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Long‐range dynamics and broken symmetries in gauge models. The Schwinger model
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9.In particular, the removal of the infrared cutoff in the dynamics, the identification of the essentially local algebra the local generation of symmetries, the definition of the effective dynamics, etc. look rather instructive in this model.
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14.That is, the strong continuity of with respect to
15.For example, by considering a Fock representation of corresponding to a nonzero mass.
16.These details will be discussed separately in a more general framework.
17.Since det this also implies
18.In the following we will often drop the ○, since the states F are uniquely determined by Eq. (4.1).
19.Clearly, since fields are singular objects (actually distributions), the meaning of is problematic.
20.A possible choice is with then converges to zero pointwisely almost everywhere and Eq. (5.1) holds because
21.More generally, one can construct the states associated to a family of states, stable under If M is an arbitrary matrix satisfying (4.2), then the corresponding and does not map into so that is not ‐weakly continuous.
22.This can also be checked explicitly by applying the argument below to
23.Convergence of to in the norm has nothing to do with the norm convergence of which is in fact excluded by the appearance of variables at infinity [see Eq. (5.8)].
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