In this paper, I introduce an intrinsic account of the quantum state. This account contains three desirable features that the standard platonistic account lacks: (1) it does not refer to any abstract mathematical objects such as complex numbers, (2) it is independent of the usual arbitrary conventions in the wave function representation, and (3) it explains why the quantum state has its amplitude and phase degrees of freedom. -/- Consequently, this account extends Hartry Field’s program outlined in Science Without Numbers (...) (1980), responds to David Malament’s long-standing impossibility conjecture (1982), and establishes an important first step towards a genuinely intrinsic and nominalistic account of quantum mechanics. I will also compare the present account to Mark Balaguer’s (1996) nominalization of quantum mechanics and discuss how it might bear on the debate about “wave function realism.” In closing, I will suggest some possible ways to extend this account to accommodate spinorial degrees of freedom and a variable number of particles (e.g. for particle creation and annihilation). -/- Along the way, I axiomatize the quantum phase structure as what I shall call a “periodic difference structure” and prove a representation theorem as well as a uniqueness theorem. These formal results could prove fruitful for further investigation into the metaphysics of phase and theoretical structure. -/- (For a more recent version of this paper, please see "The Intrinsic Structure of Quantum Mechanics" available on PhilPapers.). (shrink)

We reconsider the quantum theory of indistinguishable particles on the basis of Rieffel's notion of C*-algebraic deformation quantization. Using this formalism, we relate the operator approach of Messiah and Greenberg to the configuration space approach due to Laidlaw and DeWitt, Leinaas and Myrheim, and others. The former allows parastatistics, whereas the latter apparently leaves room for bosons and fermions only. This seems to contradict the operator approach as far as the admissibility of parastatistics is concerned. To resolve this, we first (...) prove that the topologically nontrivial configuration spaces of the second approach are quantized by the algebras of observables of the first. Second, we show that the irreducible representations of the latter may be realized by vector bundle constructions, which include the line bundles of the second approach: representations on higher-dimensional bundles cannot be excluded a priori. However, we show that the corresponding particle states may always be realized in terms of bosons and/or fermions with an unobserved internal degree of freedom. Although based on non-relativistic quantum mechanics, this conclusion is analogous to the rigorous results of the Doplicher-Haag-Roberts analysis in algebraic quantum field theory, as well to the heuristic arguments which led Gell-Mann and others to QCD. (shrink)

La meccanica quantistica è una delle più grandi conquiste intellettuali del xx secolo. Le sue leggi regolano il mondo atomico e subatomico e si riverberano su una miriade di fenomeni del mondo macroscopico, dalla formazione dei cristalli alla superconduttività, dalle proprietà dei fluidi a bassa temperatura agli spettri di emissione di una candela che brucia o di una supernova che esplode, dai meccanismi di combustione della fornace solare ai principi di base delle nanotecnologie. Non c’è quasi nulla nel mondo che (...) ci circonda su cui non soffi l’alito delle leggi quantistiche. Tuttavia, per come è usualmente presentata nei libri di testo, la meccanica quantistica è sostanzialmente un’insieme di regole per calcolare le distribuzioni di probabilità dei risultati di qualunque esperimento (nel dominio di validità della meccanica quantistica). In quanto tale, non ci fornisce direttamente una descrizione della realtà. Una descrizione della realtà, cioè un’ontologia, dovrebbe dirci che cosa c’è nel mondo e come si comporta, quali sono i processi che si realizzano a livello microscopico e, di conseguenza, fornirci una spiegazione del formalismo quantistico. (shrink)