Nelson, Edward The free Markoff field. (English) Zbl 0273.60079 J. Funct. Anal. 12, 211-227 (1973). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 246 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory PDF BibTeX XML Cite \textit{E. Nelson}, J. Funct. Anal. 12, 211--227 (1973; Zbl 0273.60079) Full Text: DOI OpenURL References: [1] Cook, J.M, The mathematics of second quantization, Trans. amer. math. soc., 74, 222-245, (1953) · Zbl 0052.22701 [2] Doob, J.L, The Brownian movement and stochastic equations, Ann. of math., 43, 351-369, (1942) · Zbl 0063.01145 [3] Fock, V, Konfigurationsraum und zweite quantelung, Z. physik., 75, 622-647, (1932) · Zbl 0004.28003 [4] Glimm, J, Boson fields with nonlinear selfinteraction in two dimensions, Commun. math. phys., 8, 12-25, (1968) · Zbl 0173.29903 [5] Glimm, J; Jaffe, A, A λ(ϑ4)2 quantum field theory without cutoffs, I, Phys. rev., 176, 1945-1951, (1968) · Zbl 0177.28203 [6] Glimm, J; Jaffe, A, The λ(ϑ4)2 quantum field theory without cutoffs II. the field operators and the approximate vacuum, Ann. of math., 91, 362-401, (1970) · Zbl 0191.27005 [7] Glimm, J; Jaffe, A, The λ(ϑ4)2 quantum field theory without cutoffs III. the physical vacuum, Acta math., 125, 203-267, (1970) · Zbl 0191.27005 [8] {\scJ. Glimm and A. Jaffe}, The λ(ϑ4)2 quantum field theory without cutoffs IV. Perturbation of the Hamiltonian, to appear. · Zbl 0191.27005 [9] Gross, L, Existence and uniqueness of physical ground states, J. funct. anal., 10, 52-109, (1972) · Zbl 0237.47012 [10] {\scF. Guerra}, Uniqueness of the vacuum energy density and Van Hove phenomenon in the infinite volume limit for two-dimensional self-coupled Bose fields, Princeton University preprint. [11] {\scF. Guerra, L. Rosen, and B. Simon}, Nelson’s symmetry and the infinite volume behavior of the vacuum in P(ϑ)2, Commun. Math. Phys., to appear. [12] Halmos, P.R, Normal dilations and extensions of operators, Summa brasil. math., 2, 125-134, (1950) [13] Hille, E, A class of reciprocal functions, Ann. of math., 27, 427-464, (1926) · JFM 52.0400.02 [14] Nelson, E, Regular probability measures on function space, Ann. of math., 69, 630-643, (1959) · Zbl 0087.13102 [15] Nelson, E, A quartic interaction in two dimensions, () [16] Nelson, E, Quantum fields and markoff fields, () · Zbl 0279.60096 [17] Nelson, E, Time-ordered operator products of sharp-time quadratic forms, J. functional analysis, 11, 211-219, (1972) · Zbl 0239.47012 [18] Nelson, E, Construction of quantum fields from markoff fields, J. functional analysis, 12, 97-112, (1973) · Zbl 0252.60053 [19] Riesz, F; Sz.-Nagy, B, Functional analysis [appendix: extensions of linear transformations in Hilbert space which extend beyond this space], (1960), Ungar New York, (transl. by L. F. Boron) [20] Segal, I.E, Tensor algebras over Hilbert spaces, Trans. amer. math. soc., 81, 106-134, (1956) · Zbl 0070.34003 [21] Segal, I.E, Construction of nonlinear local quantum processes, I, Ann. math., 92, 462-481, (1970) · Zbl 0213.40904 [22] Simon, B; Hoegh-Krohn, R, Hypercontractive semigroups and two dimensional self-coupled Bose fields, J. funct. anal., 9, 121-180, (1972) · Zbl 0241.47029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.