Quantum Spacetime and the Universe at the Big Bang, Vanishing Interactions and Fading Degrees of Freedom

Abstract

As discussed in Bahns et al. (2015) fundamental physical principles suggests that, close to cosmological singularities, the effective Planck length diverges, hence a “quantum point” becomes infinitely extended. We argue that, as a consequence, at the origin of times spacetime might reduce effectively to a single point and interactions disappear. This conclusion is supported by converging evidences in two different approaches to interacting quantum fields on Quantum Spacetime: (1) as the Planck length diverges, the field operators evaluated at a “quantum point” converge to zero, and so do the lowest order expressions for interacting fields in the Yang Feldman approach; (2) in the same limit, we find convergence of the interacting vacuum to the free one at all perturbative orders. The latter result is obtained using the adaptation, performed in Doplicher et al. (2020), of the methods of perturbative Algebraic Quantum Field Theory to Quantum Spacetime, through a novel picture of the effective Lagrangian, which maintains the ultraviolet finiteness of the perturbation expansion and allows one to prove also the existence of the adiabatic limit. It remains an open question whether the S matrix itself converges to unity and whether the limit in which the effective Planck length diverges is a unique initial condition or an unreachable limit, and only different asymptotics matter.

Renormalization on the DFR Quantum Spacetime

“…Its application to the study of quantum fields on the DFR quantum spacetime is an important addition to the already extensive body of work where other approaches to QFT have been extended to this non-commutative Minkowski spacetime. Just to name a few, there is one approach inspired in the normal order by point-splitting [9], another one based on the Yang-Feldman equa- tion [20]. The point-splitting version has been written in the pAQFT framework [15].…”

Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence

“…The resulting theory is ultraviolet finite [4], but needs an adiabatic cutoff in time, which seems difficult to remove. On the other hand, the resulting theory has interesting applications to Cosmology [13,14,12] and generalizations to curved spacetimes are being also studied [13,32,28]. For other possibilities to define interactions, see [5,33] and the review [3].…”

Hilbert Mathematics Versus Gödel Mathematics III- Hilbert Mathematics by Itself, and Gödel Mathematics Versus the Physical World within It: both as Its Particular Cases

“…The problematic of what had been "at, before, or beyond the Big Bang" can be traced back in a quite various series of papers (e.g Doplicher, Morsella, Pinamonti 2020;Klinkhamer 2020;Zen Vasconcellos,. …”