An action principle and canonical formalism for the Neveu Schwarz-Ramond string

A Lagrangian giving the constraints and boundary conditions of the Neveu Schwarz-Ramond model is presented.     

Truncation,picture-changing operation and space time supersymmetry in Neveu-Schwarz-Ramond string field theory

The representation of the inverse picture-changing operator in terms of an appropriate truncation operator is found, which means that truncated Ramond string fields are inherent to the Witten construction. Equivalence of the Witten supertransformations and the supertransformations acting on the old truncated fields is established.     

An action principle for the motion of particles

An action principle is set up for the motion of charged matter in the presence of the Einstein gravitational field. It can be applied to the motion of an extended particle and avoids the difficulties of a point particle arising from the singularities in the field.     

Functional equation for the string effective action

A functional equation for the purely gravitational part of the string effective action is found. Among its solutions are the extended Euler densities and products of Wely tensors. A possible recipe for the Ricci temrs is given.     

A complete action for the spinning string

We present an action for the Neveu-Schwarz-Ramond model from which follow both the field equations and the gauge and supergauge constraints. This is done by coupling the free-field action to two-dimensional supergravity in a geometrically clear way. The constraints arise as the supergravity field equations, the supergravity fields playing the role of Lagrange multipliers. The action is invariant under local supersymmetry transformations and, as a consequence, the field equations and the constraints are consistent. The commutator structure of the local supersymmetry algebra is exhibited. It is also shown that there exists a special gauge in which the action, the field equations and the constraints take the free-field from of the usual formulation of the Neveu-Schwarz-Ramond model.     

The geometrical form for the string space-time action

In the present article, we derive the space-time action of the bosonic string in terms of geometrical quantities. First, we study the space-time geometry felt by a probe bosonic string moving in antisymmetric and dilaton background fields. We show that the presence of the antisymmetric field leads to space-time torsion, and the presence of the dilaton field leads to space-time non-metricity. Using these results we obtain the integration measure for space-time with stringy non-metricity, requiring its preservation under parallel transport. We derive the Lagrangian depending on stringy curvature, torsion and non-metricity.     

An action for a classical string,the equation of motion and group invariant classical solutions

A string action which is essentially a Willmore functional is presented and studied. This action determines the physics of a surface in Euclidean three space which can be used to model classical string configurations. By varying this action an equation of motion for the mean curvature of the surface is obtained which is shown to govern certain classical string configurations. Several classes of classical solutions for this equation are discussed from the symmetry group point of view and an application is presented.      

Finite-width corrections to the Nambu action for the Nielsen-Olesen string

The finite-width correction terms to the Nambu action for Nielsen-Olesen strings are calculated. They consist of an extrinsic curvature squared or rigidity term and a new “twist” term. The extrinsic curvature term prevents cusps forming, rounding them off with a curvature radius of the order of the string width.     

A locally supersymmetric and reparametrization invariant action for the spinning string

We construct an action for the spinning string which is locally supersymmetric and reparametrization invariant using the techniques of supergravity. In a special gauge it is shown that the equations of motion and the constraints are those of the Neveu-Schwarz-Ramond model.     

Dimensional renormalization and the action principle

Dimensional renormalization is defined in such a way that the renormalized action principle holds. It is shown that this leads to a minimal, additive renormalization. The derivation of Ward-Takahashi indentities and Callan-Symanzik equations from the action principle is exemplified.     

Ghost vertices for the bosonic string using the group-theoretic approach to string theory

The N-string tree-level scattering vertices for the bosonic string are extended to include anticommuting (ghost) oscillators. These vertices behave correctly under the action of the BRST charge Q and reproduce the known results for the scattering of physical states. This work is an application of the group-theoretic approach to string theory.     

Geometrical string and dual spin systems

We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a two-plaquette gauge hamiltonian. The duality transformation is constructed in geometrical and algebraic language. The dual hamiltonian represents a new type of spin system with local gauge invariance. At each vertex ξ there are d (d − 1) /2 Ising spins ∧_{μ, η} = ∧_{η,μ N}. ≠ P = 1, … , d and one Ising spin Γ on every linkξ ξ + e,). For the frozen spin Γ  1 the dual hamiltonian factorizes into d (d − 1) /2 two-dimensional Ising ferromagnets and into antiferromagnets in the case Γ  −1. For fluctuating F it is a sort of spin-glass system with local gauge invariance. The generalization to p-membranes is given.     

An averaging principle for stochastic dynamical systems with Lévy noise

The purpose of this paper is to establish an averaging principle for stochastic differential equations with non-Gaussian Lévy noise. The solutions to stochastic systems with Lévy noise can be approximated by solutions to averaged stochastic differential equations in the sense of both convergence in mean square and convergence in probability. The convergence order is also estimated in terms of noise intensity. Two examples are presented to demonstrate the applications of the averaging principle, and a numerical simulation is carried out to establish the good agreement.