The perturbative approach to quantum field theory using retarded functions is extended to noncommutative theories. Unitarity as well as quantized equations of motion are studied and seen to cause problems in the case of space-time noncommutativity. A modified theory is suggested that is unitary and preserves the classical equations of motion on the quantum level. PACS: 11.10.Nx, 11.25.Db

We identify spacetime symmetry charges of 26D open bosonic string theory from an infinite number of zero-norm states (ZNS) with arbitrary high spin in the old covariant first quantized string spectrum. We give various evidences to support this identification. These include massive sigma-model calculation, Witten string field theory calculation, 2D string theory calculation and, most importantly...

The field equations of the Chern-Simons theory quantized in the axial gauge are shown to be completely determined by supersymmetry Ward identities which express the invariance of the theory under the topological supersymmetry of Delduc, Gieres and Sorella together with the usual Slavnov identity without requiring any action principle.

A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.

Two-dimensional quantum chromodynamics in the light-front frame is studied following hamiltonian methods. The theory is quantized using the path integral formalism and an effective theory similar to the Nambu-Jona Lasinio model is obtained. Confinement in two dimensions is derived by analyzing directly the constraints in the path integral.

We discuss the possible form of gluon and ghost propagators in the infrared region of Yang-Mills theory in the covariant gauge from the viewpoint of general principles of quantized gauge field theories.

We show that the bosonic string theory quantized in the Beltrami parametrization possesses a supersymmetric structure like the vectorsupersymmetry already observed in topological field theories. Supported in part by the ”Fonds zur Förderung der Wissenschaftlichen Forschung”, M008-Lise Meitner Fellowship.

Physical content of the nonrelativistic quantum field theory with non-Abelian Chern-Simons interactions is clarified with the help of the equivalent first-quantized description which we derive in any physical gauge.

The ADM Formalism is discussed in the context of 2 + 1–dimensional gravity, uniting two areas of relativity theory in which Stanley Deser has been particularly active. For spacetimes with topology IR×T 2 the partially reduced and fully reduced ADM formalism are related and quantized, and the role of " large diffeomorphisms " (the modular group) in the quantum theory is illustrated.

In the OSp invariant closed string field theory, we construct the states corresponding to parallel D-branes that are located at different points in the space-time. Using these states, we evaluate annulus amplitudes. We show that the results coincide with those of first quantized string theory. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]