Covariant quantization of thed=4 Brink-Schwarz superparticle using Lorentz harmonics

Zima, V. G.; Fedoryuk, S. A.

doi:10.1007/bf01017881

Cited by 18 publications

(11 citation statements)

References 32 publications

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“…For recent discussions of infinite-dimensional representations of the Lorentz group in a field-theoretic context, see e.g. [78][79][80].…”

Section: The Setupmentioning

confidence: 99%

3d conformal fields with manifest sl(2, ℂ)

Ponomarev

2021

J. High Energ. Phys.

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In the present paper we construct all short representation of so(3, 2) with the sl(2, ℂ) symmetry made manifest due to the use of sl(2, ℂ) spinors. This construction has a natural connection to the spinor-helicity formalism for massless fields in AdS4 suggested earlier. We then study unitarity of the resulting representations, identify them as the lowest-weight modules and as conformal fields in the three-dimensional Minkowski space. Finally, we compare these results with the existing literature and discuss the properties of these representations under contraction of so(3, 2) to the Poincare algebra.

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“…For recent discussions of infinite-dimensional representations of the Lorentz group in a field-theoretic context, see e.g. [78][79][80].…”

Section: The Setupmentioning

confidence: 99%

3d conformal fields with manifest sl(2, ℂ)

Ponomarev

2021

J. High Energ. Phys.

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“…(25). However as one can see from the explicit expressions for the coefficients in our model the inequality k 1 = k 2 is always fulfilled.…”

Section: /4 Unbroken Susymentioning

confidence: 59%

“…But in the second case the role of the central charges is played by the Lorentzscalar quantities C ab , Cab instead of Z αβ , Z α β and by the static momentum p 0 = m, p = 0 instead of the usual four-momentum. The consideration in terms of quantities with indices a, b, ... is Lorentz covariant due to the use of the bosonic variables v a α which play the role of harmonic variables [23]- [25] parametrizing an appropriate homogeneous subspace of the Lorentz group.…”

Section: Constraints Of the Modelmentioning

confidence: 99%

Uniform twistor-like formulation of massive and massless superparticles with tensorial central charges

Fedoruk

Zima

2001

Nuclear Physics B - Proceedings Supplements

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We construct the manifestly Lorentz-invariant twistorial formulation of the N = 1 D = 4 superparticle with tensorial central charges which describes massive and massless cases in a uniform manner. The tensorial central charges are realized in terms of even spinor variables and central charge coordinates. The full analysis of the number of conserved supersymmetries has been carried out. In the massive case the superparticle preserves 1/4 or 1/2 of target-space supersymmetries whereas the massless superparticle preserves two or three supersymmetries.

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“…The decomposition in the case of Minkowski spacetime is more complicated, see e.g. [48,56] for 4d case. However, for our discussion aimed to show the presence of nontrivial solution, it is sufficient, following [55], to study the solutions in the class of real analytic functions of spinor frame variables.…”

Section: A Solution Of the Bosonic Limit Of Our Matrix Field Theory Ementioning

confidence: 99%

Hamiltonian approach and quantization of D = 3,$$ \mathcal{N}=1 $$ supersymmetric non-Abelian multiwave system

Bandos

Sabido

2018

J. High Energ. Phys.

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We develop Hamiltonian formalism and quantize supersymmetric non-Abelian multiwave system (nAmW) in D=3 spacetime constructed as a simple counterpart of 11D multiple M-wave system. Its action can be obtained from massless superparticle one by putting on its worldline 1d dimensional reduction of the 3d SYM model in such a way that the new system still possesses local fermionic kappa-symmetry. The quantization results in a set of equation of supersymmetric field theory in an unusual space with su(N)-valued matrix coordinates. Their superpartners, the fermionic su(N)-valued matrices, cannot be split on coordinates and momenta in a covariant manner and hence are included as abstract operators acting on the state vector in the generic form of our D=3 Matrix model field equations. We discuss the Clifford superfield representation for the quantum state vector and in the simplest case of N = 2 elaborate it in a bit more detail. As a check of consistency, we show that the bosonic Matrix model field equations obtained by quantization of the purely bosonic limit of our D=3 nAmW system have a nontrivial solution.

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Covariant quantization of thed=4 Brink-Schwarz superparticle using Lorentz harmonics

Abstract: The first and second covariant quantization of a free massless d = 4 superparticle with pure gauge auxiliary spinor variables have been carried out.

Cited by 18 publications

References 32 publications

3d conformal fields with manifest sl(2, ℂ)

3d conformal fields with manifest sl(2, ℂ)

Uniform twistor-like formulation of massive and massless superparticles with tensorial central charges

Hamiltonian approach and quantization of D = 3,$$ \mathcal{N}=1 $$ supersymmetric non-Abelian multiwave system

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