Finite quantum theory of fields and strings. 1. Consistent quantization in the Stueckelberg-Feynman treatment

Abstract

In standard quantum field theory, where free quanta have only positive energy, the antiparticle operators were introduced “manually” and this led to the diverging zero-point energy, which meant the inconsistency of the theory. In the Stueckelberg-Feynman (SF) treatment the positive-energy antiparticles are described as the negative energy particles going backward in time and here some Lagrangians do not lead to the zero-point energy. But earlier it was believed that this treatment leads to a negative norm of states and therefore is also inconsistent. In the paper a consecutive method of canonical quantization of fields and strings in the SF treatment is formulated, where a correct choice of the action function makes the norm of states positive and the choice of a minimal Lagrangian makes it free from the zero-point energy. The symmetric chronological product of operators is introduced, turning into ordinary chronological at forward and antichronological at backward in time evolution. This leads to the causal SF propagator and to the standard diagram technique for interacting fields. String theories containing the zero-point energy of modes are inconsistent, since regularization is impossible at Planck distances due to the inevitable presence of gravity. At quantization of strings in SF treatment, there are models without zero-point energy, which are therefore finite and only consistent, but they do not have a conformal anomaly and critical dimension. The effects attributed to the zero-point energy (Lamb shift, Casimir effect) are explained across the contributions of the fields of real sources and confirm the lack of zero-point vacuum energy. This partly solves the cosmological constant problem. From the SF treatment one can turn to the antiparticle picture by means of the charge conjugation or crossing symmetries. The main consequences of the proposed consistent method of quantization of fields and strings are discussed. quantum field theory, zero-point energy, cosmological constant, antiparticles, composite models, Casimir effect, chronological ordering, propagators, string theory, conformal anomaly, dimensions