Narrow Results

We construct the manifestly Lorenz-invariant formulation of the N = 1, D=4 massive superparticle with tensorial central charges. The model contains a real parameter k and at k≠0 possesses one κ-symmetry while at k=0 the number of κ-symmetry is two. The equivalence of the formulations at all k≠0 is obtained. The local transformations of κ-symmetry are written. It is considered using the index spinor for construction of the tensorial central charges. The equivalence at classical level between the massive D=4 superparticle with one κ-symmetry and the massive D=4 spinning particle is obtained.

On the basis of the Berkovits pure spinor formalism of covariant quantization of supermembrane, we attempt to construct a M(atrix) theory which is covariant under SO(1, 10) Lorentz group. We first construct a bosonic M(atrix) theory by starting with the first-order formalism of bosonic membrane, which precisely gives us a bosonic sector of M(atrix) theory by BFSS. Next we generalize this method to the construction of M(atrix) theory of supermembranes. However, it seems to be difficult to obtain a covariant and supersymmetric M(atrix) theory from the Berkovits pure spinor formalism of supermembrane because of the matrix character of the BRST symmetry. Instead, in this paper, we construct a supersymmetric and covariant matrix model of 11D superparticle, which corresponds to a particle limit of covariant M(atrix) theory. By an explicit calculation, we show that the one-loop effective potential is trivial, thereby implying that this matrix model is a free theory at least at the one-loop level.

Lagrangian and Hamiltonian dynamics of de Azcarraga–Lukierski N = 2 massive superparticle is considered in the framework of twistor-like Lorentz-harmonic approach. The emphasis is on the study of the interaction with external Abelian gauge superfield. The requirement of preservation of all gauge symmetries of the free model including κ-symmetry yields correct expressions for the superfield strength constraints and determines the form of nonminimal interaction. We also show that for de Azcarraga–Lukierski N = 2 massive superparticle the pullback of field strength two-superform to the superworld line is not integrable in contrast to the massless superparticle.

A massive superparticle action based on the generalised line element in N = 1 global superspace is quantised canonically. A previous method of quantising this action, based on a Fock space analysis, showed that states existed in three supersymmetric multiplets, each of a different mass. The quantisation procedure presented uses the single first class constraint as an operator condition on a general N = 1 superwavefunction. The constraint produces coupled equations of motion for the component wavefunctions. Transformations of the component wavefunctions are derived that decouple the equations of motion and partition the resulting wavefunctions into three separate supermultiplets. Unlike previous quantisations of superparticle actions in N = 1 global superspace, the spinor wavefunctions satisfy the Dirac equation and the vector wavefunctions satisfy the Proca equation.

The off-shell closure of the commutators of the supersymmetry transformations, that include mass parameters, are derived by the introduction of auxiliary wavefunctions.

To avoid the ghosts arising in a previous Fock space quantisation an alternative conjugation is used in the definition of the current, based on a Krein space approach.

The action for a massless particle in 4D Minkowski space–time has a worldline-time reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the ${𝒩}$-extended superparticle is shown to be anomalous when ${𝒩}$ is odd; in the supertwistor formalism this is because a CPT-violating worldline-Chern–Simons term is needed to preserve the chiral $U(1)$ gauge invariance. This accords with the fact that no massless ${𝒩}=1$ super-Poincaré irrep is CPT-self-conjugate. There is a CPT self-conjugate supermultiplet when ${𝒩}$ is even, but it has $2^{{𝒩}+1}$ states when $\frac{1}{2}{𝒩}$ is odd (e.g. the ${𝒩}=2$ hypermultiplet) in contrast to just $2^{{𝒩}}$ when $\frac{1}{2}{𝒩}$ is even (e.g. the ${𝒩}=4$ Maxwell supermultiplet). This is shown to follow from a Kramers degeneracy of the superparticle state space when $\frac{1}{2}{𝒩}$ is odd.

We analyze the Casalbuoni–Brink–Schwarz superparticle model on a 2-dimensional curved spacetime as a super Finsler metric defined on a (2,2)-dimensional supermanifold. We propose a nonlinear Finsler connection which preserves this Finsler metric and calculates it explicitly. The equations of motion of the superparticle are reconstructed in the form of auto-parallel equations expressed by the super nonlinear connection.