224 citations · 1.3k across the 35 of their papers we have counts for
28 papers · 1 filter
The Kirillov picture for the Wigner particle
J. M. Gracia-Bondia, F. Lizzi, J. C. Varilly +1
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 unit…
The chirality theorem
José M. Gracia-Bondía, Jens Mund, Joseph C. Várilly
We show how chirality of the weak interactions stems from string independence in the string-local formalism of quantum field theory.
On the assertion that PCT violation implies Lorentz non-invariance
Michael Duetsch, Jose M. Gracia-Bondia
Out of conviction or expediency, some current research programs take for granted that "PCT violation implies violation of Lorentz invariance". We point out that this claim is still…
Notes on "quantum gravity" and non-commutative geometry
Jose M. Gracia-Bondia
I hesitated for a long time before giving shape to these notes, originally intended for preliminary reading by the attendees to the Summer School "New paths towards quantum gravity…
Quantum gauge models without classical Higgs mechanism
Michael Duetsch, Jose M. Gracia-Bondia, Florian Scheck +1
We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (Epstein-Glaser) renormalization. Th…
On the causal gauge principle
Jose M. Gracia-Bondia
Work by the Zurich school of causal (Epstein-Glaser) renormalization has shown that renormalizability in the presence of massless or massive gauge fields (as primary entities) expl…
Lectures on BRS invariance for massive boson fields
Jose M. Gracia-Bondia
These notes correspond to lectures given at the Villa de Leyva Summer School in Colombia (July 2007). Our main purpose in this short course on BRS invariance of gauge theories is t…
Fourier analysis on the affine group, quantization and noncompact Connes geometries
Victor Gayral, Jose M. Gracia-Bondia, Joseph C. Varilly
We find the Stratonovich-Weyl quantizer for the nonunimodular affine group of the line. A noncommutative product of functions on the half-plane, underlying a noncompact spectral tr…
A Lie theoretic approach to renormalization
K. Ebrahimi-Fard, J. M. Gracia-Bondia, F. Patras
Motivated by recent work of Connes and Marcolli, based on the Connes-Kreimer approach to renormalization, we augment the latter by a combinatorial, Lie algebraic point of view. Our…
Hidden symmetry and Hopf algebra
Jose M. Gracia-Bondia
We spell two conundrums, one of physical and another of mathematical nature, and explain why one helps to elucidate the other
Combinatorics of renormalization as matrix calculus
K. Ebrahimi-Fard, J. M. Gracia-Bondia, L. Guo +1
We give a simple presentation of the combinatorics of renormalization in perturbative quantum field theory in terms of triangular matrices. The prescription, that may be of calcula…
Position-dependent noncommutative products: classical construction and field theory
V. Gayral, J. M. Gracia-Bondia, F. Ruiz Ruiz
We look in Euclidean for associative star products realizing the commutation relation , where the noncommutativity parameters depend on the pos…
Trouble with space-like noncommutative field theory
V. Gayral, J. M. Gracia-Bondia, F. Ruiz Ruiz
It is argued that the one-loop effective action for a space-like noncommutative scalar field theory does not exist. This indicates that such theories are not renormalizable already…
Combinatorial Hopf algebras in quantum field theory I
Hector Figueroa, Jose M. Gracia-Bondia
This manuscript stands at the interface between combinatorial Hopf algebra theory and renormalization theory. Its plan is as follows: Section 1 is the introduction, and contains as…
The uses of Connes and Kreimer's algebraic formulation of renormalization theory
Hector Figueroa, Jose M. Gracia-Bondia
We show how, modulo the distinction between the antipode and the "twisted" or "renormalized" antipode, Connes and Kreimer's algebraic paradigm trivializes the proofs of equivalence…
Improved Epstein-Glaser Renormalization II. Lorentz invariant framework
J. M. Gracia-Bondia, S. Lazzarini
The Epstein--Glaser type T-subtraction introduced by one of the authors in a previous paper is extended to the Lorentz invariant framework. The advantage of using our subtraction i…
Noncommutative geometry and fundamental interactions: the first ten years
Jose M. Gracia-Bondia
This is the full text of a survey talk for nonspecialists, delivered at the 66th Annual Meeting of the German Physical Society in Leipzig, March 2002. We have not taken pains to su…
Improved Epstein-Glaser renormalization in coordinate space I. Euclidean framework
Jose M. Gracia-Bondia
In a series of papers, we investigate the reformulation of Epstein-Glaser renormalization in coordinate space, both in analytic and Hopf algebraic terms. This first article deals w…
Chiral Gauge Anomalies on Noncommutative R^4
J. M. Gracia-Bondia, C. P. Martin
We discuss the noncommutative counterparts of chiral gauge theories and compute the associated anomalies.
On the antipode of Kreimer's Hopf algebra
Hector Figueroa, Jose M. Gracia-Bondia
We give a new formula for the antipode of the algebra of rooted trees, directly in terms of the bialgebra structure. The equivalence, proved in this paper, among the three availabl…
On the ultraviolet behaviour of quantum fields over noncommutative manifolds
Joseph C. Varilly, Jose M. Gracia-Bondia
By exploiting the relation between Fredholm modules and the Segal-Shale-Stinespring version of canonical quantization, and taking as starting point the first-quantized fields descr…
A nonperturbative form of the spectral action principle in noncommutative geometry
H. Figueroa, J. M. Gracia-Bondia, F. Lizzi +1
Using the formalism of superconnections, we show the existence of a bosonic action functional for the standard K-cycle in noncommutative geometry, giving rise, through the spectral…
The Standard Model as a noncommutative geometry: the low energy regime
C. P. Martin, Jose M. Gracia-Bondia, Joseph C. Varilly
We render a thorough, physicist's account of the formulation of the Standard Model (SM) of particle physics within the framework of noncommutative differential geometry (NCG). We w…
Noncommutative Geometry and the Standard Model: An overview
Jose M. Gracia-Bondia
We briefly sketch the noncommutative geometry approach to the Standard Model, with attention to what can be inferred about particle masses.