The tridecompositional uniqueness theorem of Elby and Bub (1994) shows that a wavefunction in a triple tensor product Hilbert space has at most one decomposition into a sum of product wavefunctions with each set of component wavefunctions linearly independent. I demonstrate that, in many circumstances, the unique component wavefunctions and the coefficients in the expansion are both hopelessly ...

We derive all the axi-symmetric, vacuum and electrovac extremal isolated horizons. It turns out that for every horizon in this class, the induced metric tensor, the rotation 1-form potential and the pullback of the electromagnetic field necessarily coincide with those induced by the monopolar, extremal Kerr– Newman solution on the event horizon. We also discuss the general case of a symmetric, ...

the series on the right of (3) being called the Fourier Eigenfunction Series and a. the Fourier Coefficients of f(x, y). I have studied elsewhere' the problem of convergence and summability of a Fourier Eigenfunction Series. In this note I am interested in announcing a result on uniqueness of eigenfunction expansion. Actually, we have thfe following, THEOREM. Let us suppose we are given an eige...

This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called “rigging maps” associated with Refined Algebraic Quantization, a particular realization of the Dirac scheme. Our main result is to provide a condition under which the rigging map is unique, in which case we also show that it is given by group averaging techni...

Ten years ago, Dobrushin [1] proved a beautiful result showing that under suitable hypotheses, a statistical mechanical lattice system interaction has a unique equilibrium state. In particular, there is no long range order, etc. see [6,7] for related material, Israel [4] for analyticity results and Gross [3] for falloff of correlations. There does not appear to have been systematic attempts to ...

We obtain a mathematically simple characterization of all functionals coinciding with the von Neumann reduced entropy on pure states based on the Khinchin-Faddeev axiomatization of Shannon entropy and give a physical interpretation of the axioms in terms of entanglement.

The stability of physical systems depends on the existence of a state of least energy, or ground state. In gravity, this is guaranteed by the positive energy theorem. The proof employs spinor structure and can fail for certain spacetime topologies, such as those arising in non-supersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. The proof also fails for...