# zbMATH — the first resource for mathematics

 [1] Avron, J; Seiler, R; Yaffe, L, Adiabatic theorem and applications to the quantum Hall effect, Commun. Math. Phys., 110, 33-49, (1987) · Zbl 0626.58033 [2] Benini, M; Dappiaggi, C; Murro, S, Radiative observables for linearized gravity on asymptotically at spacetimes and their boundary induced states, J. Math. Phys., 55, 082301, (2014) · Zbl 1298.83044 [3] Bär, C., Ginoux, N., Pfäffle, F.: Wave Equation on Lorentzian Manifolds and Quantization. ESI Lectures in Mathematics and Physics. EMS Publishing House, Zurich (2007) · Zbl 0858.53055 [4] Cheeger, J; Gromov, M, Bounds on the von Neumann dimension of $$L^{2}$$-cohomology and the Gauss-Bonnet theorem for open manifolds, J. Differ. Geom., 21, 1-34, (1985) · Zbl 0614.53034 [5] Chernoff, P, Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Anal., 12, 401-414, (1973) · Zbl 0263.35066 [6] Dappiaggi, C., Drago N.: Constructing Hadamard states via an extended Möller operator, arXiv:1506.09122 (2015) to appear in Lett. Math. Phys. 106 (2016) · Zbl 1362.81073 [7] Derezinski, J., Gérard, C.: Scattering Theory of Classical and Quantum N-particle Systems, Texts and Monographs in Physics. Springer, Berlin (1997) · Zbl 0899.47007 [8] Drago N., Faldino F., Pinamonti N.: On the stability of KMS states in perturbative algebraic quantum field theories. arXiv:1609.01124 · Zbl 1386.81111 [9] Drago N., Hack,T.-P., Pinamonti N.: The generalized principle of perturbative agreement and the thermal mass. http://arxiv.org/abs/1502.02705 · Zbl 1362.81064 [10] Dappiaggi, C., Moretti, V., Pinamonti, N.: Rigorous steps towards holography in asymptotically at spacetimes. Rev. Math. Phys. 18, 349-416 (2006) · Zbl 1107.81040 [11] Finster, F., Murro, S., Röken, C.: The fermionic projector in a time-dependent external Potential: mass oscillation property and hadamard states. Preprint arXiv:1501.05522 [math-ph] (2015) · Zbl 0263.35066 [12] Fulling, SA; Narcowich, FJ; Wald, RM, Singularity structure of the two-point function in quantum field theory in curved spacetime, Commun. Math. Phys., 3, 257-264, (1978) · Zbl 0401.35065 [13] Fulling, SA; Narcowich, FJ; Wald, RM, Singularity structure of the two-point function in quantum field theory in curved spacetime, II, Ann. Phys., 136, 243-272, (1981) · Zbl 0495.35054 [14] Fewster, CJ; Verch, R, The necessity of the Hadamard condition, Class. Quantum Gravity, 30, 235027, (2013) · Zbl 1284.83057 [15] Gonnella, G; Kay, BS, Can locally Hadamard quantum states have nonlocal singularities?, Class. Quantum Gravity, 6, 1445, (1989) · Zbl 0678.53082 [16] Gérard, C; Wrochna, M, Construction of Hadamard states by pseudodifferential calculus, Commun. Math. Phys., 325, 713-755, (2013) · Zbl 1298.81214 [17] Gérard, C; Wrochna, M, Construction of Hadamard states by characteristic Cauchy problem, Anal. PDE, 9, 111-149, (2016) · Zbl 1334.83020 [18] Gérard, C., Oulghazi, O., Wrochna, M.: Hadamard states for the Klein-Gordon equation on Lorentzian manifolds of bounded geometry. Preprint arXiv:1602.00930 [math-ph] (2016) [19] Georgescu, V; Gérard, C; Häfner, D, Resolvent and propagation estimates for Klein-Gordon equations with non-positive energy, J. Spectr. Theory, 5, 113-192, (2015) · Zbl 1326.35212 [20] Hollands, S; R.M, Wald, Existence of local covariant time ordered products of quantum fields in curved space-time, Commun. Math. Phys., 231, 309-345, (2002) · Zbl 1015.81043 [21] Kato, T.: Perturbation Theory for Linear Operators, Classics in Mathematics. Springer, Berlin (1995) · Zbl 0836.47009 [22] Khavkine, I., Moretti V.: Algebraic QFT in curved spacetime and quasi-free Hadamard states: an introduction. arXiv:1412.5945 (2014) · Zbl 0495.35054 [23] Radzikowski, MJ, Micro-local approach to the Hadamard condition in quantum field theory on curved space-time, Commun. Math. Phys., 179, 529-553, (1996) · Zbl 0858.53055 [24] Radzikowski, MJ, A local to global singularity theorem for quantum field theory on curved space-time, Commun. Math. Phys., 180, 1-22, (1996) · Zbl 0874.58079 [25] Reed, M., Simon, B.: Methods of Modern Mathematical Physics II: Fourier Analysis, Self-adjointness. Academic Press, Cambridge (1975) · Zbl 0308.47002 [26] Roe, J, An index theorem on open manifolds I, J. Differ. Geom., 27, 87-113, (1988) · Zbl 0657.58041 [27] Sanders, K, Thermal equilibrium states of a linear scalar quantum field in stationary spacetimes, Int. J. Mod. Phys. A, 28, 1330010, (2013) · Zbl 1268.82005 [28] Schmid, J; Griesemer, M, Kato’s theorem on the integration of non-autonomous linear evolution equations, Math. Phys. Anal. Geom., 17, 265-271, (2014) · Zbl 1309.34118 [29] Wald, R.M.: Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, Chicago Lectures in Physics. University of Chicago Press, Chicago (1994) · Zbl 0842.53052 [30] Wrochna M., Zahn J.: Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime. arXiv:1407.8079 [math-ph] · Zbl 1447.81165