Quantum field theory with the generalized uncertainty principle II: Quantum Electrodynamics

Bosso, Pasquale; Das, Saurya; Todorinov, Vasil

doi:10.1016/j.aop.2020.168350

Cited by 16 publications

(11 citation statements)

References 31 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%

“…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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Bosso

Luciano

2021

Eur. Phys. J. C

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“…3. Effective Quantum Field Theory with minimum length 64,65 Having cleared up the frame dependence and the composition law problem for our model, we can proceed to apply it to quantum field theory.…”

Section: Lorentz Invariant Minimum Length and The Composition Law Pro...mentioning

confidence: 99%

“…The calculations for the scattering amplitudes can be quite cumbersome so we will not present them in full here. If the reader is interested the full calculations are presented in 64,65,69 .…”

Section: Rgup Corrections To Qed Scattering Amplitudesmentioning

confidence: 99%

Effective field theory from Relativistic Generalized Uncertainty

Todorinov¹,

Das²,

Bosso³

2022

Preprint

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Theories of Quantum Gravity predict a minimum measurable length and a corresponding modification of the Heisenberg Uncertainty Principle to the so-called Generalized Uncertainty Principle (GUP). However, this modification is usually formulated in nonrelativistic language, making it unclear whether the minimum length is Lorentz invariant. We have formulated a Relativistic Generalized Uncertainty Principle, resulting in a Lorentz invariant minimum measurable length and the resolution of the composition law problem. This proved to be an important step in the formulation of Quantum Field Theory with minimum length. We derived the Lagrangians consistent with the existence of minimal length and describing the behaviour of scalar, spinor, and U(1) gauge fields. We calculated the Feynman rules (propagators and vertices) associated with these Lagrangians. Furthermore, we calculated the Quantum Gravity corrected scattering cross-sections for a lepton-lepton scattering. Finally, we compared our results with current experiments, which allowed us to improve the bounds on the scale at which quantum gravity phenomena will become relevant.

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“…It is widely assumed by physicists from last few decades that an existence of a minimal length is necessary for the consistent formulation of quantum gravity theories and it has been observed from the studies of blackhole that for any type of quantum gravity theory to exist, there should first exist a minimum measurable length in the theory that is near the magnitude of Plank's length. References for studying quantum theories at minimal length are [1][2][3][4][5][6][7][8][9][10][11][12]. Further exposure to the references regarding minimal length gravity theories alongside with quantum mechanics and quantum field theories can be found in [13].…”

Section: Introductionmentioning

confidence: 99%

Rotationally Symmetric Yang-Mills Gauge Theory and Generalized Uncertainty Principle

Omprakash¹

2022

Trends Sci

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Recently, it has been of considerably high interest to introduce the notion of minimal length in quantum mechanics and quantum field theories to get a proper description of quantum gravity. In this paper, we have attempted to unify the notion of minimal length with R×S^3 topological field theories which were introduced by Carmeli and Malin in 1985 [14]. We have collectively called this (R×S^3 )_H topological field theories where the “H” in the sub-script stands for Heisenberg’s notion of minimal length. A proper description for equations like Schrodinger’s equation, Klein-Gordon equation and QED, QCD Lagrangian on (R×S^3 )_H topology is derived. HIGHLIGHTS It has been of considerably high interest to incorporate existing theories with the notion of minimal length because it is thought to unify theories at large scale with the quantum world In this paper, we have done a similar unification by incorporating Rotaionally symmetric field theories with the notion of minimal length The derived equations work consistently under local and global gauge transformations

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Quantum field theory with the generalized uncertainty principle II: Quantum Electrodynamics

Cited by 16 publications

References 31 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

Effective field theory from Relativistic Generalized Uncertainty

Rotationally Symmetric Yang-Mills Gauge Theory and Generalized Uncertainty Principle

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