Marco de Cesare (King's Coll. London) , Fedele Lizzi (Naples U. & INFN, Naples & ICC, Barcelona U.) , Mairi Sakellariadou (King's Coll. London)

We consider implications of the microscopic dynamics of spacetime for the evolution of cosmological models. We argue that quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which is thus considered as a macroscopic effective dynamical quantity. Consistency with Riemannian geometry entails the presence of a time-dependent dark energy term in the […]

Carmelo P. Martin, Josip Trampetićand Jiangyang You

We show that in the perturbative regime defined by the coupling constant, the θ-exact Seiberg-Witten map applied to the noncommutative U(N) Yang-Mills — with or without Supersymmetry — gives an ordinary gauge theory which is, at the quantum level, dual to the former. We do so by using the on-shell DeWitt effective action and dimensional […]

Carmelo P. Martin, Josip Trampetićand Jiangyang You

The equivalence of the noncommutative U(N) quantum field theories related by the θ-exact Seiberg- Witten maps is, in this paper, proven to all orders in the perturbation theory with respect to the coupling constant. We show that this holds for super Yang-Mills theories with N 1⁄4 0, 1, 2, 4 supersymmetry. A direct check of […]

Francesco D'Andrea (Naples U. & INFN, Naples) , Maxim A. Kurkov (ABC Federal U.) , Fedele Lizzi (Naples U. & INFN, Naples & Barcelona U., ECM)

In this paper, we discuss two features of the noncommutative geometry and spectral action approach to the Standard Model: the fact that the model is inherently Euclidean, and that it requires a quadrupling of the fermionic degrees of freedom. We show how the two issues are intimately related. We give a precise prescription for the […]

Carmelo P. Martin (Madrid, Autonoma U.), Josip Trampetic (Boskovic Inst., Zagreb & Munich, Max Planck Inst.), Jiangyang You (Boskovic Inst., Zagreb).

Abstract: We compute the one-loop 1PI contributions to all the propagators of the noncommutative (NC) N = 1, 2, 4 super Yang-Mills (SYM) U(1) theories defined by the means of the θ-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then we extract the UV divergent contributions and the noncommutative IR divergences. We show that all […]

Fedele Lizzi

I make some considerations on the quantization of spacetime from a spectral point of view. The considerations range from the renormalization flow, to the standard model, to a new phase of spacetime.

Catarina Bastos (Lisbon, IST), Alex E. Bernardini (Sao Carlos Federal U.), Orfeu Bertolami (Porto U.), Nuno Costa Dias (GFMUL, Lisbon & Lusofona U.), João Nuno Prata (Escola Superior Nautica Infante D. Henrique)

One examines putative corrections to the Bell operator due to the noncommutativity in the phase-space. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the […]

Gianpiero Mangano, Fedele Lizzi, and Alberto Porzio

Motivated by the Dirac idea that fundamental constants are dynamical variables and by conjectures on quantum structure of space–time at small distances, we consider the possibility that Planck constant ℏ is a time depending quantity, undergoing random Gaussian fluctuations around its measured constant mean value, with variance σ2 and a typical correlation timescale Δt. We […]

Fedele Lizzi, Manolo Rivera, Patrizia Vitale

We calculate the Green functions for a scalar field theory with quartic interactions for which the fields are multiplied with a generic translation invariant star product. Our analysis involves both noncommutative products, for which there is the canonical commutation relation among coordinates, and nonlocal commutative products. We give explicit expressions for the one-loop corrections to […]

Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom

We analyze the running at one-loop of the gauge couplings in the spectral Pati-Salam model that was derived in the framework of noncommutative geometry. There are a few different scenarios for the scalar particle content which are determined by the precise form of the Dirac operator for the finite noncommutative space. We consider these different […]

C. P. Martin and David G. Navarro

We deduce an evolution equation for an arbitrary hybrid Seiberg-Witten map for compact gauge groups by using the antifield formalism. We show how this evolution equation can be used to obtain the hybrid Seiberg-Witten map as an expansion, which is θ-exact, in the number of ordinary fields. We compute explicitly this expansion up to order […]

Mairi Sakellariadou, Apimook Watcharangkool

We consider the spectral action within the context of a 4-dimensional manifold with torsion and show that, in the vacuum case, the equations of motion reduce to Einstein’s equations, securing the linear stability of the theory. To subsequently investigate the nonvacuum case, we consider the spectral action of an almost commutative torsion geometry and show […]