Vertex operators of closed bosonic string

A closed bosonic string emission and absorption vertex operator is constructed in the framework of the path-integral formulation of string theories. The vertex operator is a functional of an external string wave function as well as a string coordinate and a metric variable. Conformal invariance is the guiding principle of the construction. By demanding the metric variable to be decoupled from the theory a set of Virasoro conditions is obtained for the external string wave function and a number of conformal breaking terms to be added to the generating functional.     

Spectra of Liouville operators

Spectra of the generators of time translations (Liouville operators) on representation spaces determined by thermodynamic equilibrium states are compared and their nature is investigated.     

Covariant field theory of the compactified closed bosonic string

We covariantly first-quantize, via the BRST approach, the closed bosonic string compactified on a torus — in particular the 18-dimensional theory with E₈ × E₈ gauge bosons. Further, we give the corresponding free field theory. Thus the model is ready for the introduction of string interactions, and may be very useful for the study of gauge interactions in string theories.     

The finite gauge transformations in closed string field theory

The finite gauge transformations for the classical nonpolynomial closed string field theory are constructed by iteration of infinitesimal transformations. A simple rule for the determination of the coefficients of the arising series is found.Supported by funds provided by the Max Kade Foundation.     

Lorentz invariance of lightcone string field theory: (I). Bosonic closed string

We construct the Lorentz generators for bosonic closed lightcone string field theory with cubic interactions, and prove that the Lorentz algebra closes if the spacetime dimension is 26.     

Coset representation of closed loop space in string field theory

By taking analogy with Minkowski space, we construct a closed loop space CM which is an infinite-dimensional coset space and discuss some of its consequences.     

The cosmological constant of modular closed string field theory. I

We formulate closed string field theory as a quantum theory of modular geometry. We determine the full interacting quantum hamiltonian to all loop orders in perturbation theory. The free action has a new highly non-linear symmetry acting on the string field, and the kinetic operator. Perturbatively we demonstrate that the new theory gives the correct expression for the cosmological constant that is ultraviolet finite to one-loop order.     

Scalar field potentials for closed and open cosmological models

We develop a technique for the reconstruction of the potential for a scalar field or a tachyon field, reproducing a given cosmological evolution in a closed and open isotropic cosmological models. Such potentials are explicitly written down for the cases of the evolutions driven by a generic barotropic fluid and by radiation plus a cosmological constant, for the case of a scalar field. For tachyon and pseudo-tachyon fields the potentials are reconstructed for some special cases, corresponding to particular values of the barotropic index.     

Embedded eigenvalues of Sturm Liouville operators

In this work we study the behavior of embedded eigenvalues of Sturm-Liouville problems in the half axis under local perturbations. When the derivative of the spectral function is strictly positive, we prove that the embedded eigenvalues either disappear or remain fixed. In this case we show that local perturbations cannot add eigenvalues in the continuous spectrum. If the condition on the spectral function is removed then a local perturbation can add infinitely many eigenvalues.     

Stationary rotating string world models with a magnetic field

Following the techniques used by Letelier and Stachel some new physically relevant stationary solutions of string cosmology with magnetic field are presented. In these solutions, the flow vector of matter has non-zero rotation and the cosmological constant is taken to be non-zero. Previously known solutions are derived as particular cases from our class of solutions. Some string models with vanishing cosmological constant are also discussed.     

Field theory of the interacting string: The closed string

We recast dual models in the language of a quantum field theory of functional fields, restricting ourselves for simplicity to the closed string model. We derive the dynamics for both scalar and spinor functional fields from a unique parametrization invariant action. Passages to the Hamiltonian formalism and second quantization are explicitly worked out for the closed mesonic string in the front form. The results are equivalent to those obtained earlier by GGRT, i.e. no ghost fields at the price of an anomalous number of space-time dimensions and a tachyon. Finally, we use the parametrization invariance requirement on the action to derive couplings of closed strings to local fields by extending a global U(1) invariance built in the free action into a local one in the functional sense. We construct the self-couplings of closed string fields by requiring these to be consistent with the gauge invariance of the external fields. This procedure uniquely leads (for the open string) to the string splitting picture of Nambu and Mandelstam. The closed string is found to cross itself and then split up into two others. Both open and closed strings have quartic interactions corresponding to strand (for the open string) and lobe (for the closed string) exchanges. The case of the interacting fermionic model is not treated here.