory without cutoffs III. The physical vacuum. Acta Math. (to appear).
[5] Glimm, J.: Yukawa coupling of quantum fields in two dimensions I. Commun. Math. Phys.5, 343 (1967). · Zbl 0155.57001 · doi:10.1007/BF01646449
[6] —- Jaffe, A.: An infinite renormalization of the Hamiltonian is necessary. J. Math. Phys.10, 2213 (1969). · Zbl 0184.54203 · doi:10.1063/1.1664825
[7] Nelson, E.: A quartic interaction in two dimensions, in Mathematical theory of elementary particles. Ed. by R. Goodman and I. Segal. Cambridge: M.I.T. Press 1966.
[8] Glimm, J.: Boson fields with nonlinear self-interaction in two dimensions. Commun. Math. Phys.8, 12 (1968). · Zbl 0173.29903 · doi:10.1007/BF01646421
[9] Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966. · Zbl 0148.12601
[10] Rosen, L.: The 2n quantum field theory: higher order estimates (to appear).
[11] Segal, I.: Notes towards the construction of non-linear relativistic quantum fields I. Proc. Nat. Acad. Sci. U.S.57, 1178 (1967). · Zbl 0162.57801 · doi:10.1073/pnas.57.5.1178
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