The triviality of the Abelian Thirring quantum field model

Triviality—Quantum Decoherence of Fermionic Quantum Chromodynamics SU(N c ) in the Presence of an External Strong U(∞) Flavored Constant Noise Field

“…Note that the same matter loop C xx appearing in (12) enters in the definition of all loop space objects in (5). As a consequence, we have produced a loop space analysis supporting that at very large noise strength (g (∞) → +∞), one has exactly the strong triviality of the SU(N c ) on the sector of the quark Abelian currents, in the mathematical sense that the dominant loops on the loop path integral (5) …”

“…In the fermionic loop space framework [1][2][3][4][5][6][7][8][9][10][11], we can express the quark functional determinant, (1)-which has been obtained as an effective generating functional for the color N c -singlet quark current after integrating out the Euclidean quark action-as a purely functional on the bosonic bordered loop space composed of all trajectories C xx = {X μ (σ ),…”

“…The sum over the closed bosonic loops C xx , with end-point x is given by the proper-time bosonic path integral below [1][2][3][4][5][6][7][8] …”

“…Recently, we have proposed a bosonic loop space formalism for understanding the important problem of triviality in interacting Gauge Field theories [1][2][3][4][5][6][7][8]. The basic idea used in our work above mentioned in order to analyze such kind of quantum triviality phenomena was the systematic use of the framework of the loop space to rewrite particle-field path integrals in terms of its ensembre of quantum trajectories and the introduction of a noisily electromagnetic field as an external quantized reservoir.…”

A connection between fermionic strings and quantum gravity states: a loop space approach

“…which is not relevant in our study!) as another formal Einstein gravitation quantum state to be used in the analysis which follows [21][22][23][24][25][26], an important result by itself.…”