Related papers: Magnetic monopoles in noncommutative quantum mecha…
We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content…
The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetric in the way the boundary conditions at $r=0$ and $r \rightarrow \infty$ are…
Building on the theory of noncommutative complex structures, the notion of a noncommutative K\"ahler structure is introduced. In the quantum homogeneous space case many of the fundamental results of classical K\"ahler geometry are shown to…
We consider Hilbert's sixth problem on the axiomatization of physics starting with a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. The two sided version of the commutation…
In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
The volume of the quantum mechanical state space over $n$-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of…
We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…
We search for a possible mathematical formulation of some of the key ideas of the relational interpretation of quantum mechanics and study their consequences. We also briefly overview some proposals of relational quantum mechanics for an…
In this paper we construct a noncommutative space of ``pointed Drinfeld modules'' that generalizes to the case of function fields the noncommutative spaces of commensurability classes of Q-lattices. It extends the usual moduli spaces of…
Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative…
This is an update on the quasicentral modulus, an invariant for an n-tuple of Hilbert space operators and a rearrangement invariant norm, that plays a key-role in sharp multivariable generalizations of the classical Weyl-von Neumann-Kuroda…
Unified theories of strong, weak and electromagnetic interactions which have electric charge quantization predict the existence of topologically stable magnetic monopoles. Intermediate scale monopoles are comparable with detection energies…
We transform static solutions of space-noncommutative Dirac-Born-Infeld theory (DBI) into static solutions of space-time noncommutative DBI. Via Seiberg-Witten map we match this symmetry transformation with a corresponding symmetry of…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
The non-perturbative solution to the strong CP problem with magnetic monopoles as originally proposed by the author is described. It is shown that the gauge orbit space with gauge potentials and gauge tranformations restricted on the space…
We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…
Analysis of state reconstruction both classical and quantum mechanical on equal footing is outlined. The meaning of "mutual unbiased bases" (MUB) of Hilbert spaces is explained in detail. An alternative quantum state reconstruction, that…
We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their…
We study the separability of the state space of loop quantum gravity. In the standard construction, the kinematical Hilbert space of the diffeomorphism-invariant states is nonseparable. This is a consequence of the fact that the knot-space…