Renormalization of the Commutative Scalar Theory with Harmonic Term to All Orders

We apply the worldline formalism to the Grosse-Wulkenhaar model and obtain an expression for the one-loop effective action which provides an efficient way for computing Schwinger functions in this theory. Using this expression we obtain the quantum corrections to the effective background and the β-functions, which are known to vanish at the selfdual point. The case of degenerate noncommutativity is also considered. Our main result can be straightforwardly applied to any polynomial self-interaction of the scalar field and we consider that the worldline approach could be useful for studying effective actions of noncommutative gauge fields as well as in other non-local models or in higher-derivative field theories.

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“…Note that dx {x 2 ⋆ φ ⋆ φ} = dx {x 2 φ 2 + θ 2 (∂φ) 2 } 7. Note that, as expected, one-loop field renormalization vanishes for θ = 0[20].…”

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confidence: 54%

Worldline approach to the Grosse-Wulkenhaar model

Viñas

Pisani

2014

J. High Energ. Phys.

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“…which becomes a renormalizable model (m = 1, 2) to all orders [52,53,54] for Ω = 0. This model possesses new interesting properties concerning its vacuum configurations [55], its Connes-Kreimer algebra [56], its symmetries [57,58], its commutative limit [59], its beta function [60] and finally its solvability for θ → ∞ [61]. Note that there exists now another renormalizable real scalar theory on the Moyal space [62,63].…”

Section: Application To Qftmentioning

confidence: 99%

Noncommutative supergeometry and quantum supergroups

Goursac

2015

J. Phys.: Conf. Ser.

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This is a review of concepts of noncommutative supergeometry -namely Hilbert superspace, C*-superalgebra, quantum supergroup -and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic analysis of Lie supergroups, non-formal deformation quantization of supermanifolds, quantum field theory on noncommutative spaces; and we give explicit examples as deformation of flat superspaces, noncommutative supertori, solvable topological quantum supergroups.

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The Jacobian Conjecture, a Reduction of the Degree to the Quadratic Case

Sportiello

Tanasă

2016

Ann. Henri Poincaré

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The Jacobian Conjecture states that any locally invertible polynomial system in C n is globally invertible with polynomial inverse. Bass et al. (Bull Am Math Soc 7(2):287-330, 1982) proved a reduction theorem stating that the conjecture is true for any degree of the polynomial system if it is true in degree three. This degree reduction is obtained with the price of increasing the dimension n. We prove here a theorem concerning partial elimination of variables, which implies a reduction of the generic case to the quadratic one. The price to pay is the introduction of a supplementary parameter 0 ≤ n ≤ n, parameter which represents the dimension of a linear subspace where some particular conditions on the system must hold. We first give a purely algebraic proof of this reduction result and we then expose a distinct proof, in a Quantum Field Theoretical formulation, using the intermediate field method.

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Renormalization of the Commutative Scalar Theory with Harmonic Term to All Orders

Cited by 3 publications

References 52 publications

Worldline approach to the Grosse-Wulkenhaar model

Worldline approach to the Grosse-Wulkenhaar model

Noncommutative supergeometry and quantum supergroups

The Jacobian Conjecture, a Reduction of the Degree to the Quadratic Case

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