Nonassociative Snyder 
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 quantum field theory

Meljanac, Stjepan; Mignemi, Salvatore; Trampetić, Josip; You, Jiangyang

doi:10.1103/physrevd.96.045021

Cited by 31 publications

(38 citation statements)

References 45 publications

(61 reference statements)

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“…3, we have only considered the momentum-conserving integrals I 1 , I 2 , and I 3 , respectively. There are, as already discussed in [44] and in the prior parts of this article, a number of momentum nonconserving ones as well. Unlike the momentum-conserving integrals, we do not have an explicit integrated expression for such integrals.…”

Section: General Considerations Of the Momentum Nonconserving Integralmentioning

confidence: 99%

“…This should give the same results as a summation over all orders in a perturbative expansion in β, like the one of [44]. We expect nonperturbative quantum effects like the celebrated UV/IR mixing in Moyal space [12] to reappear in this approach.…”

Section: Introductionmentioning

confidence: 99%

“…The general definitions of δðD 4 ðσðp 1 ; p 2 ; l; −lÞÞÞ and g 3 ðσðp 1 ; p 2 ; l; −lÞÞ are given in [44]. In particular, σ denotes a permutation P 4 over the momenta in both arguments, respectively.…”

Section: One-loop Two-point Functionsmentioning

confidence: 99%

“…Using the functional method in momentum space, the generating functional of the scalar field theory with ϕ 4 interactions on the Snyder deformed Euclidean space can be defined [44]. Considering Figs.…”

Section: One-loop Two-point Functionsmentioning

confidence: 99%

“…The Snyder model has also been treated from different points of view in [39][40][41][42][43]. Most recently, in [37] the construction of QFT on Snyder spacetime has finally started and some general formulation is proposed, but limited to the perturbative expansion with respect to deformation parameter β only [44].…”

Section: Introductionmentioning

confidence: 99%

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UV-IR mixing in nonassociative Snyder ϕ4 theory

et al. 2018

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Using a quantization of the nonassociative and noncommutative Snyder ϕ 4 scalar field theory in a Hermitian realization, we present in this article analytical formulas for the momentum-conserving part of the one-loop two-point function of this theory in D-, 4-, and 3-dimensional Euclidean spaces, which are exact with respect to the noncommutative deformation parameter β. We prove that these integrals are regularized by the Snyder deformation. These results indicate that the Snyder deformation does partially regularize the UV divergences of the undeformed theory, as it was proposed decades ago. Furthermore, it is observed that different nonassociative ϕ 4 products can generate different momentum-conserving integrals. Finally, most importantly, a logarithmic infrared divergence emerges in one of these interaction terms. We then analyze sample momentum nonconserving integral qualitatively and show that it could exhibit IR divergence too. Therefore, infrared divergences should exist, in general, in the Snyder ϕ 4 theory. We consider infrared divergences at the limit p → 0 as UV/IR mixings induced by nonassociativity, since they are associated to the matching UV divergence in the zero-momentum limit and appear in specific types of nonassociative ϕ 4 products. We also discuss the extrapolation of the Snyder deformation parameter β to negative values as well as certain general properties of one-loop quantum corrections in Snyder ϕ 4 theory at the zero-momentum limit.

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Section: General Considerations Of the Momentum Nonconserving Integralmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: One-loop Two-point Functionsmentioning

confidence: 99%

Section: One-loop Two-point Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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UV-IR mixing in nonassociative Snyder ϕ4 theory

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Noncommutativity and Nonassociativity of Closed Bosonic String on T‐dual Toroidal Backgrounds

Nikolić

Obrić

2018

Fortschritte der Physik

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In this article we consider closed bosonic string in the presence of constant metric and Kalb‐Ramond field with one non‐zero component, Bxy=Hz, where field strength H is infinitesimal. Using Buscher T‐duality procedure we dualize along x and y directions and using generalized T‐duality procedure along z direction imposing trivial winding conditions. After first two T‐dualizations we obtain Q flux theory which is just locally well defined, while after all three T‐dualizations we obtain nonlocal R flux theory. Origin of non‐locality is variable ΔV defined as line integral, which appears as an argument of the background fields. Rewriting T‐dual transformation laws in the canonical form and using standard Poisson algebra, we obtained that Q flux theory is commutative one and the R flux theory is noncommutative and nonassociative one. Consequently, there is a correlation between non‐locality and closed string noncommutativity and nonassociativity.

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Snyder-de Sitter Meets the Grosse-Wulkenhaar Model

Franchino-Viñas

Mignemi

2020

Progress and Visions in Quantum Theory in View of Gravity

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We study an interacting λ φ 4 ⋆ scalar field defined on Snyder-de Sitter space. Due to the noncommutativity as well as the curvature of this space, the renormalization of the two-point function differs from the commutative case. In particular, we show that the theory in the limit of small curvature and noncommutativity is described by a model similar to the Grosse-Wulkenhaar one. Moreover, very much akin to what happens in the Grosse-Wulkenhaar model, our computation demonstrates that there exists a fixed point in the renormalization group flow of the harmonic and mass terms.

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Nonassociative Snyder ϕ4 quantum field theory

Cited by 31 publications

References 45 publications

UV-IR mixing in nonassociative Snyder ϕ4 theory

UV-IR mixing in nonassociative Snyder ϕ4 theory

Noncommutativity and Nonassociativity of Closed Bosonic String on T‐dual Toroidal Backgrounds

Snyder-de Sitter Meets the Grosse-Wulkenhaar Model

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