Complex classical fields: An example

Araki, 1963, Representations of the canonical commutation relations describing a nonrelativistic infinite free Bose gas, J. Math. Phys., 4, 637, 10.1063/1.1704002 Bratteli, 1981 Bros, 1994, Towards a relativistic KMS condition, Nuclear Phys. B, 429, 291, 10.1016/0550-3213(94)00298-3 Bros, 1996, Axiomatic analyticity properties and representations of particles in thermal quantum field theory, Ann. Inst. H. Poincaré, 64, 495 Buchholz, 1986, Causal independence and the energy-level density of states in local quantum field theory, Comm. Math. Phys., 106, 321, 10.1007/BF01454978 Chernoff, 1968, Note on product formulas for operator semigroups, J. Funct. Anal., 2, 238, 10.1016/0022-1236(68)90020-7 Eckmann, 1973, An application of Tomitaʼs theory of modular Hilbert algebras: duality for free Bose fields, J. Funct. Anal., 13, 1, 10.1016/0022-1236(73)90062-1 Ferrante Glimm, 1970, The λΦ24 quantum field theory without cutoffs: II. The field operators and the approximate vacuum, Ann. of Math., 91, 362, 10.2307/1970582 Glimm, 1970, Energy-momentum spectrum and vacuum expectation values in quantum field theory, J. Math. Phys., 11, 3335, 10.1063/1.1665134 Glimm, 1971, Quantum field theory models Glimm, 1972, The λ(ϕ4)2 quantum field theory without cut-offs. IV. Perturbations of the Hamiltonian, J. Math. Phys., 13, 1568, 10.1063/1.1665879 Guralnik, 2010, Complexified path integrals and the phases of quantum field theory, Ann. Physics, 325, 2486, 10.1016/j.aop.2010.06.001 Haag, 1967, On the equilibrium states in quantum statistical mechanics, Comm. Math. Phys., 5, 215, 10.1007/BF01646342 Heifets, 1977, The energy-momentum spectrum in the P(φ)2 quantum field theory, Comm. Math. Phys., 56, 161, 10.1007/BF01611501 Heifets, 1977, The energy-momentum spectrum in the Yukawa2 quantum field theory, Comm. Math. Phys., 57, 31, 10.1007/BF01651692 Høegh-Krohn, 1974, Relativistic quantum statistical mechanics in two-dimensional spacetime, Comm. Math. Phys., 38, 195, 10.1007/BF01651542 Rajan Hoole, Arthur Jaffe, Christian Jäkel, Quantization domains, preprint. Jaffe, 1999, Twist positivity, Ann. Physics, 278, 10, 10.1006/aphy.1999.5918 Jaffe, 2013, Complex classical fields: A framework for reflection positivity, Comm. Math. Phys. Jäkel, 2013, The relativistic KMS condition for the thermal n-point functions of the P(ϕ)2 model, Comm. Math. Phys. Kay, 1985, A uniqueness result for quasi-free KMS states, Helv. Phys. Acta, 58, 1017 Kubo, 1957, Statistical mechanical theory of irreversible processes I, J. Math. Soc. Japan, 12, 570 Martin, 1959, Theory of many-particle systems. I, Phys. Rev., 115, 1342, 10.1103/PhysRev.115.1342 Rosen, 1971, The (ϕ2n)2 quantum field theory: higher order estimates, Comm. Pure Appl. Math., XXIV, 417, 10.1002/cpa.3160240306