Non-local Conservation Laws and Flow Equations¶ for Supersymmetric Integrable Hierarchies

An infinite series of Grassmann-odd and Grassmann-even flow equations is defined for a class of supersymmetric integrable hierarchies associated with loop superalgebras. All these flows commute with the mutually commuting bosonic ones originally considered to define these hierarchies and, hence, provide extra fermionic and bosonic symmetries that include the built-in N=1 supersymmetry transformation. The corresponding non-local conserved quantities are also constructed. As an example, the particular case of the principal supersymmetric hierarchies associated with the affine superalgebras with a fermionic simple root system is discussed in detail.     

The BV Formalization of Chern-Simons Theory on Deformed Superspace

In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-Simons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky (BV) formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.     

The BV Formalization of Chern-Simons Theory on Deformed Superspace

In this paper we will study non-abelian Chern-Simons theory on a deformed superspace. We will deform the superspace in such a way that it includes the noncommutativity between bosonic and fermionic coordinates. We will first analyse the BRST and the anti-BRST symmetries of the Chern-Simons theory on this deformed superspace. Then we will analyse the extended BRST and the extended anti-BRST symmetries of this theory in the Batalin-Vilkovisky (BV) formalism. Finally, we will express these extended BRST and extended anti-BRST symmetries in extended superspace formalism by introducing new Grassmann coordinates.     

Quantum Isometries of the Finite Noncommutative Geometry of the Standard Model

We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M × F, where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.     

Local symmetries and phase space dynamics of finite-dimensional systems

A method to implement reparametrization covariance and additional local symmetries for finite-dimensional systems in a phase space is presented. The approach is a physically and group-theoretically motivated alternative to the Dirac-Bergman algorithm for theories with Hamiltonian constraints. The method is applied to bosonic and fermionic systems with both first and second class constaints.     

Hidden symmetries in minimal five-dimensional supergravity

We study the hidden symmetries arising in the dimensional reduction of d=5, supergravity to three dimensions. Extending previous partial results for the bosonic part, we give a derivation that includes fermionic terms, shedding light on the appearance of the local hidden symmetry SO(4) in the reduction.     

Exact Solutions of Supersymmetric KdV-a System via Bosonization Approach

Bosonization approach is applied in solving the most general N=1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a (sKdV-a) equation. By introducing some fermionic parameters in the expansion of the superfield, the sKdV-a equation is transformed to a new coupled bosonic system. The Lie point symmetries of this model are considered and similarity reductions of it are conducted. Several types of similarity reduction solutions of the coupled bosonic equations are simply obtained for all values of a. Some kinds of exact solutions of the sKdV-a equation are discussed which was not considered integrable previously.     

Exact Solutions of Supersymmetric KdV-a System via Bosonization Approach

Bosonization approach is applied in solving the most general N=1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a (sKdV-a) equation. By introducing some fermionic parameters in the expansion of the superfield, the sKdV-a equation is transformed to a new coupled bosonic system. The Lie point symmetries of this model are considered and similarity reductions of it are conducted. Several types of similarity reduction solutions of the coupled bosonic equations are simply obtained for all values of a. Some kinds of exact solutions of the sKdV-a equation are discussed which was not considered integrable previously.     

Spin description in the star product and path integral formalisms

Spin can be described in the star product formalism by extending the bosonic Moyal product in the fermionic sector. One can then establish the relation to other approaches that describe spin with fermionic variables. The fermionic star product formalism and the fermionic path integral formalism are related in analogy to their bosonic counterparts.     

Gauge-invariant effective lagrangians for goldstone-like particles of supersymmetric technicolor models

We point out that generally the low-energy spectrum in supersymmetric technicolor models contains quasi-Goldstone fermions and quasi-Goldstone bosons in addition to the usual (pseudo)- Goldstone bosons. Using the language of Kähler geometry, we present a step-by-step procedure for constructing gauge-invariant non-linear lagrangians involving the fermionic and bosonic Goldstone particles in situations in which supersymmetry is preserved. Both the cases of fully gauged and partially gauged global symmetries are considered. We discuss the dynamical version of the super-Higgs mechanism, and we illustrate it with the supersymmetric Susskind-Weinberg technicolor model.     

OSp[D+1,3 | 2] unifies the conformal symmetry and BRST

We show that the conformal transformations on the invariant metric of OSp[D,2 | 2], which is the group unifying Lorentz and BRST symmetries, are generated by OSp[D+1, 3 | 2], which thus unifies the conformal and BRST symmetries. We explicitly construct the generators for the scalar and for the spinning particle. We express the generators in terms of the energy-momentum tensor and study their action on the fields. We also study the linear realization of OSp[D+1, 3 | 2] on a space of D+4 bosonic and 2 fermionic variables. Field quantization is also examined.     

Dynamical creation of bosonic cooper-like pairs

We propose a scheme to create a metastable state of paired bosonic atoms in an optical lattice. The most salient features of this state are that the wave function of each pair is a Bell state and that the pair size spans half the lattice, similar to fermionic Cooper pairs. This mesoscopic state can be created with a dynamical process that involves crossing a quantum phase transition and which is supported by the symmetries of the physical system. We characterize the final state by means of a measurable two-particle correlator that detects both the presence of the pairs and their size.     

Are bosonic replicas faulty?

Motivated by the ongoing discussion about a seeming asymmetry in the performance of fermionic and bosonic replicas, we present an exact, nonperturbative approach to both fermionic and bosonic zero-dimensional replica field theories belonging to the broadly interpreted beta=2 Dyson symmetry class. We then utilize the formalism developed to demonstrate that the bosonic replicas do correctly reproduce the microscopic spectral density in the QCD-inspired chiral Gaussian unitary ensemble. This disproves the myth that the bosonic replica field theories are intrinsically faulty.     

Superparticles in D>11

Actions for two-superparticle system in (10,2) dimensions and three-superparticle systems in (11,3) dimensions are constructed. These actions have worldline bosonic and fermionic local symmetries, and target space global supersymmety generalizing the reparametrization, κ-symmetry and Poincaré supersymmetry of the usual superparticle. With the second particle, or the second and third particles on-shell, they describe a superparticle propagating in the background of a second superparticle in (10,2) dimensions, or two other superparticles in (11,3) dimensions. Symmetries of the action are shown to exist in presence of super Yang-Mills background as well.     

Quantum Correlations in Systems of Indistinguishable Particles

We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated by recent experiments and theoretical investigations on quantum dots and neutral atoms in microtraps as tools for quantum information processing. We present analogies between distinguishable particles, bosons, and fermions in low-dimensional Hilbert spaces. We introduce the notion of Slater rank for pure states of pairs of fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable particles. This concept is generalized to mixed states and provides a correlation measure for indistinguishable particles. Then we generalize these notions to pure fermionic and bosonic states in higher-dimensional Hilbert spaces and also to the multi-particle case. We review the results on quantum correlations in mixed fermionic states and discuss the concept of fermionic Slater witnesses. Then the theory of quantum correlations in mixed bosonic states and of bosonic Slater witnesses is formulated. In both cases we provide methods of constructing optimal Slater witnesses that detect the degree of quantum correlations in mixed fermionic and bosonic states.     

Semiclassical quantization of the supermembrane

We approach the quantization of the eleven-dimensional supermembrane from a semiclassical viewpoint. We quantize the fluctuations around a topologically-stabilized toroidal background, and find that the bosonic and fermionic contributions to the vacuum energy cancel. This result appears to depend crucially on the fermionic gauge symmetry and spacetime supersymmetry.     

Cliffordization, spin, and fermionic star products

Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the algebraic properties of quantum field theory. In the context of quantum mechanics they provide a quantization procedure for systems with either bosonic or fermionic degrees of freedom. We illustrate this procedure for a number of physical examples, including bosonic, fermionic, and supersymmetric oscillators. We show how non-relativistic and relativistic particles with spin can be naturally described in this framework.     

Can supersymmetric theories be bosonized?

We investigate the possibility of transforming supersymmetric theories into pure;y fermionic or bosonic forms. The supersymmetric sine-Gordon lagrangian is rewritten in a purely fermionic form, and the Fermi equivalent of the original supersymmetry transformation is derived. This transformation represents an invariance only at the quantum level, when the effects of the chiral anomaly have been taken into account. When supersymmetric theories are written in purely bosonic forms, a non-local bosonic transformation takes place of the supersymmetry transformation. In both cases the supersymmetry algebra, as realized on the fields, is lost.