Finite Field Theory on Noncommutative Geometries

Cho, S.; Hinterding, R.; Madore, J.; Steinacker, Harold

doi:10.1142/s0218271800000153

Cited by 52 publications

(74 citation statements)

References 45 publications

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“…An imme-diate question is how to generalize the Green function (5.2) to noncommutative instanton backgrounds. The free scalar Green function was already defined in noncommutative space in [66,67]. Using this Green function, the propagators in the noncommutative instanton background may be obtained as long as an annoying ordering problem is carefully treated.…”

Section: Discussionmentioning

confidence: 99%

Zero modes and the Atiyah-Singer index in noncommutative instantons

2002

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We study the bosonic and fermionic zero modes in noncommutative instanton backgrounds based on the ADHM construction. In k instanton background in U(N) gauge theory, we show how to explicitly construct 4Nk (2Nk) bosonic (fermionic) zero modes in the adjoint representation and 2k (k) bosonic (fermionic) zero modes in the fundamental representation from the ADHM construction. The number of fermionic zero modes is also shown to be exactly equal to the Atiyah-Singer index of the Dirac operator in the noncommutative instanton background. We point out that (super)conformal zero modes in non-BPS instantons are affected by the noncommutativity. The role of Lorentz symmetry breaking by the noncommutativity is also briefly discussed to figure out the structure of U(1) instantons.

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Section: Discussionmentioning

confidence: 99%

Zero modes and the Atiyah-Singer index in noncommutative instantons

2002

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“…This vague idea can actually be implemented by explicit calculations [123,43,49,75,17,104,23,78]. There is now however a new complication.…”

Section: The Basic Ideamentioning

confidence: 99%

“…Another concept from quantum mechanics which is useful in concrete applications is that of a coherent state. This was first used in a finite noncommutative geometry by Grosse & Prešnajder [59] and later applied [75,17,23] to the calculation of propagators on infinite noncommutative geometries, which now become regular 2-point functions and yield finite vacuum fluctuations. Although efforts have been made in this direction [23] these fluctuations have not been satisfactorily included as a source of the gravitational field, even in some 'quasi-commutative' approximation.…”

Section: Historical Introductionmentioning

confidence: 99%

Introduction to Non-Commutative Geometry

Madore¹

1999

Proceedings of Corfu Summer Institute on Elementary Particle Physics — PoS(corfu98)

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A review is made of some recent results in noncommutative geometry, especially those aspects which might in some way be of use in the study of strings and membranes. Efforts to add a gravitational field to noncommutative models of space-time are also reviewed. Special emphasis is placed on the case which could be considered as the noncommutative analog of a parallelizable space-time. It is argued that, at least in this case, there is a rigid relation between the noncommutative structure of the space-time on the one hand and the nature of the gravitational field which remains as a 'shadow' in the commutative limit on the other.

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“…To efficiently describe all evaporation phases of a black hole one must include the quantum field theory (QFT) effects in curved spacetime and ensure the controlled behavior of the theory at very high energies [29]. Noncommutativity (NCY) is one of the promising ways to approach QFT in curved spacetime [30][31][32][33][34], which arises naturally also in string theory [35][36][37][38]. It has been widely accepted that quantum gravity must entail an uncertainty principle which prevents the exact position measurement below the Planck scale [39].…”

Section: Introductionmentioning

confidence: 99%

Accretion onto a noncommutative geometry inspired black hole

Kumar

Ghosh

2017

Eur. Phys. J. C

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The spherically symmetric accretion onto a noncommutative (NC) inspired Schwarzschild black hole is treated for a polytropic fluid. The critical accretion rateṀ, sonic speed a s and other flow parameters are generalized for the NC inspired static black hole and compared with the results obtained for the standard Schwarzschild black holes. Also explicit expressions for gas compression ratios and temperature profiles below the accretion radius and at the event horizon are derived. This analysis is a generalization of Michel's solution to the NC geometry. Owing to the NC corrected black hole, the accretion flow parameters also have been modified. It turns out thatṀ ≈ M 2 is still achievable but r s seems to be substantially decreased due to the NC effects. They in turn do affect the accretion process.

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Finite Field Theory on Noncommutative Geometries

Cited by 52 publications

References 45 publications

Zero modes and the Atiyah-Singer index in noncommutative instantons

Zero modes and the Atiyah-Singer index in noncommutative instantons

Introduction to Non-Commutative Geometry

Accretion onto a noncommutative geometry inspired black hole

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