INTERPRETING A FIELD IN ITS HEISENBERG GROUP

Interpreting Heisenberg Interpreting Quantum States

The paper investigates possible readings of the later Heisenberg's remarks on the nature of quantum states. It discusses, in particular, whether Heisenberg should be seen as a proponent of the epistemic conception of states---the view that quantum states are not descriptions of quantum systems but rather reflect the state assigning observers' epistemic relations to these systems. On the one han...

The Heisenberg Group and Conformal Field Theory

A mathematical construction of the conformal field theory (CFT) associated to a compact torus, also called the “nonlinear σ-model” or “lattice-CFT”, is given. Underlying this approach to CFT is a unitary modular functor, the construction of which follows from a “Quantization commutes with reduction”type of theorem for unitary quantizations of the moduli spaces of holomorphic torusbundles and ac...

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

Discrete Heisenberg-Weyl Group and Modular Group

It is shown that the generators of two discrete Heisenberg-Weyl groups with irrational rotation numbers θ and −1/θ generate the whole algebra B of bounded operators on L2(R). The natural action of the modular group in B is implied. Applications to dynamical algebras appearing in lattice regularization and some duality principles are discussed. Writing a contribution to a memorial volume one alw...

Interpreting Effective Field Theories

An effective field theory (EFT) is a theory of the dynamics of a physical system at energies small compared to a given cut-off. Low-energy states with respect to this cut-off are effectively independent of states at high energies; hence one may study the low-energy dynamics without the need for a detailed description of the high-energy dynamics. Many authors have suggested that, because of the ...