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REVIEW 3 major objections 5 minor 57 references

Yang-Mills Field in the $\kappa$-space-time

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper constructs an SU(N) Yang-Mills theory on κ-Minkowski spacetime, to first order in the deformation parameter, with deformed field strengths given by the ordinary ones rescaled by energy-dependent factors and with an action…

desk verdict The SU(N) extension is a reasonable idea, but the construction is internally inconsistent because p0 is treated as both a differential operator and a c-number. read the letter →

arxiv 2411.11501 v6 pith:CL7ZH3OM submitted 2024-11-18 hep-th gr-qchep-ph

Bhagya. R , E. Harikumar This is my paper · ORCID
classification hep-thgr-qchep-ph MSC 81T1381R60 PACS 11.15.-q02.40.Gh
keywords κ-MinkowskispacetimeSU(N)Yang-MillstheorynoncommutativegaugedeformedfieldstrengthJacobiidentityisospin-carryingparticledeformationparametercommutativelimit
topics Yang-Mills Mass Gap
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper constructs an SU(N) Yang-Mills theory on κ-Minkowski spacetime, keeping only terms linear in the deformation parameter $a$. It claims that the deformed field strength is the ordinary field strength multiplied by an energy-dependent factor: the electric-type components $F^a_{0i}$ acquire $(1 - a p_0/\hbar)$ and the magnetic-type components $F^a_{ij}$ acquire $(1 - 2a p_0/\hbar)$. Using Jacobi identities among κ-deformed coordinates, velocities, and isospin generators, the deformed field strength is shown to satisfy homogeneous Yang-Mills equations, and the Lagrangian built from it is invariant under ordinary SU(N) gauge transformations. If this is right, it provides the first noncommutative gauge theory in κ-spacetime whose gauge group and commutative limit match the usual Yang-Mills theory, a step toward a standard model on κ-spacetime.

What carries the argument

The central object is the κ-deformed gauge covariant derivative, defined through the coordinate realization $\hat{x}_i = x_i(1 - a p_0/\hbar)$ with $\hat{x}_0 = x_0$, so that $\tilde{D}_0$ is undeformed while $\tilde{D}_i = (1 - a p_0/\hbar)(\partial_i - e A_i)$. Here $p_0$ is the energy scale of the probe that sees the noncommutativity. The argument is carried by Jacobi identities applied to velocities, coordinates, and su(N) generators, together with the κ-deformed equation of motion for an isospin-carrying particle. The load-bearing identity is the commutator $[\tilde{D}_0,\tilde{D}_i] = -e F_{0i}(1 - a p_0/\hbar)$ and $[\tilde{D}_i,\tilde{D}_j] = -e F_{ij}(1 - 2a p_0/\hbar)$, which links the algebraic derivation of the homogeneous Yang-Mills equations to the Lagrangian construction.

What would settle it

Evaluate the claimed commutator identity $[\tilde{D}_0,\tilde{D}_i]\phi = -eF_{0i}(1 - a p_0/\hbar)\phi$ with $p_0$ treated as the operator $i\hbar\partial_0$ acting on time-dependent gauge fields; if terms containing $\partial_0 A_i$ or $\partial_0 \phi$ survive at first order in $a$, the identity fails, and the same check applies to $[\tilde{D}_i,\tilde{D}_j]\phi$ with the factor $(1 - 2a p_0/\hbar)$ needing to commute through $F_{ij}$ rather than differentiate it.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that a non-abelian gauge theory with gauge group SU(N) can be consistently formulated on κ-Minkowski spacetime to first order in $a$. The deformation changes the gauge covariant derivative only in its spatial part, scaling it by $(1 - a p_0/\hbar)$, and as a result the commutator of two deformed covariant derivatives gives the ordinary SU(N) field strength multiplied by $(1 - a p_0/\hbar)$ for the $0i$ components and by $(1 - 2a p_0/\hbar)$ for the $ij$ components. These deformed field strengths obey the homogeneous Yang-Mills equations derived from Jacobi identities, and the action (4.21) yields the remaining equations as Euler-Lagrange equations. The whole construction is invariant under the usual SU(N) gauge transformations, is not invariant under U(N), and reduces exactly to commutative Yang-Mills theory when $a \to 0$.

Load-bearing premise

The calculation assumes that $p_0$ behaves as a commuting external energy scale when it appears in the deformed coordinates and field strengths; if $p_0$ is instead a derivative operator acting on the gauge fields, the factorized expressions $\hat{F} = F(1 - c a p_0/\hbar)$ miss first-order commutator terms, and the gauge-covariance and Euler-Lagrange steps would need to be rederived.

Editorial extensions

If this is right

  • In the limit $a \to 0$, the deformed field strengths, equations of motion, Lagrangian, and force equation all reduce to standard SU(N) Yang-Mills results.
  • The action is invariant under ordinary SU(N) gauge transformations, so the same gauge group as in commutative spacetime can be used in a κ-deformed standard model, unlike earlier noncommutative models that required U(N).
  • Because the electric and magnetic sectors are deformed by different factors, $(1 - a p_0/\hbar)$ versus $(1 - 2a p_0/\hbar)$, the deformation distinguishes electric from magnetic behavior.
  • The remaining Yang-Mills equations follow from varying the Lagrangian, so the full classical theory is determined by a deformed action rather than by the Jacobi-identity route alone.
  • The force on an isospin-carrying particle picks up explicit $a$-dependent corrections that vanish in the commutative limit.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If $p_0$ is read as a genuine probe energy, the deformation acts like an energy-dependent rescaling of the electric and magnetic gauge couplings; measuring the relative strength of the two sectors at different energies would expose the κ-correction.
  • The construction is deliberately first-order in $a$; beyond that order the field strengths may need to take values in an enveloping algebra rather than the Lie algebra, an issue the paper itself leaves open.
  • The same Jacobi-identity machinery could in principle be applied to other coordinate-dependent noncommutative spacetimes, since the required inputs are only a realization of the coordinates and an equation of motion for the charged particle.
  • A structural prediction of the action (4.21) is that the deformed SU(N) field strengths contain no additional $a$-dependent cubic terms in the gauge fields, in contrast with earlier κ-U(1) models; this difference should show up in explicit vertex functions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript constructs an SU(N) Yang–Mills theory on κ-Minkowski spacetime to first order in the deformation parameter a, following Feynman's approach. It derives a κ-deformed Wong equation from a κ-deformed Dirac Hamiltonian, uses Jacobi identities to obtain homogeneous Yang–Mills equations, defines deformed field strengths F̂^a_{0i}=F^a_{0i}(1 − a p0/ħ) and F̂^a_{ij}=F^a_{ij}(1 − 2a p0/ħ), writes a Lagrangian (4.21) claimed to be SU(N) invariant, and derives a force law for isospin-carrying particles. The paper aims to provide the first SU(N) gauge theory on κ-spacetime with the correct commutative limit.

Significance. If the central construction were correct, the paper would fill a gap in the κ-Minkowski gauge-theory literature: previous constructions were mostly U(1) or U(N) invariant, whereas this paper claims an SU(N)-invariant theory with the same gauge group as the standard model. The approach via the covariant Feynman–Tanimura method is distinct from star-product or twist deformations, and the explicit formulas (4.15), (4.18), and (4.21) give concrete, testable predictions for the a-dependent modifications. The paper also usefully connects the realization of κ-coordinates with the Dirac Hamiltonian and engages with an active body of literature. However, as detailed in the major comments, the internal consistency of the construction is not established, and the central claim is thereby undermined.

major comments (3)
  1. [§3–§4 (Eqs. (3.4), (4.15), (4.18), (4.21))] The variable p0 plays two inconsistent roles. In §3, p0 = iħ∂0 is used in the realization x̂_i = x_i(1 − a p0/ħ), and the commutator calculations leading to (4.15) and (4.18) treat p0 as a differential operator. In contrast, the paragraph after (4.21) declares p0 to be 'the energy scale of the non commutative space-time, that is, the energy of the probe that sees the non commutativity', i.e., a c-number. If p0 is a c-number, then [x̂_0, x̂_i] = 0 and the κ-Minkowski relation (2.16) is not satisfied; the construction is not set on a noncommutative spacetime. If p0 is the operator iħ∂0, then F̂0i = F0i(1 − a p0/ħ) is not a multiplicative deformation: p0 acting on F0i and A produces derivatives, the commutator [D̃_i, D̃_j] is not proportional to F_ij(1 − 2a p0/ħ), and ordinary SU(N) gauge transformations do not preserve the deformed field strength because p0 does not commute with x-dependent gauge parameters. No single consistent reading of p0 supports both the derivation of (4.15)/(4.18) and the gauge-invariant Lagrangian (4.21).
  2. [§4, Eq. (4.22)] The Euler–Lagrange equations (4.22) are stated without showing the variation of (4.21), and they do not follow from the Lagrangian even under the c-number interpretation. Varying the term −1/2 (1 − a p0/ħ)^2 F^a_{0i}F^{a0i} gives a contribution with coefficient (1 − a p0/ħ)^2 multiplying D^i F^a_{i0}, while varying −1/4 (1 − 2a p0/ħ)^2 F^a_{ij}F^{aij} gives (1 − 2a p0/ħ)^2 D^j F^a_{ji}. The coefficients and index structure of (4.22)—in particular the single factor (1 − 2a p0/ħ) in front of (D_i F^{0i})^a and the absence of a corresponding factor in the (D_0 F^{i0})^a term—are not those obtained from (4.21). The claimed derivation of the dynamical Yang–Mills equations from the Lagrangian is therefore unsupported.
  3. [§4, Eqs. (4.11)–(4.12) and (4.19)–(4.20)] The homogeneous equations (4.11)–(4.12) are asserted to follow from the Jacobi identity and the decomposition (4.4), but the intermediate steps are not shown. The deformed derivatives D̃_0 and D̃_i contain the operator p0, and the Jacobi identity involves products of p0 with F̂ and A; the verification of the Bianchi-type identities is nontrivial. Likewise, the commutators (4.19) and (4.20) are stated without calculation. If p0 is a differential operator, (4.19) and (4.20) acquire additional terms from p0 acting on A and on the test function φ; if p0 is a c-number, these commutators reduce to the ordinary commutative ones and do not demonstrate a noncommutative deformation. Thus the compatibility between the Jacobi-identity field strengths and the covariant-derivative commutators is claimed but not verified.
minor comments (5)
  1. [Eq. (3.13)] The computation D0 x̂_j = (∂0 + ia/2 ∇^2)(x_j − a p0 x_j/ħ) appears to drop terms from ∇^2 acting on p0 and on the product x_j p0; please show the first-order expansion explicitly.
  2. [Throughout] The notation D_μ is overloaded: it denotes the Dirac derivative in (3.5) and the gauge covariant derivative in (2.14) and (4.22); the paper should use distinct symbols for these two objects.
  3. [§4, around Eq. (4.2)] The assumption that δη_{μν} is independent of x̂ and that [˙x̂_μ, dδη_{νρ}/dτ] = 0 is introduced without justification; since δη_{μν} is said to depend only on p_μ, the paper should clarify how this follows from the realization (3.4).
  4. [Eq. (4.21)] If p0 is an energy scale, its nature (Lorentz scalar or time-component of a four-vector) and its numerical value should be specified; otherwise the claim of deformed Lorentz covariance is not well defined.
  5. [§6, Conclusion] The defense of the minimal-coupling prescription argues that A must be a function of commutative coordinates because the κ-Dirac equation is expressed in commutative momenta; this is an assumption, not a derivation, and it is precisely one of the points that a gauge theory on κ-spacetime should justify.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: deformed factors follow directly from the stated realization, and quoted prior results are independent support.

full rationale

The derivation chain is self-contained at the level claimed. The deformed factors (1−a p0/ħ) and (1−2a p0/ħ) in F̂0i and F̂ij are direct consequences of the explicitly chosen realization x̂i = xi(1 − a p0/ħ) (Section 3, eq. (3.4)), used consistently in the velocity commutators (4.15) and (4.18); no parameter is fitted and no target result is assumed. The homogeneous equations (4.11)-(4.12) are obtained from Jacobi identities after F̂ is introduced in eq. (4.4); this is the standard Feynman–Tanimura construction, not a definition of the Yang–Mills equations. The commutators of the gauge covariant derivative are presented as a compatibility check (eqs. (4.19)-(4.20)), not as an independent prediction, so the internal-consistency nature of that check is acknowledged by the paper itself. The Lagrangian (4.21) is built from the derived F̂ factors; its Euler–Lagrange equations are standard consequences, and its SU(N) invariance follows from the usual covariance of F, so no circularity is introduced there. Self-citations to [26] (Dirac derivatives) and [54,55] (metric correction) are parameter-free published results with independent coauthors and do not contain the target Yang–Mills result; under the rule that such citations are real evidence, they do not raise the circularity score. A substantive concern is whether p0 can simultaneously be the operator iħ∂0, used in the commutator derivations, and the c-number 'energy scale' in eq. (4.21); that is a consistency/correctness issue, not a circularity reduction, and therefore is noted here rather than scored as circularity. The admitted limitations in the Conclusion (higher-order terms, uniqueness of minimal coupling) are likewise open technical issues, not circular steps.

Assumptions & free parameters 1 free parameters · 8 assumptions · 0 invented entities

The construction rests on the κ-Minkowski background, a specific realization of coordinates, the κ-Dirac derivatives, a non-symmetric metric correction with a stated independence property, and a minimal coupling prescription that keeps gauge fields commutative. The only new scale is p0, the probe energy, whose value is not fixed.

free parameters (1)
  • p0 (probe energy)
    The deformed field strengths and Lagrangian depend on the combination a p0/ħ, where p0 is described as the energy of the probe that sees noncommutativity. Its value is not fixed by the theory; the size of the corrections is therefore model dependent.
assumptions (8)
  • domain assumption κ-Minkowski commutation relation [x̂_μ, x̂_ν] = i(a_μ x̂_ν − a_ν x̂_μ) with a_0=a=1/κ, a_i=0
    Background spacetime structure from refs [4-6]; it defines the deformed geometry in which the gauge theory is constructed.
  • domain assumption Realization x̂_0=x_0, x̂_i=x_i(1−a p0/ħ), first order in a (choice ψ=1, φ=e^{-ia∂_0})
    Taken from ref [23]. The specific numerical coefficients (1 and 2 in F̂) depend on this realization choice; different realizations could alter the form of the corrections.
  • domain assumption Dirac derivatives D_0=∂_0+(ia/2)∇², D_i=∂_i
    From refs [23,26]; used to write the κ-deformed Dirac equation that produces the Wong equation.
  • ad hoc to paper The κ-deformed metric η̂_{μν}=η_{μν}+a δη_{μν} with δη_{μν} non-symmetric, independent of x̂, and [x̂̇_μ, dδη_{νρ}/dτ]=0
    Introduced in eq (4.2) and used to derive (4.11)-(4.12) and to split Ŝ_{μν}. The property [x̂̇_μ, dδη_{νρ}/dτ]=0 is asserted after eq (4.12) with justification via refs [54,55], both from the same group; no computation is shown.
  • domain assumption Isospin generators I^a commute with κ-coordinates, in particular [x̂_0, I^a]=0
    Eq (4.5), needed to derive [x̂̇_0, I^a] and the gauge covariant derivative; assumes the isospin charge is independent of position.
  • ad hoc to paper Minimal coupling p_μ→p_μ−eA_μ with gauge fields living in commutative spacetime
    Eq (3.7). The paper argues that using Â( x̂ ) would make eq (4.7) inconsistent; this modeling choice determines that all deformation enters through the Dirac derivative and realization, not through a deformed gauge connection.
  • domain assumption Taylor expansion φ^a(x̂_i)=φ^a(x_i)−(a/ħ)x_j∂_jφ^a p_0 and the ordering x left of p
    Used in eq (4.10) and section 5 to compute commutators of velocities with Lie algebra-valued functions; ordering choices affect first-order terms.
  • standard math Covariant generalization of Feynman approach with τ as the evolution parameter and Wong's equation
    The framework of Tanimura ref [49]; assumed without modification except for the κ-deformed inputs.

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Pith. "Pith review of Yang-Mills Field in the $\kappa$-space-time." pith.science (2026). https://pith.science/paper/CL7ZH3OM

@misc{pith2026241111501,
  author       = {Pith},
  title        = {Pith review of: Yang-Mills Field in the $\kappa$-space-time},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CL7ZH3OM}},
  note         = {Machine review of arXiv:2411.11501}
}
abstract

In this paper, we construct $SU(N)$ Yang-Mills theory in the $\kappa$-space-time, valid up to first order in the deformation parameter $a$, using the generalisation of Feynman's approach. Using the $\kappa$-deformed Wong's equation derived, in the Jacobi identity involving velocities and coordinates of $\kappa$-deformed space-time, the $\kappa$-deformed homogeneous Yang-Mills equations are derived. We show the compatibility between the $\kappa$-deformed field strength derived using the Jacobi identity and the commutators of the gauge covariant derivative, up to first order in $a$. The $\kappa$-deformed field strength is covariant under $SU(N)$ gauge transformations. We then construct the Lagrangian for Yang-Mills theory in $\kappa$-deformed space-time and show that it is invariant under $SU(N)$ transformation and not under U(N) transformation. We also derive the expression for the force experienced by an isospin-carrying particle in the presence of Yang-Mills field in the $\kappa$-space-time.

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Works this paper leans on

57 extracted references · 41 canonical work pages

  1. [1]

    Connes, Noncommutative geometry, Academic Press London(1994)

    A. Connes, Noncommutative geometry, Academic Press London(1994)

    work page 1994

  2. [2]

    Landi, An Introduction to noncommutative spaces and their geometry, Lect

    G. Landi, An Introduction to noncommutative spaces and their geometry, Lect. Notes Phys. Monogr.51 (1997) 1, arXiv:hep-th/9701078

    arXiv 1997

  3. [3]

    Kowalski-Glikman, Introduction to doubly special relativity, Lect

    J. Kowalski-Glikman, Introduction to doubly special relativity, Lect. Notes Phys.669 (2005) 131, arXiv:hep- th/0405273

    work page arXiv 2005

  4. [4]

    Lukierski, A

    J. Lukierski, A. Nowicki, H. Ruegg, New quantum Poincare algebra and κ deformed field theory, Phys. Lett. B 293 (1992) 344

    work page 1992

  5. [5]

    Lukierski, H

    J. Lukierski, H. Ruegg, Quantum kappa Poincare in any dimension,Phys. Lett. B329 (1994) 189, arXiv:hep- th/9310117

    work page arXiv 1994

  6. [6]

    Majid, H

    S. Majid, H. Ruegg, Bicrossproduct structure of κ Poincare group and noncommutative geometry, Phys. Lett. B 334 (1994) 348, arXiv:hep-th/9405107

    arXiv 1994

  7. [7]

    Freidel, E

    L. Freidel, E. R. Livine, 3D Quantum Gravity and Effective Noncommutative Quantum Field Theory, Phys. Rev. Lett.96 (2006) 221301, arXiv:hep-th/0512113

    arXiv 2006

  8. [8]

    Towards Quantum Noncommutative $\kappa$-deformed Field Theory

    M. Daszkiewicz, J. Lukierski, M. Woronowicz, Towards quantum noncommutative kappa-deformed field theory, Phys. Rev. D77 (2008) 105007, arXiv:0708.1561 [hep-th]

    work page Pith review arXiv 2008

Show all 57 references
  1. [9]

    Kosinski, J

    P. Kosinski, J. Lukierski, P. Maslanka, Local D=4 field theory on kappa deformed Minkowski space, Phys. Rev. D 62 (2000) 025004, arXiv:hep-th/9902037

    2000 arXiv

  2. [10]

    Kosinski, J

    P. Kosinski, J. Lukierski, P. Maslanka, κ-deformed Wigner construction of relativistic wave functions and free fields on κ-Minkowski space, Nucl. Phys. Proc. Suppl.102 (2001) 161, arXiv:hep-th/0103127

    2001 arXiv

  3. [11]

    Kosinski, P

    P. Kosinski, P. Maslanka, J. Lukierski, A. Sitarz, Generalized kappa-Deformations and Deformed Relativistic Scalar Fields on Noncommutative Minkowski Space,Conference on topics in Mathematical Physics, General Relativity, and Cosmology on the occasion of the 75th Birthday of J...

    2003

  4. [12]

    Amelino-Camelia, M

    G. Amelino-Camelia, M. Arzano, Coproduct and star product in field theories on Lie-algebra noncommu- tative space-times, Phys. Rev. D65 (2002) 084044, arXiv:hep-th/0105120

    2002 arXiv

  5. [13]

    Dimitrijevic, F

    M. Dimitrijevic, F. Meyer, L. Moller, J. Wess, Gauge theories on the κ-Minkowski spacetime, Eur. Phys. J. C 36 (2004) 117, arXiv:hep-th/0310116

    2004 arXiv

  6. [14]

    Dimitrijevic, L

    M. Dimitrijevic, L. Jonke, L. Moller, E. Tsouchnika, J. Wess, M. Wohlgenannt, Deformed field theory on kappa space-time, Eur. Phys. J. C31 (2003) 129, arXiv:hep-th/0307149

    2003 arXiv

  7. [15]

    Dimitrijevic, L

    M. Dimitrijevic, L. Jonke, L. Moller, E. Tsouchnika, J. Wess, M. Wohlgenannt, Field theory on kappa- spacetime, Czech. J. Phys.54 (2004) 1243, arXiv:hep-th/0407187

    2004 arXiv

  8. [16]

    Dimitrijevic, L

    M. Dimitrijevic, L. Jonke, A Twisted look on kappa-Minkowski: U(1) gauge theory, JHEP 12 (2011) 080, arXiv:1107.3475 [hep-th]

    2011 arXiv

  9. [17]

    Dimitrijevic, L

    M. Dimitrijevic, L. Jonke, L. Moller, U(1) gauge field theory on kappa-Minkowski space, JHEP 09 (2005) 068, arXiv:hep-th/0504129

    2005 arXiv

  10. [18]

    Dimitrijevic, L

    M. Dimitrijevic, L. Jonke, Gauge theory on kappa-Minkowski revisited: The Twist approach, J. Phys. Conf. Ser. 343 (2012) 012049, arXiv:1110.6767 [hep-th]

    2012 arXiv

  11. [19]

    Dimitrijevic, L

    M. Dimitrijevic, L. Jonke, A. Pachol, Gauge theory on Twisted κ-Minkowski: Old Problems and Possible Solutions, SIGMA 10 (2014) 063, arXiv:1403.1857 [hep-th]

    2014 arXiv

  12. [20]

    Meier, S

    T. Meier, S. J. van Tongeren, Quadratic Twist-Noncommutative Gauge Theory, Phys. Rev. Lett.131 (2023) 121603, arXiv:2301.08757 [hep-th]

    2023 arXiv

  13. [21]

    Meier, S

    T. Meier, S. J. van Tongeren, Gauge theory on twist-noncommutative spaces, JHEP 12 (2023) 045, arXiv:2305.15470

    2023 arXiv

  14. [22]

    Hersent, P

    K. Hersent, P. Mathieu, Jean-Christophe Wallet, Gauge theories on quantum spaces, Physics Reports1014 (2023) 1, arXiv:2210.11890 [hep-th]

    2023 arXiv

  15. [23]

    Meljanac, M

    S. Meljanac, M. Stojic, New realizations of Lie algebra kappa-deformed Euclidean space, Eur. Phys. J. C 47 (2006) 531, arXiv:hep-th/0605133

    2006 arXiv

  16. [24]

    T. R. Govindarajan, K. S. Gupta, E. Harikumar, S. Meljanac, D. Meljanac, Twisted statistics in kappa- Minkowski spacetime, Phys. Rev. D77 (2008) 105010, arXiv:0802.1576 [hep-th]

    2008 arXiv

  17. [25]

    T. R. Govindarajan, K. S. Gupta, E. Harikumar, S. Meljanac, D. Meljanac, Deformed Oscillator Algebras and QFT in kappa-Minkowski Spacetime, Phys. Rev. D80 (2009) 025014, arXiv:0903.2355 [hep-th]

    2009 arXiv

  18. [26]

    Harikumar, M

    E. Harikumar, M. Sivakumar, N. Srinivas, κ-deformed Dirac Equation, Mod. Phys. Lett. A26 (2011) 1103, arXiv:0910.5778 [hep-th]

    2011 arXiv

  19. [27]

    Harikumar, Maxwell’s equation on the κ-Minkowski spacetime and Electric-Magnetic duality, EPL 90 (2010) 21001, arXiv:1002.3202 [hep-th]

    E. Harikumar, Maxwell’s equation on the κ-Minkowski spacetime and Electric-Magnetic duality, EPL 90 (2010) 21001, arXiv:1002.3202 [hep-th]

    2010 arXiv

  20. [28]

    Harikumar, T

    E. Harikumar, T. Juric, S. Meljanac, Electrodynamics on κ-Minkowski space-time, Phys. Rev. D84 (2011) 085020, arXiv:1107.3936 [hep-th]

    2011 arXiv

  21. [29]

    Harikumar, T

    E. Harikumar, T. Juric, S. Meljanac, Geodesic equation in κ-Minkowski spacetime, Phys. Rev. D86 (2012) 045002, arXiv:1203.1564 [hep-th]

    2012 arXiv

  22. [30]

    Vitale, Jean-Christophe Wallet, Noncommutative field theories on R3 λ: Towards UV/IR mixing freedom, JHEP 04 (2013) 115, arXiv:1212.5131 [hep-th]

    P. Vitale, Jean-Christophe Wallet, Noncommutative field theories on R3 λ: Towards UV/IR mixing freedom, JHEP 04 (2013) 115, arXiv:1212.5131 [hep-th]

    2013 arXiv

  23. [31]

    Vitale, Noncommutative field theory on R3 λ, Fortsch

    P. Vitale, Noncommutative field theory on R3 λ, Fortsch. Phys.62 (2014) 825, arXiv:1406.1372 [hep-th]

    2014 arXiv

  24. [32]

    A. Gere, P. Vitale, Jean-Christophe Wallet, Quantum gauge theories on noncommutative three-dimensional space, Phys. Rev. D90 (2014) 045019, arXiv:1312.6145 [hep-th]

    2014 arXiv

  25. [33]

    Marmo, P

    G. Marmo, P. Vitale, A. Zampini, Noncommutative differential calculus for Moyal subalgebras, J. Geom. Phys. 56 (2006) 611, arXiv:hep-th/0411223

    2006 arXiv

  26. [34]

    Marmo, P

    G. Marmo, P. Vitale, A. Zampini, Derivation based differential calculi for noncommutative algebras de- forming a class of three dimensional spaces, J. Geom. Phys.136 (2019) 104, arXiv:1805.06300 [math.QA]

    2019 arXiv

  27. [35]

    D. V. Vassilevich, Twist to close, Mod. Phys. Lett. A21 (2006) 1279, arXiv:hep-th/0602185

    2006 arXiv

  28. [36]

    Chaichian, A

    M. Chaichian, A. Tureanu, G. Zet, Twist as a Symmetry Principle and the Noncommutative Gauge Theory Formulation, Phys. Lett. B651 (2007) 319, arXiv:hep-th/0607179. 13

    2007 arXiv

  29. [37]

    Chaichian, A

    M. Chaichian, A. Tureanu, Twist Symmetry and Gauge Invariance,Phys. Lett. B637 (2006) 199, arXiv:hep- th/0604025

    2006

  30. [38]

    Aschieri, M

    P. Aschieri, M. Dimitrijevic, F. Meyer, S. Schraml, J. Wess, Twisted gauge theories, Lett. Math. Phys.78 (2006) 61, arXiv:hep-th/0603024

    2006 arXiv

  31. [39]

    Aschieri, F

    P. Aschieri, F. Lizzi, P. Vitale, Twisting all the way: From Classical Mechanics to Quantum Fields, Phys. Rev. D 77 (2008) 025037, arXiv:hep-th/0708.3002

    2008 arXiv

  32. [40]

    V. G. Kupriyanov, P. Vitale, A novel approach to non-commutative gauge theory, JHEP 08 (2020) 041, arXiv:hep-th/2004.14901

    2020 arXiv

  33. [41]

    V. G. Kupriyanov, M. Kurkov, P. Vitale, κ-Minkowski-deformation of U(1) gauge theory, JHEP 01 (2021) 102, arXiv:2010.09863

    2021 arXiv

  34. [42]

    Blumenhagen, I

    R. Blumenhagen, I. Brunner, V. Kupriyanov, D. Lust, Bootstrapping Non-commutative Gauge Theories from L∞ algebras, JHEP 05 (2018) 097, arXiv:hep-th/1803.00732

    2018 arXiv

  35. [43]

    Kupriyanov, L∞-Bootstrap Approach to Non-Commutative Gauge Theories, Fortsch

    V.G. Kupriyanov, L∞-Bootstrap Approach to Non-Commutative Gauge Theories, Fortsch. Phys.67 (2019) 8, arXiv:hep-th/1903.02867

    2019 arXiv

  36. [44]

    Kontsevich, Deformation quantization of Poisson manifolds

    M. Kontsevich, Deformation quantization of Poisson manifolds. 1, Lett. Math. Phys.66 (2003) 157, arXiv:q- alg/9709040

    2003

  37. [45]

    V. G. Kupriyanov, M. A. Kurkov, P. Vitale, Lie-Poisson gauge theories and κ-Minkowski electrodynamics, JHEP 11 (2023) 200, arXiv:2304.04857

    2023 arXiv

  38. [46]

    O. Abla, M. J. Neves, Poisson electrodynamics on κ-Minkowski space-time, Phys. Lett. B864 (2025) 139385, arXiv:2412.17202 [hep-th]

    2025 arXiv

  39. [47]

    F. J. Dyson, Feynman’s proof of Maxwell equations, Am. J. Phys.58 (1990) 209

    1990

  40. [48]

    C. R. Lee, The Feynman-Dyson proof of the gauge field equations, Phys. Lett. A148 (1990) 146

    1990

  41. [49]

    Tanimura, Relativistic generalization and extension to the nonAbelian gauge theory of Feynman’s proof of the Maxwell equations, Annals Phys

    S. Tanimura, Relativistic generalization and extension to the nonAbelian gauge theory of Feynman’s proof of the Maxwell equations, Annals Phys. 220 (1992) 229, arXiv:hep-th/9306066

    1992 arXiv

  42. [50]

    S. K. Wong, Field and particle equations for the classical Yang-Mills field and particles with isotopic spin, Nuovo Cim. A65 (1970) 689

    1970

  43. [51]

    Harikumar, A

    E. Harikumar, A. K. Kapoor, Newton’s Equation on the kappa space-time and the Kepler problem, Mod. Phys. Lett. A25 (2010) 2991, arXiv:1003.4603 [hep-th]

    2010 arXiv

  44. [52]

    M. C. Land, N. Shnerb, L. P. Horwitz, On Feynman’s approach to the Foundations of Gauge Theory, J. Math. Phys. 36 (1995) 3263, arXiv:hep-th/9308003

    1995 arXiv

  45. [53]

    Miyazaki, K

    H. Miyazaki, K. Fujii, Remarks on Tanimura’s reformulation of general relativistic version of Feyn- man’s proof about Maxwell equations, Kyoto University Research Information Repository67 (1996) 373, (https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/87035)

    1996

  46. [54]

    Harikumar, N

    E. Harikumar, N. S. Zuhair, Hawking Radiation in κ-spacetime, Int. J. Mod. Phys. A32 (2017) 1750072, arXiv:1609.05288 [hep-th]

    2017 arXiv

  47. [55]

    Harikumar, Wormhole Solutions in deformed space-time, Eur

    Harsha Sreekumar, E. Harikumar, Wormhole Solutions in deformed space-time, Eur. Phys. J. C85 (2025), arXiv:2412.07409 [gr-qc]

    2025 arXiv

  48. [56]

    Chaichian, P

    M. Chaichian, P. Presnajder, M. M. Sheikh-Jabbari, A. Tureanu, Noncommutative Gauge Field Theories: A no-go theorem, Phys. Lett. B526 (2002) 132, arXiv:hep-th/0107037

    2002 arXiv

  49. [57]

    Calmet, M

    X. Calmet, M. Wohlgenannt, Effective field theories on noncommutative space-time, Phys. Rev. D68 (2003) 025016, arXiv:hep-ph/0305027. 14

    2003 arXiv

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