Massive Superparticle Research Articles

Super black hole from cosmological supergravity with a massive superparticle

We describe in superspace a classical theory of two dimensional (1,1) cosmological dilaton supergravity coupled to a massive superparticle. We give an exact non-trivial superspace solution for the compensator superfield that describes the supergravity, and then use this solution to construct a model of a two-dimensional supersymmetric black hole.

K-Symmetry and anomalous magnetic moment of superparticles

It is shown thatk-symmetry breaking arising upon the minimal inclusion of an interaction of massive spin-1/2 particles with anN=2 extended Maxwell supermultiplet is restored by taking into account their anomalous magnetic moment (AMM). Thek-invariant action of massive superparticles is constructed, and it is shown thatk-symmetry uniquely fixes the value of their AMM.

BRST gauge fixing and the algebra of global supersymmetry

Global supersymmetry (SUSY) in supersymmetric gauge theory is generally broken by gauge fixing. A prescription to extract physical information from such SUSY algebra broken by gauge fixing is analyzed in the path integral framework. If δ SUSY δ BRST Ψ = δ BRST δ SUSY Ψ for a gauge fixing “fermion” Ψ the SUSY charge density is written as a sum of the piece which is naively expected without gauge fixing and a BRST exact piece. If δ SUSY δ SUSY δ BRST = δ BRST δ SUSY δ SUSY Ψ, the equal-time anti-commutator of SUSY charge is written as a sum of a physical piece and a BRST exact piece. We illustrate these properties for N = 1 and N = 2 supersymmetric Yang-Mills theories and for a D = 10 massive superparticle (or “D-particle”) where the κ-symmetry provides extra complications.

Supergravity from a massive superparticle and the simplest super black hole

We describe in superspace a theory of a massive superparticle coupled to a version of two-dimensional (1,1) dilaton supergravity. The (1 + 1)-dimensional supergravity is generated by the stress-energy of the superparticle, and the evolution of the superparticle is reciprocally influenced by the supergravity. We obtain exact superspace solutions for both the superparticle worldline and the supergravity fields. We use the resultant non-trivial compensator superfield solution to construct a model of a two-dimensional supersymmetric black hole.

Weak Dirac bracket construction and the superparticle covariant quantization problem

The general procedure for constructing a consistent covariant Dirac-type bracket for the models with mixed first and second class constraints is presented. The proposed scheme essentially relies upon explicit separation of the initial constraints into infinitely reducible first and second class ones (by making use of some covariant projectors). Reducibility of the second class constraints involved manifests itself in weakening some properties of the bracket as compared to the standard Dirac one. In particular, a commutation of any quantity with the second class constraints and the Jacobi identity holds on the second class constraints surface only. The procedure developed is realized for a N = 1 Brink-Schwarz superparticle in arbitrary dimension and for a N = 1, D = 9 massive superparticle with the Wess-Zumino term. The possibility to apply the bracket for quantizing the superparticles within the framework of the recent unified algebra approach by Batalin and Tyutin [20–22] is examined. It is shown, in particular, that for a D = 9 massive superparticle it is impossible to construct a Dirac-type bracket possessing a (strong) Jacobi identity in a full phase space.

Arbitrary superspin massive superparticles

We propose an exactly solvable model for a massive N-extended superparticle with pure (half-)integer superspin Y, Y = 0, 1 2 , 1, 3 2 , …. Regardless of the superspinvalue, the configuration space is R 4|4N × S 2, where S 2 corresponds to spinning degrees of freedom. Being explicitly super-Poincaré invariant, the model possesses two gauge symmetries implying strong conservation of the squared momentum and superspin. Hamilton constrained dynamics is developed and canomical quantization is studied. For N = 1 we show that the physical super wave-functions are to be on-shell massive chiral superfields. Central-charge and higher-dimensional generalizations of the model are given.

Collective coordinates and constrained hamiltonian systems

A general method of incorporating collective coordinates (transformation of fields into an overcomplete basis) with constrained hamiltonian systems is given where the original phase space variables and collective coordinates can be bosonic or/and fermionic. This method is illustrated by applying it to the SU(2) Yang-Mills-Higgs theory and its BFV-BRST quantization is discussed. Moreover, this formalism is used to give a systematic way of converting second class constraints into effectively first class ones, by considering second class constraints as first class constraints and gauge fixing conditions. This approach is applied to the massive superparticle, Proca lagrangian, and some topological quantum field theories.

A ϰ-symmetry calculus for superparticles

We develop a ϰ-symmetry calculus for the d = 2 and d = 3, N = 2 massive superparticles, which enables us to construct higher order ϰ-invariant actions. The method relies on a reformulation of these models as supersymmetric sigma models that are invariant under local worldline superconformal transformations. We show that the ϰ-symmetry is embedded in the superconformal symmetry so that a calculus for the ϰ-symmetry is equivalent to a tensor calculus for the latter. We develop such a calculus without the introduction of a worldline supergravity multiplet.

Off-shell BRST quantization of the massive superparticle

The massive superparticle in D = 9 is covariantly quantized by using a generalized lagrangian BRST formalism. The method is based on the structure of the classical gauge algebra, and ensures the off-shell nilpotency of the BRST symmetry of the gauge-fixed action by introducing a set of auxilliary fields with non-vanishing ghost numbers.

Faddeev-Batalin-Fradkin extended phase space for superparticle quantization

Faddeev, Batalin, and Fradkin's (FBF) method of quantization in an extended phase space treats first- and second-class constraints in a symmetrical manner. It is employed here to study a long lasting problem: the covariant quantization of the zero mode of the Green and Schwarz superstring—the superparticle. The essence of this problem lies with the difficulty in covariant separation of first- and second-class constraints in the system. The construction of the FBF extended phase space, its physical content, and its use is explained in detail for several different systems. In the FBF phase space second-class constraints become first class and conventional BRST quantization techniques can be used. The method of FBF is compared to the Stueckelberg-type approach and general conclusions are drawn on restoration of local symmetries in extended phase space. The massive superparticle action is studied and Siegel's local fermionic symmetry in the extended phase space is discussed. The massless limit results in two vector supermultiplets, and the covariant superparticle wave function and propagator are calculated provided certain decoupled fermionic compensators are explicitly retained.

ON COVARIANT QUANTIZATION OF MASSIVE SUPERPARTICLE WITH FIRST CLASS CONSTRAINTS

We use the technique of Batalin and Fradkin to convert the second class fermionic constraints of the massive superparticle into first class constraints. Then the Batalin-Vilkovisky formalism is used to quantize covariantly the resulting theory. Appropriate gauge fixing conditions lead to a completely quadratic action. But the presence of Batalin-Fradkin decoupled components apparently removes the advantage gained from the conversion of second class constraints into first class constraints.

Massive superparticle in d=2+1 and sigma model solitons

The authors show that the gauge-fixed N=2, d=2+1 massive superparticle has an N=4 worldline supersymmetry that is partially broken down to N=2 by the central charge in the supersymmetry algebra. The fact that this model has partial breaking of supersymmetry implies that it is the leading term in the effective action for the solitons of N=2 supersymmetric, 2+1-dimensional sigma models that saturate a Bogomol'nyi bound. Invariant actions can be obtained using the method of non-linear realisations applied to the N=2 super-Poincare group in three dimensions. By explicitly including the central charge in the algebra, the superparticle action appears as a Wess-Zumino-type term. They also construct a supersymmetry extension of a term quadratic in the extrinsic curvature of the worldline, which corresponds to the first correction in the effective action of the soliton.

Particle actions as Wess-Zumino terms for spacetime (super) symmetry groups

Certain particle mechanics actions can be interpreted as Wess-Zumino terms. Two new examples are the non-relativistic spin- 1 2 particle and the relativistic (1 + 1)-dimensional massive superparticle. We show that their actions can be derived systematically from the non-linear realisation of the super-galilean and super-Poincaré groups, respectively, by taking into account the central charge in the algebra. In both cases the action is the lowest component of a Goldstone superfield conjugate to the central charge.

Quantization of the superparticle action in the FBF extended phase space

Covariant quantization of the zero mode of the Green and Schwarz superstring—the superlattice is studied. The essence of this long lasting problem lies within the difficulty in covariant separation of first- and second-class constraints in these systems. A recent new approach of Faddeev, Batalin and Fradkin (FBF) which treats first- and second-class constraints in a symmetrical way is employed here. In the FBF extended phase space second-class constraints become first class and conventional BRST quantization techniques can be used. The method of FBF is compared to the Stuekelberg-type approach and general conclusions are drawn on restoration of local symmetries in extended phase space. The massive superparticle action is studied and Siegel's local fermionic symmetry in the extended phase space is discussed. The massless limit results here in two disjoint vector supermultiplets.

Canonical quantisation of massless superparticles

As an exercise in applying Dirac's methods, massless superparticles are quantised non-covariantly both without and with gauge fixing. The effects on their global symmetries are studied, and all operator ordering questions are discussed and resolved in detail. This allows a direct comparison with a recent treatment of massive superparticles in which covariant but otherwise similar techniques were used. It also provides an illustration of the generic behaviour of global symmetries under non-covariant quantisation procedures.

Superparticle with extrinsic curvature

The leading term in the low-energy effective action for a particle-like solution of a supersymmetric field theory is the massive superparticle action. We construct the leading supersymmetric and fermionic gauge-invariant correction to the action, quadratic in the extrinsic curvature of the particle's worldline. A systematic construction of this and higher-order invariants is given by means of the method of non-linear realisations of spacetime symmetries.

Massive superparticles with Siegel symmetry and their covariant canonical quantisation

We study massive superparticles with Siegel symmetry as toy models of the Green-Schwarz string, and as mechanics actions furnishing minimal representations of supersymmetry upon quantisation. A general construction yielding all such theories is given, and it is shown that the simplest class can be derived from massless models in higher dimensions. We consider the quantisation of massive superparticles using the canonical methods of Dirac, and show that the first-class and second-class constraints can always be defined so as to respect all global symmetries, giving a completely covariant method of quantisation. (This cannot be done in the massless case.) The quantisation is carried out explicitly for the simplest class of models: Dirac brackets are computed and all necessary consistency checks performed. We prove that no operator-ordering problems arise by finding a set of variables for which the covariant Dirac brackets become free canonical graded commutation relations. By considering features shared by massive superparticles and the Green-Schwarz string (but not present for massless superparticles) we argue that the latter should admit a similar covariant quantisation.

MASSIVE SPINNING SUPERPARTICLE

We consider new supersymmetric particle model, describing the massive extension of D=4 spinning superparticle model, derived in Ref. 1. It is shown that our model can be described by the D=5 massless spinning superparticle model after dimensional reduction D=5→D=4 and putting the fifth momentum P5=m. The known massive superparticle and massive spinning particle models can be obtained as special cases. The first quantization of the massive spinning superparticle model gives a N=2 massive vector multiplet (one complex scalar, two Dirac spinors, one massive complex vector field).

The spectrum of spinning superparticles

We construct the action and transformation rules of a massless spinning superparticle in D dimensions which has N worldline as well as M target space supersymmetries. The spectrum of physical states for different values of N, M and D is presented. We also discuss the action, symmetries and spectrum of massive spinning superparticles.

Covariant Hamiltonian formulation of the massive superparticle

The method of covariant Hamiltonian formulation for a superparticle is generalised to the massive case. The covariant quantum (anti) commutators are realised without anomaly. The authors deal with the d=10 case in detail and discuss briefly the d=4 case as well.