Time As a Geometric Property of Space

Chappell, James M.; Hartnett, John G.; Iannella, Nicolangelo; Iqbal, Azhar; Abbott, Derek

doi:10.3389/fphy.2016.00044

Cited by 7 publications

(7 citation statements)

References 21 publications

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“…+ -dimensional one might correspond to "dead worlds", devoid of observers, and we should find ourselves inhabiting a ( ) 3 1 + -dimensional space-time [4]. The natural description of the ( ) 3 1 + -space-time with the one-dimensional time can be provided on the base of the Clifford geometric algebra [5]. In the opposite case of multidimensional time, the violation of the causal structure of the space-time and the movement backwards in the time dimensions are possible [6].…”

Section: Introductionmentioning

confidence: 99%

Space-Time Properties as Quantum Effects. Restrictions Imposed by Grothendieck’s Scheme Theory

Lutsev¹

2019

JMP

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In this paper we consider properties of the four-dimensional space-time manifold  caused by the proposition that, according to the scheme theory, the manifold  is locally isomorphic to the spectrum of the algebra  , () Spec ≅   , where  is the commutative algebra of distributions of quantum-field densities. Points of the manifold  are defined as maximal ideals of density distributions. In order to determine the algebra  , it is necessary to define multiplication on densities and to eliminate those densities, which cannot be multiplied. This leads to essential restrictions imposed on densities and on space-time properties. It is found that the only possible case, when the commutative algebra  exists, is the case, when the quantum fields are in the space-time manifold  with the structure group () 3,1 SO (Lorentz group). The algebra  consists of distributions of densities with singularities in the closed future light cone subset. On account of the local isomorphism () Spec ≅   , the quantum fields exist only in the space-time manifold with the one-dimensional arrow of time. In the fermion sector the restrictions caused by the possibility to define the multiplication on the densities of spinor fields can explain the chirality violation. It is found that for bosons in the Higgs sector the charge conjugation symmetry violation on the densities of states can be observed. This symmetry violation can explain the matter-antimatter imbalance. It is found that in theoretical models with non-abelian gauge fields instanton distributions are impossible and tunneling effects between different topological vacua | n〉 do not occur. Diagram expansion with respect to the -algebra variables is considered.

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Section: Introductionmentioning

confidence: 99%

Space-Time Properties as Quantum Effects. Restrictions Imposed by Grothendieck’s Scheme Theory

Lutsev¹

2019

JMP

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“…At the same time, it notes that all but the (3 + 1)-dimensional one might correspond to "dead worlds", devoid of observers, and we should find ourselves inhabiting a (3 + 1)-dimensional space-time [4]. The natural description of the (3 + 1)-space-time with the one-dimensional time can be provided on the base of the Clifford geometric algebra [5]. In the opposite case of multidimensional time, the violation of the causal structure of the space-time and the movement backwards in the time dimensions are possible [6].…”

Section: Introductionmentioning

confidence: 99%

Algebra of distributions of quantum-field densities and space-time properties

Lutsev¹

2017

Preprint

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In this paper we consider properties of the space-time manifold M caused by the proposition that, according to the scheme theory, the manifold M is locally isomorphic to the spectrum of the algebra A, M ∼ = Spec(A), where A is the commutative algebra of distributions of quantumfield densities. In order to determine the algebra A, it is necessary to define multiplication on densities and to eliminate those densities, which cannot be multiplied. This leads to essential restrictions imposed on densities and on space-time properties. It is found that the only possible case, when the commutative algebra A exists, is the case, when the quantum fields are in the spacetime manifold M with the structure group SO(3, 1) (Lorentz group). The algebra A consists of distributions of densities with singularities in the closed future light cone subset. On account of the local isomorphism M ∼ = Spec(A), the quantum fields exist only in the space-time manifold with the one-dimensional arrow of time. In the fermion sector the restrictions caused by the possibility to define the multiplication on the densities of spinor fields can explain the chirality violation. It is found that for bosons in the Higgs sector the charge conjugation symmetry violation on the densities of states can be observed. This symmetry violation can explain the matter-antimatter imbalance.

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“…See[39,57] for general discussion 14. Reference[16], section 1.4 and 4.3.3;[56], sections 3 and 8 15.…”

mentioning

confidence: 99%

An alternative formalism for generating pre-Higgs ${SU}{(2)}_{L}\otimes U{(1)}_{Y}$ electroweak unification that intrinsically accommodates SU(2) left-chiral asymmetry

Wolk¹

2019

Phys. Scr.

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The technology which generated intrinsically local gauge invariant and chirally symmetric U 1 EM ( ) and SU 3 c ( ) Lagrangians is extended to include an intrinsically local gauge invariant, left-chiral SU 2 L ( ) Lagrangian for three massless vector gauge fields, thereby internally accommodating the phenomenon that only left-chiral Dirac fields interact via the W m gauge field. Pre-Higgs mechanism( ) electroweak unification is also shown to be a natural consequence of the formalism. The formalism's relation to the Poincaré group is also touched upon.

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Time As a Geometric Property of Space

Cited by 7 publications

References 21 publications

Space-Time Properties as Quantum Effects. Restrictions Imposed by Grothendieck’s Scheme Theory

Space-Time Properties as Quantum Effects. Restrictions Imposed by Grothendieck’s Scheme Theory

Algebra of distributions of quantum-field densities and space-time properties

An alternative formalism for generating pre-Higgs ${SU}{(2)}_{L}\otimes U{(1)}_{Y}$ electroweak unification that intrinsically accommodates SU(2) left-chiral asymmetry

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