Communications In Mathematical Physics - Volume 273 by M. Aizenman (Chief Editor) PDF

By M. Aizenman (Chief Editor)

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Other fixed points of f a,b 2. The right endpoint of J is neutral, topologically attracting from the left and topologically repelling from the right; the left endpoint of J is repelling; there are no n in J . other fixed points of f a,b Double Standard Maps 45 Fig. 1. Four cases n in the 3. Both endpoints of J are repelling; there is an attracting fixed point of f a,b n interior of J ; there are no other fixed points of f a,b in J . n , repelling from both sides. 4. The set J consists of one neutral fixed point of f a,b Proof.

There are no curvature terms in the terms that we have displayed, but those arise from the other poles 0, −i. These contributions may be obtained in closed form using the Minkowski integrals of [8]. The end result is a sum of terms µνσρ µνσρ (ξ1 , ξ2 , ξ3 ), where Wa are Lorentz invariant distributions in the a Rµνσρ Wa Riemannian normal coordinates ξi of xi around x3 . However, the expressions for these distributions are rather complicated and will therefore be given elsewhere [25]. It should be clear that our method is not confined to the above example, but in principle only limited by the ability to perform complicated Minkowski integrals of Feynman type.

Math. Phys. 180, 633–652 (1996) 4. : Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on physical backgrounds. Commun. Math. Phys. 208, 623–661 (2000) 5. ” Commun. Math. Phys. 237, 31 (2003); see also K. ” In: XIVth Int. Congress on Mathematical Physics (Lisbon 2003), RiverEdge Co: World Scientific, 2006 6. : Infinite Conformal Symmetry In Two-Dimensional Quantum Field Theory. Nucl. Phys. B 241, 333 (1984) 7. : Causal independence and the energy level density of states in local quantum field theory.

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Communications In Mathematical Physics - Volume 273 by M. Aizenman (Chief Editor)

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