<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:math>-cohomology, and classification of translation-invariant non-commutative quantum field theories

Varshovi, Amir Abbass

doi:10.1016/j.geomphys.2014.05.014

Cited by 5 publications

(6 citation statements)

References 36 publications

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“…product [22]. In this regard, our study of the NC disc could contribute to the comparison between the use of Moyal and Voros products in the formulation of field theories [23][24][25][26][27][28] in the presence of boundaries. 3 We also point out that whereas the definition of B 2 F appears as the natural extension of the procedures used to define S 2 F and T 2 F , our definition -which does not rely on the symmetries of the base manifold-could in principle be applied to quantum fields confined in an arbitrary subregion of the NC plane.…”

Section: Introductionmentioning

confidence: 90%

Boundaries in the Moyal plane

Falomir

Viñas

Pisani

et al. 2013

J. High Energ. Phys.

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We study the oscillations of a scalar field on a noncommutative disc implementing the boundary as the limit case of an interaction with an appropriately chosen confining background. The space of quantum fluctuations of the field is finite dimensional and displays the rotational and parity symmetry of the disc. We perform a numerical evaluation of the (finite) Casimir energy and obtain similar results as for the fuzzy sphere and torus.

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Section: Introductionmentioning

confidence: 90%

Boundaries in the Moyal plane

Falomir

Viñas

Pisani

et al. 2013

J. High Energ. Phys.

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“…Therefore, this redefinition can be absorbed thoroughly by the pathintegral measure and thus it never actually contributes to the scattering matrix of the theory. This is evidently a direct consequence of the "quantum equivalence theorem" which states that the whole physical effects of a (renormalizable) translation-invariant noncommutative quantum field theory are preserved through a α * -cohomology class [44].…”

Section: Generalization To All Translation-invariant Noncommutative Smentioning

confidence: 98%

“…In Refs. [44,45], it has been shown that for any ⋆ ′ there exists an appropriate function β : R 2 → R which for any set of functions, say {f 1 , . .…”

Section: Generalization To All Translation-invariant Noncommutative Smentioning

confidence: 99%

“…Essentially, using the theory of α * -cohomology [42,43] to characterize the quantum behaviors of translation-invariant noncommutative quantum field theories, has shown that [44,45] (a) The whole quantum behavior of two translation-invariant noncommutative versions of a specific renormalizable quantum field theory with two α * -cohomologous star products, say ⋆ 1 and ⋆ 2 , coincide precisely. In fact, the equality of scattering matrices of theories L ⋆ 1 and L ⋆ 2 holds for any renormalizable theory L and for each ⋆ 1 ∼ ⋆ 2 [44].…”

Section: Multi-fermion-loop Contribution To the Photon Self-energy Se...mentioning

confidence: 99%

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Perturbative effective action for the photon in noncommutative QED2 and exactness of the Schwinger mass

2018

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In this paper, we discuss the noncommutative QED 2 in the S-matrix framework. We are interested in perturbatively proving that the exact Schwinger mass μ 2 ¼ e 2 π does not receive noncommutative corrections to any order in loop expansion. In this sense, the S-matrix approach is useful since it allows us to work with the effective action Γ½A (interaction term) to compute the corresponding gauge field 1PI two-point function at higher orders. Furthermore, by means of α Ã -cohomology, we generalize the QED 2 S-matrix analysis in the Moyal star product to all translation-invariant star products.

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“…In particular we will make a complete study for the case of Translational Invariant Star Products (TISP). These products have been introduced in [6] and studied also in [7][8][9][10][11]. They all reproduce the standard commutation relation…”

Section: Introductionmentioning

confidence: 99%

Green’s functions for translation invariant star products

2015

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We calculate the Green functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both noncommutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to the two and four point functions. We find that the phenomenon of ultraviolet/infrared mixing is always a consequence of the presence of noncommuting variables. The commutative part of the product does not have the mixing.

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α∗-cohomology, and classification of translation-invariant non-commutative quantum field theories

Cited by 5 publications

References 36 publications

Boundaries in the Moyal plane

Boundaries in the Moyal plane

Perturbative effective action for the photon in noncommutative QED2 and exactness of the Schwinger mass

Green’s functions for translation invariant star products

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