[en] This book constitutes the proceedings of an International School of Supersymmetry held in Mexico City in 1981. Lectures presented include an introduction to supersymmetry (symmetries in relativistic quantum field theory, supersymmetry in quantum field theory, Dirac matrices and Majorana spinors, supersymmetric Yang-Mills theory, scalar multiplet and auxiliary fields, supergravity, N=1 supersymmetric theories, extended supersymmetry algebras, representations of extended supersymmetry, N=4 supersymmetric Yang-Mills theory, extended supergravity), superfields (irreducible representations and chiral superfields, invariants and ''tensor calculus,'' gauge superfield, N=1 supergravity), grand unification with and without supersymmetry (supersymmetric models), Yang-Mills theories with global and local supersymmetry (Higgs and Superhiggs effect in unified field theories), and supergroups and their representations (fermion and Grassmann numbers, supertrace and superdeterminant, harmonic oscillator representation, the Tilde operator, eigenvalues of Casimir operators, branching rules, Kac-Dynkin diagrams and supertableaux)

[en] The paper concerns the spinorial dynamical structure of the four presently known supersymmetric massive vector systems. The 3D superspace, the standard scalar and vector massive supermultiplets, the Abelian topological massive vector system and the self-dual model, and the super-non-Abelian topological massive vector system, are all discussed. (U.K.)

[en] We study the quantization of the electromagnetic sector of the Myers-Pospelov model coupled to standard fermions. Our main objective, based upon experimental and observational evidence, is to construct an effective theory which is a genuine perturbation of QED, such that setting the Lorentz invariance violation parameters to zero will reproduce it. To this end we provide a physically motivated prescription, based on the effective character of the model, regarding the way in which the model should be constructed and how the QED limit should be approached. This amounts to the introduction of an additional coarse-graining physical energy scale M, under which we can trust the effective field theory formulation. The prescription is successfully tested in the calculation of the Lorentz invariance violating contributions arising from the electron self-energy. Such radiative corrections turn out to be properly scaled by very small factors for any reasonable values of the parameters and no fine-tuning problems are found. Microcausality violations are highly suppressed and occur only in a spacelike region extremely close to the light cone. The stability of the model is guaranteed by restricting to concordant frames satisfying 1-|v_max|>6.5x10^-11.

[en] Classical finite-energy exact solutions of a spin 0-1/2 two dimensional supersymmetric model are investigated. The static case can be completely integrated in terms of any solution of the purely bosonic sector, for an arbitrary potential. The localized fermionic part of the solution can always be rotated to zero by a supersymmetry transformation. This is not the case for the Grassmannian part of the scalar field which can be localized also. Stationary solutions for the fermionic field with potentials corresponding to the phi⁴ and sine-Gordon theories, for specific choices of the purely bosonic sector, are also considered. In the former case we find a single localized fermionic solution which can not be rotated to zero by a supersymmetry transformation. In the latter case no such solution exists. (author)

[en] We construct a perturbative expansion of the scalar sector in the Myers-Pospelov model, up to second order in the Lorentz violating parameter and taking into account its higher-order time derivative character. This expansion allows us to construct an hermitian positive-definite Hamiltonian which provides a correct basis for quantization. Demanding that the modified normal frequencies remain real requires the introduction of an upper bound in the magnitude |k| of the momentum, which is a manifestation of the effective character of the model. The free scalar propagator, including the corresponding modified dispersion relations, is also calculated to the given order, thus providing the starting point to consider radiative corrections when interactions are introduced

[en] The equivalence between the Non-Abelian Nambu model (NANM) and Yang Mills theory is proved, after demanding the Gauss laws at some initial time to the first one. Thereby, the Lorentz violation encoded into the constraint that defines the NANM is physically unobservable. As result, the Goldstone bosons in the NANM arising from the spontaneous symmetry breaking can be identified as the standard gauge fields. (paper)

[en] In this note we summarize the exact solution of the doubly compactified Schwinger model (CSM), defined by the condition that the domain of the electromagnetic degree of freedom c=1/L∫₀^LdxA₁ is -c-bar< c<+c-bar. The results are contrasted with the standard situation, where -∞< c<+∞, which we call the non-compact case (NCSM). Both theories are also compactified in a circle of length L for the space variable x

[en] We calculate the magnetic field produced by a capacitor formed by two semispherical perfectly conducting plates of radius a, subjected to a potential difference and surrounded by a spherical shell of a topologically insulating material having internal radius r ₁ and external radius r ₂. Fixing r ₂ = 1 μm and considering the case where the shell touches the metallic plates, i. e. when r ₁ = a, we find that the maximum magnetic field occurs at the external surface of the shell when r ₁≲ 0.75 μm. For these cases we examine the effect in the two remaining variables: the thickness of the shell and axial angular dependence of the magnetic field. For r ₁ = 0.5 μm we find a highly isotropic angular distribution with an average field of magnitude $|\mathbf{B}|\approx <!--\; ???\; -->0.2$ G. The angular anisotropy increases with r ₁, yielding $0.17\mathrm{G}\lesssim <!--\; ???\; -->|\mathbf{B}|\lesssim <!--\; ???\; -->0.35\mathrm{G}$ for r ₁ = 0.62 μm and $0.1\mathrm{G}\lesssim <!--\; ???\; -->|\mathbf{B}|\lesssim <!--\; ???\; -->0.6\mathrm{G}$ for r ₁ = 0.75 μm. These magnitudes fall within the sensitivities of magnetometers based upon nitrogen-vacancy centers in diamond, as well as of devices using scanning SQUID magnetometry. In the latter case we obtain fluxes in the range of (6 − 10) × 10⁻¹⁰ G cm² for a pickup loop of radius 10 μm centered at the axial symmetry axis and located parallel to the equatorial plane at distances ranging from 2 to 6 μm from the center of the capacitor. (paper)

[en] The SU(2)⊗SU(2) extension of the Jaynes–Cummings model provides a quantum mechanical system with a finite Hilbert space together with a maximum energy level in the spectrum. The model, which remains exactly solvable, is based on the replacement of the bosonic (creation and annihilation) operators by spin operators defined to act within a definite SU(2) irreducible representation, in such a way that the photon field has a finite number of excitations. The usual Heisenberg–Weyl (h(1)) algebra can be obtained by contraction of the su(2) Lie algebra. We analyze the behavior of both the atomic and field quantum properties, like collapse and revivals, photon antibunching and squeezing, giving special attention to their dependence upon the maximum number of photon excitations. (paper)

[en] Even though models with spontaneous Lorentz-symmetry breaking also damage gauge invariance, an interesting possibility that emerges is to interpret the resultant massless Goldstone bosons as the gauge bosons of the related gauge theory. In this contribution we review the conditions under which gauge invariance is recovered from such models. To illustrate our general approach we consider the classical Abelian bumblebee and Nambu models. In the former case we prove its connection with electrodynamics by a procedure which takes proper care of the gauge-fixing conditions. In the case of the Abelian Nambu model its relation with electrodynamics is established in such a way that the generalization to the non-Abelian case is straightforward. (paper)