Superposition principle in Algebraic quantum theory

Horuzhy, S. S.

doi:10.1007/bf01036150

Cited by 5 publications

(11 citation statements)

References 7 publications

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“…For some of the implications for foundations issues, see Earman and Ruetsche (2007). 17 For a general discussion of the superposition principle in the algebraic formulation of QM, see Horuzhy (1975). (iii)(b) and (iii)(c) sometime hold and sometime fail. 18 The failure of (iii)(b) can be expressed as follows.…”

Section: Weak Superselection Rulesmentioning

confidence: 98%

Superselection Rules for Philosophers

Earman

2008

Erkenn

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The overaraching goal of this paper is to elucidate the nature of superselection rules in a manner that is accessible to philosophers of science and that brings out the connections between superselection and some of the most fundamental interpretational issues in quantum physics. The formalism of von Neumann algebras is used to characterize three different senses of superselection rules (dubbed, weak, strong, and very strong) and to provide useful necessary and sufficient conditions for each sense. It is then shown how the Haag-Kastler algebraic approach to quantum physics holds the promise of a uniform and comprehensive account of the origin of superselection rules. Some of the challenges that must be met before this promise can be kept are discussed. The focus then turns to the role of superselection rules in solutions to the measurement problem and the emergence of classical properties. It is claimed that the role for ''hard'' superselection rules is limited, but ''soft'' (a.k.a. environmental) superselection rules or N. P. Landsman's situational superselection rules may have a major role to play. Finally, an assessment is given of the recently revived attempts to deconstruct superselection rules.

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Section: Weak Superselection Rulesmentioning

confidence: 98%

Superselection Rules for Philosophers

Earman

2008

Erkenn

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“…As is known [38], there are unit rays which are physically unrealizable. There exist physical restrictions (superselection rules) on the execution of superposition principle (for more details see [39,40,41]). In 1952, Wigner, Wightman and Wick [38] showed that existence of superselection rules is related with the measurability of relative phase of the superposition.…”

Section: Coherent Subspacesmentioning

confidence: 99%

Spinor Structure and Matter Spectrum

Варламов

2016

Int J Theor Phys

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Classification of relativistic wave equations is given on the ground of interlocking representations of the Lorentz group. A system of interlocking representations is associated with a system of eigenvector subspaces of the energy operator. Such a correspondence allows one to define matter spectrum, where the each level of this spectrum presents a some state of elementary particle. An elementary particle is understood as a superposition of state vectors in nonseparable Hilbert space. Classification of indecomposable systems of relativistic wave equations is produced for bosonic and fermionic fields on an equal footing (including Dirac and Maxwell equations). All these fields are equivalent levels of matter spectrum, which differ from each other by the value of mass and spin. It is shown that a spectrum of the energy operator, corresponding to a given matter level, is non-degenerate for the fields of type $(l,0)\oplus(0,l)$, where $l$ is a spin value, whereas for arbitrary spin chains we have degenerate spectrum. Energy spectra of the stability levels (electron and proton states) of the matter spectrum are studied in detail. It is shown that these stability levels have a nature of threshold scales of the fractal structure associated with the system of interlocking representations of the Lorentz group.Comment: 36 page

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“…Since the state space of a particle involved in the OCS is complete (see, e.g., [23]) (and no matter what stage of this process is regarded), the self-adjoint operator σ 3 can be treated (see [4] as well as [5]) as the superselection operator which divides the state space H rig as , in the k-representation, into two coherent (superselection) sectors (H rig as is the rigged Hilbert space H rig associated with the initial and final stages of the OCS):…”

Section: K-representationmentioning

confidence: 99%

“…According to the modern theory of SSRs [3][4][5][6][7][8] any superposition of pure states from the same coherent sector represents another pure state in this sector, while any superposition of pure states from different sectors represents a mixed state. In order to illustrate one feature of such a kind superpositions let us consider the following example.…”

Section: K-representationmentioning

confidence: 99%

“…At the present the SSRs are associated with the prohibition of coherent superpositions of pure states of particles with different spins, electric charges, masses, etc. (see [1,2] and [3][4][5][6][7][8][9][10]). With regard to pure one-particle states associated with the same spin, charge and mass, the modern quantum theory does not imply the existence of SSRs which would restrict the action of the superposition principle in this class of states.…”

Section: Introductionmentioning

confidence: 99%

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Dichotomous-context-induced superselection rule for a one-dimensional completed scattering

Chuprikov

2014

Preprint

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It is shown that in the state space of a quantum particle involved in a one-dimensional completed scattering (OCS) there is a superselection rule (SSR) induced by the dichotomous physical context that determines the properties of a quantum ensemble of scattering particles in the disjoint spatial regions located on the different sides of the potential barrier at asymptotically large distances from it. At the initial stage of the OCS this context is associated, in the general case, with two sources of particles located on the different sides of the barrier; and at the final stage it is associated, in the general case, with two particle detectors located on different sides of the barrier. The role of a superselection operator is played by the Pauli matrix σ 3 that divides the space of in-and out-asymptotes into two coherent sectors. In the course of the OCS, its unitary quantum dynamics crosses these sectors. In particular, in the scattering problem with one source and two detectors, a pure initial state of a particle is converted into a mixed final state. According to this rule, the OCS is a complex quantum process consisting of two coherent subprocesses -transmission and reflection; the average value of any observable as well as characteristic times can be defined for the subprocesses only. It is shown that the quantum dynamics of both subprocesses at all stages of scattering is uniquely determined by the initial state of the whole ensemble of particles and by the final states of transmitted and reflected particles.

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Superposition principle in Algebraic quantum theory

Cited by 5 publications

References 7 publications

Superselection Rules for Philosophers

Superselection Rules for Philosophers

Spinor Structure and Matter Spectrum

Dichotomous-context-induced superselection rule for a one-dimensional completed scattering

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