Classical Solutions for the Supersymmetric Grassmannian Sigma Models in Two Dimensions. I : Nuclear Physics (original) (raw)
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Classical Solutions for the Supersymmetric Grassmannian Sigma Models in Two Dimensions. I
Progress of Theoretical Physics, 1984
The supersymmetric version of the complex Grassmannian sigma models (defined on the Grassmann manifold) in two euclidean dimensions is studied. By adopting the newly found solutions of the purely bosonic Grassmannian sigma model as the background fields, we• construct explicit fermion classical solutions for the supersymmetric linearized Dirac equations. These fermion solutions are obtained in an elementary way just like their bosonic partners.
Classical solutions in Grassmannian σ-models
Letters in Mathematical Physics, 1981
We study the generalisation of the CP n−1 model in two-dimensional Euclidean space-time to Grassmannian σ-models having a non-Abelian gauge group. Some classes of classical solutions are displayed. It appears that the general solutions involve complicated constraints.
Supersymmetry and the Dirac equation
Annals of Physics, 1988
We discuss in detail two supersymmetries of the 4-dimensional Dirac operator D-italic-dash-bar² where D-italic-dash-bar = partial-dash-bar-ieA-italic-dash-bar, namely the usual chiral supersymmetry and a separate complex supersymmetry. Using SUSY methods developed to categorize solvable potentials in 1-dimensional quantum mechanics we systematically study the cases where the spectrum, eigenfunctions, and S-matrix of D-italic-dash-bar² can be obtained analytically. We relate these solutions to
Classical solutions in two-dimensional supersymmetric field theories
Nuclear Physics B - NUCL PHYS B, 1977
Classical solutions of some supersymmetric field theories in two dimensiofis are investigated. These solutions are constructed by solving first-order differential equations in superspace, which are the supersymmetric extension of the analogous equations used in the purely bosonic sector.
Zeitschrift für Physik C Particles and Fields, 1990
We present solutions of a fermion-boson model based on the supersymmetric (Susy) extension of the U(N) a-models with the Wess-Zumino-Witten (WZW) term. We study some properties of these solutions. We point out that the obtained solutions are related to the components of the energy-momentum tensor of the purely bosonic U(N)a-model and that some classes of these solutions are traceless.
Physics Letters B, 1989
A remarkable equivalence is established between the theories of spinning particles or superparticles using anticommuting Grassmann variables on the one hand and commuting c-number spinors on the other. We consider both real and complex Grassmann variables and map the equations of motion and the supersymmetry transformation from one theory to another. The more intuitive c-number theory allows us to generalize the notion of Zitterbewegung to strings and membranes. A hidden supersymmetry exists in the classical model of the Dirac electron.
General solutions of the supersymmetric ℂP2 sigma model and its generalisation to ℂPN−1
Journal of Mathematical Physics, 2016
A new approach for the construction of finite action solutions of the supersymmetric CP N−1 sigma model is presented. We show that this approach produces more nonholomorphic solutions than those obtained in previous approaches. We study the CP 2 model in detail and present its solutions in an explicit form. We also show how to generalise this construction to N > 3.
Grassmann Numbers and Clifford-Jordan-Wigner Representation of Supersymmetry
Journal of physics, 2013
The elementary particles of Physics are classified according to the behavior of the multi-particle states under exchange of identical particles: bosonic states are symmetric while fermionic states are antisymmetric. This manifests itself also in the commutation properties of the respective creation operators: bosonic creation operators commute while fermionic ones anticommute. It is natural therefore to study bosons using commuting entities (e.g. complex variables), whereas to describe fermions, anticommuting variables are more naturally suited. In this paper we introduce these anticommuting-and at first sight unfamiliar-variables (Grassmann numbers) and investigate their properties. In particular, we briefly discuss differential and integral calculus on Grassmann numbers. Work supported in part by DOE contracts No. DE-AC-0276-ER 03074 and 03075; NSF Grant No. DMS-8917754.
Bosonized supersymmetry from the Majorana-Dirac-Staunton theory and massive higher-spin fields
Physical Review D, 2008
We propose a (3+1)D linear set of covariant vector equations, which unify the spin 0 ``new Dirac equation'' with its spin 1/2 counterpart, proposed by Staunton. Our equations describe a spin (0,1/2) supermultiplet with different numbers of degrees of freedom in the bosonic and fermionic sectors. The translation-invariant spin deegres of freedom are carried by two copies of the Heisenberg algebra. This allows us to realize space-time supersymmetry in a bosonized form. The grading structure is provided by an internal reflection operator. Then the construction is generalized by means of the Majorana equation to a supersymmetric theory of massive higher-spin particles. The resulting theory is characterized by a nonlinear symmetry superalgebra, that, in the large-spin limit, reduces to the super-Poincare algebra with or without tensorial central charge.
Geometry and duality in supersymmetric σ-models
Nuclear Physics B, 1996
The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear σ-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis sheds light on the boson-fermion symphysis of the dual transition, and on the new geometry of the DSM. 1 i.e. preserve canonical commutation relations. Canonical transformations in quantum mechanics underlie Dirac's path integral formulation [4], and have been discussed extensively in field theory, e.g. [5, 6, 7].