17 citations · 83 across the 28 of their papers we have counts for
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Scalar field on non-integer dimensional spaces
R. Trinchero
Deformations of the canonical spectral triples over the n-dimensional torus are considered. These deformations have a discrete dimension spectrum consisting of non-integer values l…
On the treatment of divergent integrals in perturbative quantum field theory
R. Trinchero
A simple integral that illustrates the concepts of regularization, subtraction, renormalization and renormalization group employed in perturbative quantum field theory(PQFT) is con…
Examples of non integer dimensional geometries
R. Trinchero
Two examples of spectral triples with non-integer dimension spectrum are considered. These triples involve commutative C*-algebras. The first example has complex dimension spectrum…
Integrable models and star structures
Ariel O. Garcia, Roberto C. Trinchero
We consider the representations of Hopf algebras involved in some physical models, namely, factorizable S-matrix models (FSM's), one-dimensional quantum spin chains (QSC's) and sta…
Associated quantum vector bundles and symplectic structure on a quantum plane
R. Coquereaux, A. O. Garcia, R. Trinchero
We define a quantum generalization of the algebra of functions over an associated vector bundle of a principal bundle. Here the role of a quantum principal bundle is played by a Ho…
Hopf stars, twisted Hopf stars and scalar products on quantum spaces
R. Coquereaux, A. O. Garcia, R. Trinchero
The properties of Hopf star operations and twisted Hopf stars operations on quantum groups are discussed in relation with the theory of representations (star representations). Inva…
Geometry of the reduced quantum plane
R. Coquereaux, A. O. Garcia, R. Trinchero
We consider the space M of NxN matrices as a reduced quantum plane and discuss its geometry under the action and coaction of finite dimensional quantum groups (a quotient of U_q(SL…
Differential calculus and connections on a quantum plane at a cubic root of unity
R. Coquereaux, A. O. Garcia, R. Trinchero
We consider the algebra of N x N matrices as a reduced quantum plane on which a finite-dimensional quantum group H acts. This quantum group is a quotient of U_q(sl(2,C)), q being a…