Covariant quantization of a quark-binding string

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Abstract
An important tool for the investigation of relativistic quantum field theories of strong interactions is the study of their strong-coupling limits. These lead to semigeometric models in which the quark-binding fields reduce to constraining volumes (bags), surfaces (bubbles), or lines (strings). These models are usually first treated classically and then quantized by canonical quantization. The present model was previously investigated by Giles and Tye and by Tye and originated from the "SLAC bubble." A two-dimensional timelike cylinder is embedded in four-dimensional Minkowski space. Massless Dirac fields (quarks) are constrained to it. These can carry any internal-symmetry label. At a fixed time the model represents a loop (closed string) on which quarks circulate. The covariant quantization is possible in a special guage and for timelike (rather than null plane) dynamics if care is taken to treat the corresponding gauge conditions in an internally consistent way. Simultaneity of relative positions of this extended structure in every instantaneous rest frame leads to additional constraints which ensure the absence of ghost states. All primary constraints are proved to be first class also for the quantized system. There are no secondary constraints. The theory is manifestly covariant; the Poincaré algebra is verified explicitly. There are no tachyonic states since the total momentum points into the future light cone. Linearly rising Regge trajectories result as in the free string.