Massive Superparticle with Spinorial Central Charges

2006

Physics Letters B

We propose the relativistic point particle models invariant under the bosonic counterpart of SUSY. The particles move along the world lines in four dimensional Minkowski space extended by N commuting Weyl spinors. The models provide after first quantization the non-Grassmann counterpart of chiral superfields, satisfying Klein-Gordon equation. Free higher spin fields obtained by expansions of such chiral superfields satisfy the N = 2 Bargman-Wigner equations in massive case and Fierz-Pauli equations in massless case. * On leave of absence from Ukrainian Engineering-Pedagogical Academy, Kharkov, Ukraine.

Section: Discussionmentioning

confidence: 76%

Massive relativistic particle models with bosonic counterpart of supersymmetry

Fedoruk

2006

Physics Letters B

“…Following the massive relativistic particle case (see [13,14,15]) the main tools in the equivalence proof are the string generalizations of Cartan-Penrose string momenta (see (6) and (35)) and the incidence relations (25). The action (27) in conformal gauge e a m = δ a m is the commonly used bilinear action for twistorial string.…”

Section: Discussionmentioning

confidence: 99%

“…Recently also there were described in D = 4 twotwistor space T (2) = T ⊗ T the models describing free relativistic massive particles with spin [5,13,14,15]. The corresponding action was derived by suitable choice of the variables from the following free two-twistor oneform…”

mentioning

confidence: 99%

Twistorial versus spacetime formulations: Unification of various string models

Fedoruk¹,

2007

Phys. Rev. D

We introduce the D = 4 twistorial tensionfull bosonic string by considering the canonical twistorial 2-form in two-twistor space. We demonstrate its equivalence to two bosonic string models: due to Siegel (with covariant worldsheet vectorial string momenta P m µ (τ, σ)) and the one with tensorial string momenta P [µν] (τ, σ). We show how to obtain in mixed space-time-twistor formulation the Soroka-Sorokin-Tkach-Volkov (SSTV) string model and subsequently by harmonic gauge fixing the Bandos-Zheltukhin (BZ) model, with constrained spinorial coordinates.

“…We use bar for complex conjugate quantities,λ iα = (λ αi ), and tilde for Dirac-conjugated d = 2 spinors,λ iα =λ jα (ρ 0 ) j i . 8 The matrix of charge conjugation is the 2 × 2 skew-symmetric tensor ǫ ij . For definiteness, we take ǫ 12 = 1.…”

Section: Tensionful D = 4 Membrane (P = 2) In Intermediate Spinomentioning

confidence: 99%

“…Thus the spinor λα i has two indices: it is spinor in D dimensions with the components described by indexα and as well spinor in d dimensions with index i; we employ also the spinorλα i which is a Dirac-conjugated spinor with respect to both indices: Inserting (62) in the action (8) we shall obtain the intermediate spinor-space-time formulation. Due to the mass-shell for the vectorial momenta (see (23)) the elementary spinors λα i will be constrained (compare with (35) and (45)).…”

Section: Purely Twistorial Formulation Of the Membrane (P = 2) Inmentioning

confidence: 99%

Two-twistor description of a membrane

Fedoruk¹,

2007

Phys. Rev. D

We describe D = 4 twistorial membrane in terms of two twistorial three-dimensional world-volume fields. We start with the D-dimensional p-brane generalizations of two phase space string formulations: the one with p + 1 vectorial fourmomenta, and the second with tensorial momenta of (p + 1)-th rank. Further we consider tensionful membrane case in D = 4. By using the membrane generalization of Cartan-Penrose formula we express the fourmomenta by spinorial fields and obtain the intermediate spinor-space-time formulation. Further by expressing the world-volume dreibein and the membrane space-time coordinate fields in terms of two twistor fields one obtains the purely twistorial formulation. It appears that the action is generated by a geometric three-form on twotwistor space. Finally we comment on higher-dimensional (D > 4) twistorial p-brane models and their superextensions.