Kaku Ogawa

Covariant Quantization of String Based on BRS Invariance

Abstract Covariant canonical quantization of the bosonic string is performed, based on the BRS invariance principle. Defining a physical state by a modified form of Kugo-Ojimas subsidiary condition QB|phys〉 = 0 (QB = BRS charge), we prove a no-ghost theorem in a simple manner. There an interesting relation between critical dimension and BRS symmetry is noticed; namely, the conditions D = 26 and α0 = 1 for the space-time dimension D and the zero-intercept α0 of leading trajectory are required by the nilpotency QB2 = 0 of the BRS charge. In addition, ghost number fractionization is observed in this system.

Manifestly covariant field theory of interacting string I

Abstract A manifestly covariant field theory is constructed for the interacting bosonic open string. A very simple string action is presented which is invariant under an inhomogeneous nilpotent BRS transformation. The on-shell scattering amplitudes in this theory reproduce the Koba-Nielsen amplitudes at the tree level, aside from a contributions from a necessary quartic interaction term.

Pregeometrical String Field Theory: Creation of Space-time and Motion

Abstract A space-time-metric-independent and gauge-invariant formulation of closed-string field theory is proposed. The action contains no kinetic term and consists solely of a cubic term in the string field. The kinetic term can be generated through the condensation of an infinitesimally small string.

The gauge invariant action of the interacting string field

Abstract The gauge invariant action of the interacting bosonic string field is constructed for both open and closed string cases, on the basis of the vertices which were used in our previous gauge-fixed action. In both cases, the usual dual amplitudes are correctly reproduced at the tree level. The algebra of gauge transformations is clarified. It closes off-shell for the closed string case, while it closes only on-shell and has field-dependent “structure constants” for the open string case. We also discuss the gauge-fixing procedure and the relation of these theories to the previous gauge-fixed actions. It is pointed out that the gauge-fixing procedure becomes quite non-trivial generally in the interacting string theories.

BRS invariance of the Witten type vertex

Abstract It is proved rigorously that the Witten type 3-string vertex is BRS invariant if and only if the space-time dimension is equal to 26. We use the fermionic representation for the reparametrization ghost.

Generalized Schrödinger representation and its application to gauge field theories

A generalization of the Schrodinger representation is presented and applied to theories with indefinite metric as well as those with positive definite metric. It enables us to construct the wavefunctional formalism of the quantum electromagnetic field equivalent to the operator formalism in covariant gauges. The theoretical foundation of the Wick rotation of the dynamical variable A0(x) is established.