Diffusion on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>κ</mml:mi></mml:mrow></mml:math>-Minkowski space

Arzano, Michele; Trześniewski, Tomasz

doi:10.1103/physrevd.89.124024

Cited by 59 publications

(125 citation statements)

References 28 publications

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“…The left-hand side is gauge invariant and, therefore, so is the right-hand side. Saturating with D ν yields the deformed conservation law (18). In the non-Abelian case, the left-hand side of Eq.…”

Section: Interacting Fermionsmentioning

confidence: 99%

“…The transition between the two regimes varies depending on the model but it is continuous in general. Examples include causal dynamical triangulations [5][6][7], asymptotically safe quantum gravity [8,9], loop quantum gravity and spin foams [10][11][12], Hořava-Lifshitz gravity [7,9,13], noncommutative geometry [14][15][16] and κ-Minkowski spacetime [17,18], nonlocal quantum gravity [19], Stelle's gravity [20], spacetimes with black holes [21][22][23], fuzzy spacetimes [24], random combs [25,26], random multigraphs [27,28], and causal sets [29].…”

Section: A Dimensional Flow and Multiscale Theoriesmentioning

confidence: 99%

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Standard Model in multiscale theories and observational constraints

2016

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We construct and analyze the Standard Model of electroweak and strong interactions in multiscale spacetimes with (i) weighted derivatives and (ii) q-derivatives. Both theories can be formulated in two different frames, called fractional and integer picture. By definition, the fractional picture is where physical predictions should be made. (i) In the theory with weighted derivatives, it is shown that gauge invariance and the requirement of having constant masses in all reference frames make the Standard Model in the integer picture indistinguishable from the ordinary one. Experiments involving only weak and strong forces are insensitive to a change of spacetime dimensionality also in the fractional picture, and only the electromagnetic and gravitational sectors can break the degeneracy. For the simplest multiscale measures with only one characteristic time, length and energy scale t Ã , l Ã and E Ã , we compute the Lamb shift in the hydrogen atom and constrain the multiscale correction to the ordinary result, getting the absolute upper bound t Ã < 10 −23 s. For the natural choice α 0 ¼ 1=2 of the fractional exponent in the measure, this bound is strengthened to t Ã < 10 −29 s, corresponding to l Ã < 10 −20 m and E Ã > 28 TeV. Stronger bounds are obtained from the measurement of the fine-structure constant.(ii) In the theory with q-derivatives, considering the muon decay rate and the Lamb shift in light atoms, we obtain the independent absolute upper bounds t Ã < 10 −13 s and E Ã > 35 MeV. For α 0 ¼ 1=2, the Lamb shift alone yields t Ã < 10

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Section: Interacting Fermionsmentioning

confidence: 99%

Section: A Dimensional Flow and Multiscale Theoriesmentioning

confidence: 99%

Standard Model in multiscale theories and observational constraints

2016

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“…Finally, D S (T ) may be modified through non-trivial quantum fluctuations of spacetime predicted by a fundamental theory of gravity. This set includes the multifractal spacetimes occurring in the gravitational Asymptotic Safety program [33,[45][46][47][48], the microscopic structure of spacetime within Loop Quantum Gravity [49][50][51][52][53][54], Causal Set Theory [55] or the propagation of particles on κ-Minkowski [56,57] and other non-commutative spaces [58].…”

Section: Introductionmentioning

confidence: 99%

Spectral dimensions from the spectral action

2015

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The generalised spectral dimension DS(T ) provides a powerful tool for comparing different approaches to quantum gravity. In this work, we apply this formalism to the classical spectral actions obtained within the framework of almost-commutative geometry. Analysing the propagation of spin-0, spin-1 and spin-2 fields, we show that a non-trivial spectral dimension arises already at the classical level. The effective field theory interpretation of the spectral action yields plateaustructures interpolating between a fixed spin-independent DS(T ) = dS for short and DS(T ) = 4 for long diffusion times T . Going beyond effective field theory the spectral dimension is completely dominated by the high-momentum properties of the spectral action, yielding DS(T ) = 0 for all spins. Our results support earlier claims that high-energy bosons do not propagate.

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“…In this case the generators of the corresponding Lie algebra are given by combinations of the generators of the Lie algebra so(n + 1, 1) and are represented by (n + 2) × (n + 2) matrices [46]. However, in order to include translations, to obtain a matrix representation for the Lie algebra t ⊕ an(n), it will be necessary to work in a different representation.…”

Section: D(t ) = T ×An(n)mentioning

confidence: 99%

“…The Lie algebra an(n), when its generators are identified with space-time coordinates, is known in the literature as the n + 1-dimensional κ-Minkowski space. For further technical details on κ-deformations the interested reader can consult [37][38][39][40][41][42][43][44][45][46]. The main goal of this Section will be to show that starting from minimal ingredients, namely the structures constants the Lie algebra an(n),…”

Section: Deforming Momentum Space To the An (N) Groupmentioning

confidence: 99%

Deformed phase spaces with group valued momenta

Arzano

Nettel

2016

Phys. Rev. D

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We introduce a general framework for describing deformed phase spaces with group valued momenta. Using techniques from the theory of Poisson-Lie groups and Lie bi-algebras we develop tools for constructing Poisson structures on the deformed phase space starting from the minimal input of the algebraic structure of the generators of the momentum Lie group. The tools developed are used to derive Poisson structures on examples of group momentum space much studied in the literature such as the n-dimensional generalization of the κ-deformed momentum space and the SL(2, Ê) momentum space in three space-time dimensions. We discuss classical momentum observables associated to multi-particle systems and argue that these combine according the usual four-vector addition despite the non-abelian group structure of momentum space.

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Diffusion onκ-Minkowski space

Cited by 59 publications

References 28 publications

Standard Model in multiscale theories and observational constraints

Standard Model in multiscale theories and observational constraints

Spectral dimensions from the spectral action

Deformed phase spaces with group valued momenta

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