Time-symmetric relativistic and quantum theories. 3. Time-symmetric QFT

Abstract

Time-symmetric relativity theory (TSR) based on Zisman-Stueckelberg-Feynman (ZSF) interpretation includes reference frames going backward in time, maximally expanding their symmetry group to general Lorentz group O(1,3) with 4-inversion (Article 1). Similar time-symmetric (TS) extensions of relativistic quantum mechanics (TS RQM) (Article 2) and QFT (TS QFT) (this article) avoid problems of former RQM and QFT. Former QFT introduced unfounded hypotheses about physical quantum fields in entire space for each type of particle, and these hypotheses led to insoluble problems. TS QFT is limited to known external interaction fields, and describes particles using theory of many-particle systems. In second quantization method, single-particle wave functions and operators, which increase or decrease number of particles in system, form operator amplitudes of transition probabilities. These amplitudes are complex, act in their state spaces for given energy sign, and lead to positive state norm. As in quantum mechanics, they, together with conjugate amplitude, form canonical pair. Canonical formalism in relativity theory is consistent at using Hamilton-Jacobi (HJ) formalism, where 3-momentum and Hamiltonian enter into HJ equation in the same degree. Differential form of relativistic HJ equation is Klein-Gordon (KG) equation, expressing the relationship between energy and momentum, and is general equation for physical components of all operator amplitudes. For bosons, KG equation suffices; for fermions, linearization of HJ equation is required, leading to special first-order equations, such as Dirac equation. Operators of observables are normally ordered, and there are no zero-point fluctuations in ground states. Probability current is determined by 4-momentum and has the same sign; interaction currents are also proportional to probability current and change sign with 4-momentum, which corrects the currents in fermion theory. Introducing interactions into HJ equation leads to new contact terms. Time-symmetric orderings of operator amplitudes lead to causal propagators and usual diagram technique. Taking into account external gravitational field of quanta at Planck length, gravitational radius of the system, and dilation of their proper times in this field lead to gravitational self-regularization of loop diagrams. This makes perturbation theory series in Standard Model (SM) and quantum gravity finite and convergent. Contributions of chiral anomalies are finite and cancel out in SM.