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Singularity structure of the two-point function in quantum field theory in curved spacetime, II
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Singularity Structure of the Two-Point Function in Quantum Field Theory in Curved Spacetime, II. S. A. FULLING AND F. J. NARCOWICH, Department of Mathematics, Texas A&M University, College Station, Texas 77843; AND ROBERT M. WALD, Enrico Fermi Institute. University of Chicago. Chicago, Illinois 60637. We prove that, for a massive, scalar, quantum field in a wide class of static spacetimes, the two-point structure of the Hadamard form. In particular. this function (OWf &vi + #(Y) @)I 0) h as singularity implies that the point-splitting renormalization prescription is well defined in these spacetimes. As a corollary of this result and a previous result of Fulling, Sweeny, and Wald, we show that in an arbitrary globally hyperbolic spacetime there always exists a large class of states for which the singular part of the two-point function has the Hadamard form. In addition, we prove that, for a closed universe which is both initially and finally static, the S-matrix exists.
Spin Wares. Department
Vortices, Fermions, of Physics. Brown
and Duality University,
in the Ising and Baxter Models. Providence. Rhode Island 02912.
MICHAEL
C. OGILVIE.
Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex + spin-wave decomposition, that the 2;Villain models are related to a class of continuum field theories with analogous duality properties. Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin waves conspire to produce a free. massive Majorana field theory in the continuum limit. The continuum limit of the Baxter model is also studied. and the recent results of Kadanoff and Brown are rederived and extended.
OF
PAPERS
TO
APPEAR
IN
FUTURE
417
ISSUES
Singularity Structure of the Two-Point Function in Quantum Field Theory in Curved Spacetime, II. S. A. FULLING AND F. J. NARCOWICH, Department of Mathematics, Texas A&M University, College Station, Texas 77843; AND ROBERT M. WALD, Enrico Fermi Institute. University of Chicago. Chicago, Illinois 60637. We prove that, for a massive, scalar, quantum field in a wide class of static spacetimes, the two-point structure of the Hadamard form. In particular. this function (OWf &vi + #(Y) @)I 0) h as singularity implies that the point-splitting renormalization prescription is well defined in these spacetimes. As a corollary of this result and a previous result of Fulling, Sweeny, and Wald, we show that in an arbitrary globally hyperbolic spacetime there always exists a large class of states for which the singular part of the two-point function has the Hadamard form. In addition, we prove that, for a closed universe which is both initially and finally static, the S-matrix exists.
Spin Wares. Department
Vortices, Fermions, of Physics. Brown
and Duality University,
in the Ising and Baxter Models. Providence. Rhode Island 02912.
MICHAEL
C. OGILVIE.
Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex + spin-wave decomposition, that the 2;Villain models are related to a class of continuum field theories with analogous duality properties. Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin waves conspire to produce a free. massive Majorana field theory in the continuum limit. The continuum limit of the Baxter model is also studied. and the recent results of Kadanoff and Brown are rederived and extended.