On Hansen’s Version of Spectral Theory and the Moyal Product

Hennings, Mark A.; Dubin, D. A.

doi:10.2977/prims/1260476653

Cited by 3 publications

(4 citation statements)

References 24 publications

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“…It appears that the computations of the loop diagrams can be rather easily performed, thanks to the simple structure of the star-product (16). We refer to [19], [23], [24] for technical details.…”

Section: Past (One-loop) Results For Noncommutative Scalar Fields The...mentioning

confidence: 99%

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Gauge Theories on kappa-Minkowski spaces: Results and prospects.

Wallet¹,

Hersent²

2022

Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)

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Recent results obtained in -Poincaré invariant gauge theories on -Minkowski space are reviewed and commented. A Weyl quantization procedure can be applied to convolution algebras to derive a convenient star product. For such a star product, gauge invariant polynomial action functional depending on the curvature exists only in 5 dimensions. The corresponding noncommutative differential calculus and the related connection are twisted together with the BRST structure linked to the gauge invariance. Phenomenological consequences stemming from the existence of one extra dimension are commented. Some consequences of the appearance of a non-vanishing one-loop tadpole upon BRST gauge-fixing are discussed.

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Section: Past (One-loop) Results For Noncommutative Scalar Fields The...mentioning

confidence: 99%

“…the right-invariant measure) defines a twisted trace w.r.t. the star-product (16), which is expressed by the following formula…”

Section: Pos(corfu2021)286mentioning

confidence: 99%

Gauge Theories on kappa-Minkowski spaces: Results and prospects.

Wallet¹,

Hersent²

2022

Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)

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“…See e.g. [16] for a convenient presentation. One essential ingredient of the above scheme is the use of convolution algebras.…”

Section: Convolution Algebras and Weyl Quantizationmentioning

confidence: 99%

Gauge theory models on $κ$-Minkowski space: Results and prospects

Hersent¹,

Wallet²

2022

Preprint

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Recent results obtained in κ-Poincaré invariant gauge theories on κ-Minkowski space are reviewed and commented. A Weyl quantization procedure can be applied to convolution algebras to derive a convenient star product. For such a star product, gauge invariant polynomial action functional depending on the curvature exists only in 5 dimensions. The corresponding noncommutative differential calculus and the related connection are twisted together with the BRST structure linked to the gauge invariance. Phenomenological consequences stemming from the existence of one extra dimension are commented. Some consequences of the appearance of a non-vanishing one-loop tadpole upon BRST gauge-fixing are discussed.

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“…Here, the composition law can be directly read from (2.3) and reflects the nontrivial coproduct structure of the κ-Poincaré algebra, see (A4). Let π U ∶ G 2 → BðHÞ denote a (strongly continuous) unitary representation of G 2 where H is some suitable Hilbert space and BðHÞ is the (C Ã -)algebra of bounded operators on H. A star product defining the 2-dimensional κ-Minkowski space can be obtained in a way similar to the usual Weyl quantization leading to the construction of Moyal product on the Moyal plane R 2 θ , see [41], the Heisenberg algebra and Heisenberg group being replaced now by (2.1) and G 2 (2.6) respectively. Accordingly, it is convenient to start from L 1 ðG 2 Þ, the convolution algebra of G 2 .…”

Section: κ-Minkowski Space As a Group Algebramentioning

confidence: 99%

κ -Poincaré invariant quantum field theories with Kubo-Martin-Schwinger weight

2018

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A natural star product for 4-d κ-Minkowski space is used to investigate various classes of κ-Poincaré invariant scalar field theories with quartic interactions whose commutative limit coincides with the usual ϕ 4 theory. κ-Poincaré invariance forces the integral involved in the actions to be a twisted trace, thus defining a Kubo-Martin-Schwinger (KMS) weight for the noncommutative (C Ã -)algebra modeling the κ-Minkowski space. In all the field theories, the twist generates different planar one-loop contributions to the 2-point function which are at most UV linearly diverging. Some of these theories are free of UV/IR mixing. In the others, UV/IR mixing shows up in non-planar contributions to the 2-point function at exceptional zero external momenta while staying finite at nonzero external momenta. These results are discussed together with the possibility for the KMS weight relative to the quantum space algebra to trigger the appearance of KMS state on the algebra of observables.

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On Hansen’s Version of Spectral Theory and the Moyal Product

Cited by 3 publications

References 24 publications

Gauge Theories on kappa-Minkowski spaces: Results and prospects.

Gauge Theories on kappa-Minkowski spaces: Results and prospects.

Gauge theory models on $κ$-Minkowski space: Results and prospects

κ -Poincaré invariant quantum field theories with Kubo-Martin-Schwinger weight

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