Structure, classifcation, and conformal symmetry, of elementary particles over non-archimedean space-time

It is known that no length or time measurements are possible in sub-Planckian regions of spacetime. The Volovich hypothesis postulates that the micro-geometry of spacetime may therefore be assumed to be non-archimedean. In this letter, the consequences of this hypothesis for the structure, classification, and conformal symmetry of elementary particles, when spacetime is a flat space over a non-archimedean field such as the $p$-adic numbers, is explored. Both the Poincar\'e and Galilean groups are treated. The results are based on a new variant of the Mackey machine for projective unitary representations of semidirect product groups which are locally compact and second countable. Conformal spacetime is constructed over $p$-adic fields and the impossibility of conformal symmetry of massive and eventually massive particles is proved

The structure of the quantum mechanical state space and induced superselection rules

The role of superselection rules for the derivation of classical probability within quantum mechanics is investigated and examples of superselection rules induced by the environment are discussed.Comment: 11 pages, Standard Latex 2.0

Emergence of quantum mechanics from classical statistics

The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables "measure" properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem.Comment: clearer distinction between system and quantum observables, new references, 13 page

Physical propositions and quantum languages

The word \textit{proposition} is used in physics with different meanings, which must be distinguished to avoid interpretational problems. We construct two languages $\mathcal{L}^{\ast}(x)$ and $\mathcal{L}(x)$ with classical set-theoretical semantics which allow us to illustrate those meanings and to show that the non-Boolean lattice of propositions of quantum logic (QL) can be obtained by selecting a subset of \textit{p-testable} propositions within the Boolean lattice of all propositions associated with sentences of $\mathcal{L}(x)$. Yet, the aforesaid semantics is incompatible with the standard interpretation of quantum mechanics (QM) because of known no-go theorems. But if one accepts our criticism of these theorems and the ensuing SR (semantic realism) interpretation of QM, the incompatibility disappears, and the classical and quantum notions of truth can coexist, since they refer to different metalinguistic concepts (\textit{truth} and \textit{verifiability according to QM}, respectively). Moreover one can construct a quantum language $\mathcal{L}_{TQ}(x)$ whose Lindenbaum-Tarski algebra is isomorphic to QL, the sentences of which state (testable) properties of individual samples of physical systems, while standard QL does not bear this interpretation.Comment: 15 pages, no figure, standard Late

A Topos Perspective on State-Vector Reduction

A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all $M$-sets, where $M$ is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way. However, the formalism also suggests a new way of constructing a `neo-realist' interpretation of quantum theory in which the truth values of propositions are determined by the actions of the monoid of strings of finite projection operators. By these means, a novel topos perspective is gained on the concept of state-vector reduction

Extended Representations of Observables and States for a Noncontextual Reinterpretation of QM

A crucial and problematical feature of quantum mechanics (QM) is nonobjectivity of properties. The ESR model restores objectivity reinterpreting quantum probabilities as conditional on detection and embodying the mathematical formalism of QM into a broader noncontextual (hence local) framework. We propose here an improved presentation of the ESR model containing a more complete mathematical representation of the basic entities of the model. We also extend the model to mixtures showing that the mathematical representations of proper mixtures does not coincide with the mathematical representation of mixtures provided by QM, while the representation of improper mixtures does. This feature of the ESR model entails that some interpretative problems raising in QM when dealing with mixtures are avoided. From an empirical point of view the predictions of the ESR model depend on some parameters which may be such that they are very close to the predictions of QM in most cases. But the nonstandard representation of proper mixtures allows us to propose the scheme of an experiment that could check whether the predictions of QM or the predictions of the ESR model are correct.Comment: 17 pages, standard latex. Extensively revised versio

Generalization of entanglement to convex operational theories: Entanglement relative to a subspace of observables

We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This extends the notion of ordinary entanglement in quantum information theory to a much more general framework. Some important special cases are described, in which the distinguished observables are subspaces of the observables of a quantum system, leading to results like the identification of generalized unentangled states with Lie-group-theoretic coherent states when the special observables form an irreducibly represented Lie algebra. Some open problems, including that of generalizing the semigroup of local operations with classical communication to the convex cones setting, are discussed.Comment: 19 pages, to appear in proceedings of Quantum Structures VII, Int. J. Theor. Phy

Continuous slice functional calculus in quaternionic Hilbert spaces

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic $C^*$--algebras and to define, on each of these $C^*$--algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews in Mathematical Physic

Non-additive probabilities and quantum logic in finite quantum systems

YesA quantum system Σ(d) with variables in Z(d) and with Hilbert space H(d), is considered. It is shown that the additivity relation of Kolmogorov probabilities, is not valid in the Birkhoff-von Neumann orthocomplemented modular lattice of subspaces L(d). A second lattice Λ(d) which is distributive and contains the subsystems of Σ(d) is also considered. It is shown that in this case also, the additivity relation of Kolmogorov probabilities is not valid. This suggests that a more general (than Kolmogorov) probability theory is needed, and here we adopt the Dempster-Shafer probability theory. In both of these lattices, there are sublattices which are Boolean algebras, and within these 'islands' quantum probabilities are additive

Search for Blue Compact Dwarf Galaxies During Quiescence

Blue Compact Dwarf (BCD) galaxies are metal poor systems going through a major starburst that cannot last for long. We have identified galaxies which may be BCDs during quiescence (QBCD), i.e., before the characteristic starburst sets in or when it has faded away. These QBCD galaxies are assumed to be like the BCD host galaxies. The SDSS/DR6 database provides ~21500 QBCD candidates. We also select from SDSS/DR6 a complete sample of BCD galaxies to serve as reference. The properties of these two galaxy sets have been computed and compared. The QBCD candidates are thirty times more abundant than the BCDs, with their luminosity functions being very similar except for the scaling factor, and the expected luminosity dimming associated with the end of the starburst. QBCDs are redder than BCDs, and they have larger HII region based oxygen abundance. QBCDs also have lower surface brightness. The BCD candidates turn out to be the QBCD candidates with the largest specific star formation rate (actually, with the largest H_alpha equivalent width). One out of each three dwarf galaxies in the local universe may be a QBCD. The properties of the selected BCDs and QBCDs are consistent with a single sequence in galactic evolution, with the quiescent phase lasting thirty times longer than the starburst phase. The resulting time-averaged star formation rate is low enough to allow this cadence of BCD -- QBCD phases during the Hubble time.Comment: Accepted for publication in ApJ. 17 pages. 13 Fig