A no-go theorem for the <i>n</i>-twistor description of a massive particle

Okano, Satoshi; Deguchi, Shinichi

doi:10.1063/1.4976961

Cited by 5 publications

(5 citation statements)

References 35 publications

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“…Note also a two-twistor model along the lines of an ambitwistor string[40,41], but focussed on massless particles.2 More generally, n-twistor descriptions were considered with symmetry groups containing SU(n); in the twistor particle programme, particle multiplets were to be understood via the representation theory of such internal symmetry groups. The quantization of massive worldline models based on these descriptions has been studied by a number of authors, see[23,50] and references therein.…”

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confidence: 99%

From Twistor-Particle Models to Massive Amplitudes

Albonico¹,

Geyer²,

Mason³

2022

SIGMA

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In his twistor-particle programme of the 1970's, Roger Penrose introduced a representation of the massive particle phase space in terms of a pair of twistors subject to an internal symmetry group. Here we use this representation to introduce a chiral string whose target is a complexification of this space, extended so as to incorporate supersymmetry. We show that the gauge anomalies associated to the internal symmetry group vanish only for maximal supersymmetry, and that correlators in these string models describe amplitudes involving massive particles with manifest supersymmetry. The models and amplitude formulae exhibit a double copy structure from gauge theory on the Coulomb branch to gravity, although the graviton remains massless. The formulae are closely related to those obtained earlier by the authors expressed in terms of the polarised scattering equations.

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confidence: 99%

From Twistor-Particle Models to Massive Amplitudes

Albonico¹,

Geyer²,

Mason³

2022

SIGMA

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“…We have introduced the concepts of colored conformal symmetry U(2N, 2N) and colored twistors to address the inclusion of non-Abelian internal U(N) charges into (spinless massive) conformal particles. It is known that a genuine M-twistor description of a massive particle in four-dimensional Minkowski space fails for the case M ≥ 3 [23]. However, replacing standard twistors by colored twistors provides enough room to accommodate non-Abelian internal degrees of freedom, other than the electric charge.…”

Section: Discussionmentioning

confidence: 99%

“…Actually, it is shown in [22] that only the two-twistor formulation can successfully describe a massive particle in Minkowski space. Moreover, it is proved in [23] that the M-twistor expression of a particle's four-momentum vector reduces to the two-twistor expression for a massive particle or the one-twistor expression for a massless particle. Therefore, they conclude that the genuine M-twistor description of a massive particle in four-dimensional Minkowski space fails for the case M ≥ 3.…”

Section: Introductionmentioning

confidence: 99%

Massive conformal particles with non-Abelian charges from free U(2N,2N)-twistor dynamics: Quantization and coherent states

Calixto

2019

Journal of Geometry and Physics

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The inclusion of non-Abelian U(N ) internal charges (other than the electric charge) into Twistor Theory is accomplished through the concept of "colored twistors" (ctwistors for short) transforming under the colored conformal symmetry U(2N, 2N ). In particular, we are interested in 2N -ctwistors describing colored spinless conformal massive particles with phase space U(2N, 2N )/U(2N ) × U(2N ). Penrose formulas for incidence relations are generalized to N > 1. We propose U(2N )-gauge invariant Lagrangians for 2N -ctwistors and we quantize them through a bosonic representation, interpreting quantum states as particlehole excitations above the ground state. The connection between the corresponding Hilbert (Fock-like with constraints) space and the carrier space of a discrete series representation of U (2N, 2N ) is established through a coherent state (holomorphic) representation.

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“…Initially, the SU(n) internal symmetries of such n-twistor systems were associated with the zoo of elementary particles: e.g., n = 2 for the weak isospin doublet of leptons and n = 3 for the flavor symmetry of hadrons [84,[106][107][108][109][110][111][112][113][114][115]. However, it rather turns out that a massive particle can only be consistently described with the bi-twistor system [116,117]. Hence we interpret the SU(2) internal symmetry of a bi-twistor as a symmetry of a "kinematic" origin: the massive little group.…”

Section: Massive Ambitwistor Spacementioning

confidence: 99%

An Ambitwistor for Kerr I: Zig-Zag Symplectic Perturbation Theory

Kim¹,

Lee²

2023

Preprint

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We develop a theory of massive spinning particles interacting with background fields in four spacetime dimensions in which holomorphy and chirality play a central role. Applying a perturbation theory of symplectic forms to the massive twistor space as a Kähler manifold, we find that the spin precession behavior of a massive spinning particle is directly determined from the manner in which self-dual and anti-self-dual field strengths permeate into "complex spacetime." Especially, the particle shows the minimally coupled precession behavior if self-dual field strength continues holomorphically into the complex: the Newman-Janis shift. In general, computing the momentum impulse shows that the parameters that control generic non-holomorphic continuations are directly related to the coupling constants in the massive-massive-massless spinning on-shell amplitude of Arkani-Hamed, Huang, and Huang, and thus they are interpreted as the single-curvature Wilson coefficients given by Levi and Steinhoff, redefined on complex worldlines. Finally, exact expressions for Kerr and √ Kerr actions are bootstrapped in monochromatic self-dual planewave backgrounds from symplectivity and a matching between classical scattering and the on-shell amplitude, from which we obtain all-order exact impulses of classical observables.

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A no-go theorem for the n-twistor description of a massive particle

Cited by 5 publications

References 35 publications

From Twistor-Particle Models to Massive Amplitudes

From Twistor-Particle Models to Massive Amplitudes

Massive conformal particles with non-Abelian charges from free U(2N,2N)-twistor dynamics: Quantization and coherent states

An Ambitwistor for Kerr I: Zig-Zag Symplectic Perturbation Theory

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