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Compact (ferroand antiferromagnetic) sigma-models and noncompact (hyperbolic) sigma-models are compared in a lattice formulation in dimensions d ≥ 2. While the ferroand antiferromagnetic models are essentially equivalent, the qualitative difference to the noncompact models is highlighted. The perturbative and the large N expansions are studied in both types… (More)

- Erhard Seiler, bullet Simon
- Proceedings of the National Academy of Sciences…
- 1975

WE PROVE THAT FOR ANY TRACE CLASS OPERATORS, [FORMULA: see text].

According to the standard classification of Conformal Quantum Field Theory (CQFT) in two dimensions, the massless continuum limit of the O(2) model at the Kosterlitz-Thouless (KT) transition point should be given by the massless free scalar field; in particular the Noether current of the model should be proportional to (the dual of) the gradient of the… (More)

We prove Guerra’s theorem, 4 bounds and Frohlich bounds in the Y, and $34 field theories. Among our technical results of interest is a proof that 2 # 0 in &* and that the spatially cutoff vacuum in Ye has a charge zero component. The two main inputs are Osterwalder-Schrader positivity in the spatial direction as well as in the time direction, and a finite… (More)

- Erhard Seiler, Barry Simon
- 2004

We prove bounds of the form ZΛ^e a{Λl and ( S Z ) ^ ^ 1 in the Y2 Euclidean field theory and from this obtain Glimm's Hamiltonian bound and Schrader's linear lower bound.

In dimension D ≤ 2 the low temperature behavior of systems enjoying a continuous symmetry is dominated by super-instantons: classical configurations of arbitrarily low energy. Perturbation theory in the background of a super-instanton produces thermodynamic answers for the invariant Green’s functions that differ from the standard ones, but only in… (More)

The commonly accepted belief that non-Abelian and Abelian models are different because of the presence/absence of instantons and/or perturbative asymptotic freedom is analyzed from a historical perspective. The presentation covers the major developments which brought about this dogma, as well as all the supportive evidence produced since. For a model… (More)

- Erhard Seiler
- 2001

We discuss some subtleties in connection with the new attempts to provide a firm basis for ths Witten-Veneziano formula.

We discuss the apparent conflict between reflection positivity and positivity of the topological susceptibility in two-dimensional nonlinear sigma models and in four-dimensional gauge theories. We pay special attention to the fact that this apparent conflict is already present on the lattice; its resolution puts some nontrivial restrictions on the… (More)

- Erhard Seiler
- 2003

In this talk I give an overview of the work done during the last 15 years in collaboration with the late Adrian Patrascioiu. In this work we accumulated evidence against the commonly accepted view that theories with nonabelian symmetry – either two dimensional nonlinear σ models or four dimensional Yang-Mills theories – have the property of asymptotic… (More)