Quantum field theory with the generalized uncertainty principle I: Scalar electrodynamics

Bosso, Pasquale; Das, Saurya; Todorinov, Vasil

doi:10.1016/j.aop.2020.168319

Cited by 28 publications

(20 citation statements)

References 28 publications

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“…Notice that a similar problem has been recently addressed in Refs. [25,26], where a covariant generalization of the GUP with a Lorentz invariant minimum length [69] was used to analyze quantum gravity effects on scattering amplitudes in scalar electrodynamics. Clearly, such a covariant formulation would also pave the way for a direct extension of the QFT with the GUP to some other background besides Minkowski spacetime.…”

Section: Discussionmentioning

confidence: 99%

“…[13]. Furthermore, we set A = 0, the other orderings being recovered via the prescription (25). In this context, the transforms in Eqs.…”

Section: Momentum and (Quasi-)position Representationsmentioning

confidence: 99%

“…Implications of theories with a fundamental length are often addressed by deforming the Heisenberg Uncertainty Principle (HUP) in such a way as to accommodate a minimum uncertainty in position at Planck scale. The ensuing relation, commonly known as Generalized Uncertainty Principle (GUP), has been studied in a variety of contexts, ranging from quantum theory [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], to black hole physics [31][32][33][34][35][36][37][38][39][40][41][42][43][44] and cosmology [45,46]. Potential effects of a modified Heisenberg algebra have also been explored in graphene [47], where the minimal length is provided by the honeycomb lattice spacing.…”

Section: Introductionmentioning

confidence: 99%

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Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Bosso

Luciano

2021

Eur. Phys. J. C

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Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

show abstract

Section: Discussionmentioning

confidence: 99%

“…[13]. Furthermore, we set A = 0, the other orderings being recovered via the prescription (25). In this context, the transforms in Eqs.…”

Section: Momentum and (Quasi-)position Representationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Bosso

Luciano

2021

Eur. Phys. J. C

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“…Notice that a similar problem has been recently addressed in Refs. [23], where a covariant generalization of the GUP with a Lorentz invariant minimum length [66] was used to analyze quantum gravity effects on scattering amplitudes in scalar electrodynamics. Clearly, such a covariant formulation would also pave the way for a direct extension of the QFT with the GUP to some other background besides Minkowski spacetime.…”

Section: Discussionmentioning

confidence: 99%

“…Implications of theories with a fundamental length are often addressed by deforming the Heisenberg Uncertainty Principle (HUP) in such a way as to accommodate a minimum uncertainty in position at Planck scale. The ensuing relation, commonly known as Generalized Uncertainty Principle (GUP), has been studied in a variety of contexts, ranging from quantum theory [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], to black hole physics [28][29][30][31][32][33][34][35][36][37][38][39][40][41] and cosmology [42,43]. Potential effects of a modified Heisenberg algebra have also been explored in graphene [44], where the minimal length is provided by the honeycomb lattice spacing.…”

Section: Introductionmentioning

confidence: 99%

Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model

Bosso,

Luciano

2021

Preprint

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Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg Uncertainty Principle into the Generalized Uncertainty Principle. In this work, we study the implications of a polynomial Generalized Uncertainty Principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the Generalized Uncertainty Principle.

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Effective GUP-modified Raychaudhuri equation and black hole singularity: four models

Blanchette

Das

Rastgoo

2021

J. High Energ. Phys.

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The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically all spacetimes. We compute the generic corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole, arising from modifications to the algebra inspired by the generalized uncertainty principle (GUP) theories. Then we study four specific models of GUP, compute their effective dynamics as well as their expansion and its rate of change using the Raychaudhuri equation. We show that the modification from GUP in two of these models, where such modifications are dependent of the configuration variables, lead to finite Kretchmann scalar, expansion and its rate, hence implying the resolution of the singularity. However, the other two models for which the modifications depend on the momenta still retain their singularities even in the effective regime.

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Quantum field theory with the generalized uncertainty principle I: Scalar electrodynamics

Cited by 28 publications

References 28 publications

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model

Effective GUP-modified Raychaudhuri equation and black hole singularity: four models

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