Gauge and Poincare' Invariant Regularization and Hopf Symmetries

We consider the regularization of a gauge quantum field theory following a modification of the Polchinski proof based on the introduction of a cutoff function. We work with a Poincare' invariant deformation of the ordinary point-wise product of fields introduced by Ardalan, Arfaei, Ghasemkhani and Sadooghi, and show that it yields, through a limiting procedure of the cutoff functions, to a regularized theory, preserving all symmetries at every stage. The new gauge symmetry yields a new Hopf algebra with deformed co-structures, which is inequivalent to the standard one.Comment: Revised version. 14 pages. Incorrect statements eliminate

Higgs-Dilaton Lagrangian from Spectral Regularization

In this letter we calculate the full Higgs-Dilaton action describing the Weyl anomaly using the bosonic spectral action. This completes the work we started in our previous paper (JHEP 1110 (2011) 001). We also clarify some issues related to the dilaton and its role as collective modes of fermions under bosonization

Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis

We consider the Lie group $\mathbb{R}^D_\kappa$ generated by the Lie algebra of $\kappa$-Minkowski space. Imposing the invariance of the metric under the pull-back of diffeomorphisms induced by right translations in the group, we show that a unique right invariant metric is associated with $\mathbb{R}^D_\kappa$. This metric coincides with the metric of de Sitter space-time. We analyze the structure of unitary representations of the group $\mathbb{R}^D_\kappa$ relevant for the realization of the non-commutative $\kappa$-Minkowski space by embedding into $(2D-1)$-dimensional Heisenberg algebra. Using a suitable set of generalized coherent states, we select the particular Hilbert space and realize the non-commutative $\kappa$-Minkowski space as an algebra of the Hilbert-Schmidt operators. We define dequantization map and fuzzy variant of the Laplace-Beltrami operator such that dequantization map relates fuzzy eigenvectors with the eigenfunctions of the Laplace-Beltrami operator on the half of de Sitter space-time.Comment: 21 pages, v3 differs from version published in Fortschritte der Physik by a note and references added and adjuste

High energy bosons do not propagate

We discuss the propagation of bosons (scalars, gauge fields and gravitons) at high energy in the context of the spectral action. Using heat kernel techniques, we find that in the high-momentum limit the quadratic part of the action does not contain positive powers of the derivatives. We interpret this as the fact that the two point Green functions vanish for nearby points, where the proximity scale is given by the inverse of the cutoff

Spectral Action from Anomalies

Starting from a theory of fermions moving in a fixed gauge and gravitational background we implement the scale invariance of the theory. Upon quantization the theory is anomalous but the anomaly can be cancelled by the addition of another term to the action. This term comes out to be basically the Chamseddine Connes spectral action introduced in the context of noncommutative geometry. An alternative realization of the dilaton may involve a collective scalar mode of all fermions accumulated in a {scale-noninvariant} dilaton action. The entire spectral action describes gauge and Higgs fields coupled with gravity. Here this action is coupled with a dilaton and we discuss how it relates to the transition from the radiation to the electroweak broken phase via condensation of Higgs fields.Comment: Proceedings of the Corfu Summer Institute on Elementary Particles and Physics - Workshop on Non Commutative Field Theory and Gravity, September 8-12, 2010 Corfu Greec

Entangled Scent of a Charge

We argue that the ground state of a field theory, in the presence of charged particles, becomes an entangled state involving an infinity of soft photons. The quantum field vacuum is altered by the passage of a uniformly moving charge, leaving in its wake a different dressed ground state. In this sense a charged particle leaves its electromagnetic scent even after passing by. Unlike in classical electrodynamics the effect of the charge remains even at infinite time. The calculation is done in detail for the ground state of a spacetime wedge, although the results are more general. This agrees in spirit with recent results over the infrared aspects of field theory, although the technical details are different. These considerations open the possibility that the information carried by quantum fields, being nonlocal, does not disappear beyond the horizon of black holes.Comment: 10 pages. Minor corrections and added reference

Universal Landau Pole

Our understanding of quantum gravity suggests that at the Planck scale the usual geometry loses its meaning. If so, the quest for grand unification in a large non-abelian group naturally endowed with the property of asymptotic freedom may also lose its motivation. Instead we propose an unification of all fundamental interactions at the Planck scale in the form of a Universal Landau Pole (ULP), at which all gauge couplings diverge. The Higgs quartic coupling also diverges while the Yukawa couplings vanish. The unification is achieved with the addition of fermions with vector gauge couplings coming in multiplets and with hypercharges identical to those of the the Standard Model. The presence of these particles also prevents the Higgs quartic coupling from becoming negative, thus avoiding the instability (or metastability) of the SM vacuum.Comment: 10 pages, 3 figure. Minor changes. Final version to appear on Physical Review Letter

Inconstant Planck's constant

Motivated by the Dirac idea that fundamental constant are dynamical variables and by conjectures on quantum structure of spacetime at small distances, we consider the possibility that Planck constant $\hbar$ is a time depending quantity, undergoing random gaussian fluctuations around its measured constant mean value, with variance $\sigma^2$ and a typical correlation timescale $\Delta t$. We consider the case of propagation of a free particle and a one--dimensional harmonic oscillator coherent state, and show that the time evolution in both cases is different from the standard behaviour. Finally, we discuss how interferometric experiments or exploiting coherent electromagnetic fields in a cavity may put effective bounds on the value of $\tau= \sigma^2 \Delta t$.Comment: To appear on the International Journal of Modern Physics

Noncommutative scalar field minimally coupled to gravity

A model for noncommutative scalar fields coupled to gravity based on the generalization of the Moyal product is proposed. Solutions compatible with homogeneous and isotropic flat Robertson-Walker spaces to first non-trivial order in the perturbation of the star-product are presented. It is shown that in the context of a typical chaotic inflationary scenario, at least in the slow-roll regime, noncommutativity yields no observable effect.Comment: Talk presented at the Workshop on Quantum Gravity and Noncommutative Geometry, 20-23 July 2004, Universidade Lus\'ofona, Lisbon, Portugal. To appear at Int. J. Mod. Phys.

The Kirillov picture for the Wigner particle

We discuss the Kirillov method for massless Wigner particles, usually (mis)named "continuous spin" or "infinite spin" particles. These appear in Wigner's classification of the unitary representations of the Poincar\'e group, labelled by elements of the enveloping algebra of the Poincar\'e Lie algebra. Now, the coadjoint orbit procedure introduced by Kirillov is a prelude to quantization. Here we exhibit for those particles the classical Casimir functions on phase space, in parallel to quantum representation theory. A good set of position coordinates are identified on the coadjoint orbits of the Wigner particles; the stabilizer subgroups and the symplectic structures of these orbits are also described.Comment: 19 pages; v2: updated to coincide with published versio