Duality of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">x</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">ψ</mml:mi></mml:math>and a Statistical Interpretation of Space in Quantum Mechanics

Faraggi, Alon E.; Matone, Marco

doi:10.1103/physrevlett.78.163

Cited by 63 publications

(212 citation statements)

References 11 publications

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“…This is in perfect agreement with the conclusions of ref. [18] regarding Planck's constant, and also with those of ref. [13] regarding Newton's constant.…”

Section: The Uncertainty Principle On Configuration Spacementioning

confidence: 90%

Quantum Mechanics as a Spontaneously Broken Gauge Theory on a U(1) Gerbe

Isidro

2008

Int. J. Geom. Methods Mod. Phys.

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Any quantum-mechanical system possesses a U(1) gerbe naturally defined on configuration space. Acting on Feynman's kernel exp(iS/ ), this U(1) symmetry allows one to arbitrarily pick the origin for the classical action S, on a point-by-point basis on configuration space. This is equivalent to the statement that quantum mechanics is a U(1) gauge theory. Unlike Yang-Mills theories, however, the geometry of this gauge symmetry is not given by a fibre bundle, but rather by a gerbe. Since this gauge symmetry is spontaneously broken, an analogue of the Higgs mechanism must be present. We prove that a Heisenberg-like noncommutativity for the space coordinates is responsible for the breaking. This allows to interpret the noncommutativity of space coordinates as a Higgs mechanism on the quantum-mechanical U(1) gerbe.

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“…This is in perfect agreement with the conclusions of ref. [18] regarding Planck's constant, and also with those of ref. [13] regarding Newton's constant.…”

Section: The Uncertainty Principle On Configuration Spacementioning

confidence: 90%

Quantum Mechanics as a Spontaneously Broken Gauge Theory on a U(1) Gerbe

Isidro

2008

Int. J. Geom. Methods Mod. Phys.

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“…We focus here on the case of the standard-like models that contain both of the assignments shown in (2.2) and in (2.3) and therefore contain the exotic states that arise in the FSU5 and the SO64 models, as well as those that arise solely in the SLM models. In the following we adapt the notation 6) to denote the charges of the states arising in the exotic sectors. Here U(1) C and U(1) L are defined in terms of the worldsheet charges by…”

Section: Wilsonian Statesmentioning

confidence: 99%

“…However, stable supersymmetric dark matter requires reliance on a global symmetry, which ordinarily would be violated in string models [6], whereas recent observational data seem to disfavour a wide range of axion-like candidates [7]. Alternative dark matter candidates in string vacua exist in the form of hidden sector glueball dark matter [3], and Wilsonian dark matter candidates [4].…”

Section: Introductionmentioning

confidence: 99%

Wilsonian dark matter in string derived Z′ model

et al. 2017

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The dark matter issue is among the most perplexing in contemporary physics. The problem is more enigmatic due to the wide range of possible solutions, ranging from the ultra-light to the super-massive. String theory gives rise to plausible dark matter candidates due to the breaking of the nonAbelian Grand Unified Theory (GUT) symmetries by Wilson lines. The physical spectrum then contains states that do not satisfy the quantisation conditions of the unbroken GUT symmetry. Given that the Standard Model states are identified with broken GUT representations, and provided that any ensuing symmetry breakings are induced by components of GUT states, leaves a remnant discrete symmetry that forbid the decay of the Wilsonian states. A class of such states are obtained in a heterotic-string derived Z ′ model. The model exploits the spinor-vector duality symmetry, observed in the fermionic Z 2 × Z 2 heterotic-string orbifolds, to generate a Z ′ ∈ E 6 symmetry that may remain unbroken down to low energies. The E 6 symmetry is broken at the string level with discrete Wilson lines. The Wilsonian dark matter candidates in the string derived model are SO(10), and hence Standard Model, singlets and possess non-E 6 U (1) Z ′ charges. Depending on the U (1) Z ′ breaking scale and the reheating temperature they give rise to different scenarios for the relic abundance, and in accordance with the cosmological constraints.

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“…The role of the Legendre transformation in QM is related to the prepotential which appears in expressing the space coordinate in terms of the wave-function [10][11] [12].…”

Section: Introductionmentioning

confidence: 99%

Equivalence principle, higher-dimensional Möbius group and the hidden antisymmetric tensor of quantum mechanics

Bertoldi¹,

Faraggi²,

Matone³

2000

Class. Quantum Grav.

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135

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We show that the recently formulated Equivalence Principle (EP) implies a basic cocycle condition both in Euclidean and Minkowski spaces, which holds in any dimension. This condition, that in one-dimension is sufficient to fix the Schwarzian equation [6], implies a fundamental higher dimensional Möbius invariance which in turn univocally fixes the quantum version of the Hamilton-Jacobi equation. This holds also in the relativistic case, so that we obtain both the time-dependent Schrödinger equation and the Klein-Gordon equation in any dimension.We then show that the EP implies that masses are related by maps induced by the coordinate transformations connecting different physical systems. Furthermore, we show that the minimal coupling prescription, and therefore gauge invariance, arises quite naturally in implementing the EP. Finally, we show that there is an antisymmetric two-tensor which underlies Quantum Mechanics and sheds new light on the nature of the Quantum Hamilton-Jacobi equation.

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Duality ofxandψand a Statistical Interpretation of Space in Quantum Mechanics

Cited by 63 publications

References 11 publications

Quantum Mechanics as a Spontaneously Broken Gauge Theory on a U(1) Gerbe

Quantum Mechanics as a Spontaneously Broken Gauge Theory on a U(1) Gerbe

Wilsonian dark matter in string derived Z′ model

Equivalence principle, higher-dimensional Möbius group and the hidden antisymmetric tensor of quantum mechanics

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