Jose A. de Azcarraga

Supersymmetric particles with internal symmetries and central charges

Abstract We propose two pseudoclassical particle models invariant under extended Poincare supersymmetry with central charges. In the first model the central charge provides the mass term breaking the U( N ) internal symmetry and in the second model the U( N ) symmetry is preserved. We show that there is a complete analogy between the appearance of the nonrelativistic mass as a parameter which characterizes the central extensions of the Galilei group and the appearance of the fermion mass through the central extensions of the extended Poincare supergroup.

Quantization as a consequence of the symmetry group: An approach to geometric quantization

A method is proposed to obtain the dynamics of a system which only makes use of the group law. It incorporates many features of the traditional geometric quantization program as well as the possibility of obtaining the classical dynamics: The classical or quantum character of the theory is related to the choice of the group, avoiding thus the need of quantizing preexisting classical systems and providing a group connection between the quantum and classical systems, i.e., the classical limit. The method is applied to the free‐particle dynamics and the harmonic oscillator.

Generalized cosmological term from Maxwell symmetries

By gauging the Maxwell spacetime algebra the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six fourvector fields A_\mu^{ab}(x) associated with the six abelian tensorial charges in the Maxwell algebra. In the simplest Maxwell extension of Einstein gravity this leads to a generalized cosmological term that includes a contribution from these vector fields. We also consider going beyond the basic gravitational model by means of bilinear actions for the new Abelian gauge fields. Finally, an analogy with the supersymmetric generalization of gravity is indicated. In an Appendix, we propose an equivalent description of the model in terms of a shift of the standard spin connection by the A_\mu^{ab}(x) fields.

Variational principles on rth order jets of fibre bundles in field theory

The Hamilton and the modified Hamilton variational principles in classical field theory are studied for physical systems described by Lagrangian and Hamiltonian densities depending on arbitrary order derivatives of the field. These principles are established on the fibre bundles Jr(E), J1(Jr−1(E)), J1*(Jr−1(E)). This is accomplished by defining an appropriate Poincare–Cartan form. This form is also required in the definition of the associated symmetry problem and in the explicit construction of the Noether currents.

Gravity, p -branes, and a spacetime counterpart of the Higgs effect

We point out that the worldvolume coordinate functions

Nonrelativistic limit of supersymmetric theories

{x}^{\ensuremath{\mu}}(\ensuremath{\xi})

A note on the meaning of covariant derivatives in supersymmetry

of a p-brane, treated as an independent object interacting with dynamical gravity, are Goldstone fields for spacetime diffeomorphisms gauge symmetry. The presence of this gauge invariance is exhibited by its associated Noether identity, which expresses that the source equations follow from the gravitational equations. We discuss the spacetime counterpart of the Higgs effect and show that a p-brane does not carry any local degrees of freedom, extending early known general relativity features. Our considerations are also relevant for brane world scenarios.

Generalized curvature and the equations of D=11 supergravity

The superfield formulation of the nonrelativistic limit of supersymmetric theories is given using a precise group‐theoretical definition. The procedure is applied to the Wess–Zumino superfield Lagrangian and to supersymmetric QED.

Supersymmetric particle model with additional bosonic coordinates

We analyze in this paper the group theoretical meaning of the covariant derivatives, and show that they are horizontal left‐invariant vector fields on superspace obtained from a (super)Lie group which at the same time exhibits the structure of a principal bundle with a canonical connection. The geometrical construction is general and not restricted to the super‐Poincare group.

Contractions of Filippov algebras

It is known that, for zero fermionic sector, ψμα(x)=0, the bosonic equations of Cremmer–Julia–Scherk eleven-dimensional supergravity can be collected in a compact expression, RabαγΓbγβ=0, which is a condition on the curvature Rαβ of the generalized connection w. In this Letter we show that the equation RbcαγΓabcγβ=4i((Dˆψ)bcΓ[abc)β(ψdΓd])α, where Dˆ is the covariant derivative for the generalized connection w, collects all the bosonic equations of D=11 supergravity when the gravitino is nonvanishing, ψμα(x)≠0.