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Papers by Alexandre Laugier

Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bu... more Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, we considered the definition of orthonormal basis in Minkowski space, the structure of metric tensor relative to orthonormal basis, procedure of orthogonalization. Linear transformation of Minkowski space mapping at least one orthonormal basis into orthonormal basis is called motion. The set of motions of Minkowski space V generates not complete group SO(V) which acts single transitive on the basis manifold. Passive transformation of Minkowski space mapping at least one orthonormal basis into orthonormal basis is called quasimotion of Minkowski space. The set of passive transformations of Minkowski space generates passive representation of not complete group SO(V) on basis manifold. Since twin representations (active and passiv...

Some basic properties of the ring of integers mathbbZ\mathbb{Z}mathbbZ are extended to entire rings. In parti... more Some basic properties of the ring of integers mathbbZ\mathbb{Z}mathbbZ are extended to entire rings. In particular, arithmetic in entire principal rings is very similar than arithmetic in the ring of integers mathbbZ\mathbb{Z}mathbbZ. These arithmetic properties are derived from a star\starstar-ring extension of the considered entire ring (ring extension with conjugation) equipped with a real function which is a multiplicative structure-preserving map between two algebras. The algebra of this ring extension is studied in detail. Some examples of such ring extension are given.

Journal of High Energy Physics, 2001

We compute the tree-level four-point scattering amplitudes in string models where matter fields l... more We compute the tree-level four-point scattering amplitudes in string models where matter fields live on D-brane intersections. Extracting the contribution of massless modes, we are left with dimension-six four-fermion operators which in general receive contributions from three different sources: exchange of massive Kaluza-Klein excitations, winding modes and string oscillator states. We compute their coefficients and extract new bounds on the string scale in the brane-world scenario. This is contrasted with the situation where matter fields arise from open strings with both ends confined on the same collection of D-branes, in which case the exchange of massive string modes leads to dimension-eight operators that have been studied in the past. When matter fields live on brane intersections, the presence of dimension-six operators increase the lower bound on the string scale to 1-2 TeV, independently of the number of large extra dimensions.

Notes on Number Theory and Discrete Mathematics

We give a new proof of Lucas' theorem in elementary number theory.

The American Mathematical Monthly, 1953

In this paper we study the Fibonacci numbers and derive some interesting properties and recurrenc... more In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for Fp, where p is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, m and derive certain interesting properties related to them. Afterwards, we derive some new properties of a class of generalized Fibonacci numbers. In the last part of the paper we introduce some generalized Fibonacci polynomial sequences and we derive some results related to them.

Nuclear Physics B, 2003

We study mediation of supersymmetry breaking in the bulk, in models with primordial supersymmetry... more We study mediation of supersymmetry breaking in the bulk, in models with primordial supersymmetry breaking on D-branes at the string scale, in the TeV region. We compute the gravitino and scalar masses up to one-loop level, as well as the radion coupling to matter. We find that the latter mediates a model independent force at submillimeter distances that can be tested in micro-gravity experiments for any dimensionality of the bulk. In the case of two large dimensions, our type I string framework provides an example which allows to stabilize the radion potential and determine the desired hierarchy between the string and Planck scales.

Nuclear Physics B, 2002

We study a class of type I string models with supersymmetry broken on the world-volume of some D-... more We study a class of type I string models with supersymmetry broken on the world-volume of some D-branes and vanishing tree-level potential. Despite the non-supersymmetric spectrum, supersymmetry is non-linearly realized on these D-branes, while it is spontaneously broken in the bulk by Scherk-Schwarz boundary conditions. These models can easily accommodate 3-branes with interesting gauge groups and chiral fermions. We also study the effective field theory and in particular we compute the four-fermion couplings of the localized Goldstino with the matter fermions on the brane. * On leave of absence from CPHT, Ecole Polytechnique, UMR du CNRS 7644. 1 The parameter C f is related to the parametrisation of other authors by C f = − α 4 [17] = C f f 2 [18].

Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bu... more Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, we considered the definition of orthonormal basis in Minkowski space, the structure of metric tensor relative to orthonormal basis, procedure of orthogonalization. Linear transformation of Minkowski space mapping at least one orthonormal basis into orthonormal basis is called motion. The set of motions of Minkowski space V generates not complete group SO(V) which acts single transitive on the basis manifold. Passive transformation of Minkowski space mapping at least one orthonormal basis into orthonormal basis is called quasimotion of Minkowski space. The set of passive transformations of Minkowski space generates passive representation of not complete group SO(V) on basis manifold. Since twin representations (active and passiv...

Some basic properties of the ring of integers mathbbZ\mathbb{Z}mathbbZ are extended to entire rings. In parti... more Some basic properties of the ring of integers mathbbZ\mathbb{Z}mathbbZ are extended to entire rings. In particular, arithmetic in entire principal rings is very similar than arithmetic in the ring of integers mathbbZ\mathbb{Z}mathbbZ. These arithmetic properties are derived from a star\starstar-ring extension of the considered entire ring (ring extension with conjugation) equipped with a real function which is a multiplicative structure-preserving map between two algebras. The algebra of this ring extension is studied in detail. Some examples of such ring extension are given.

Journal of High Energy Physics, 2001

We compute the tree-level four-point scattering amplitudes in string models where matter fields l... more We compute the tree-level four-point scattering amplitudes in string models where matter fields live on D-brane intersections. Extracting the contribution of massless modes, we are left with dimension-six four-fermion operators which in general receive contributions from three different sources: exchange of massive Kaluza-Klein excitations, winding modes and string oscillator states. We compute their coefficients and extract new bounds on the string scale in the brane-world scenario. This is contrasted with the situation where matter fields arise from open strings with both ends confined on the same collection of D-branes, in which case the exchange of massive string modes leads to dimension-eight operators that have been studied in the past. When matter fields live on brane intersections, the presence of dimension-six operators increase the lower bound on the string scale to 1-2 TeV, independently of the number of large extra dimensions.

Notes on Number Theory and Discrete Mathematics

We give a new proof of Lucas' theorem in elementary number theory.

The American Mathematical Monthly, 1953

In this paper we study the Fibonacci numbers and derive some interesting properties and recurrenc... more In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for Fp, where p is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, m and derive certain interesting properties related to them. Afterwards, we derive some new properties of a class of generalized Fibonacci numbers. In the last part of the paper we introduce some generalized Fibonacci polynomial sequences and we derive some results related to them.

Nuclear Physics B, 2003

We study mediation of supersymmetry breaking in the bulk, in models with primordial supersymmetry... more We study mediation of supersymmetry breaking in the bulk, in models with primordial supersymmetry breaking on D-branes at the string scale, in the TeV region. We compute the gravitino and scalar masses up to one-loop level, as well as the radion coupling to matter. We find that the latter mediates a model independent force at submillimeter distances that can be tested in micro-gravity experiments for any dimensionality of the bulk. In the case of two large dimensions, our type I string framework provides an example which allows to stabilize the radion potential and determine the desired hierarchy between the string and Planck scales.

Nuclear Physics B, 2002

We study a class of type I string models with supersymmetry broken on the world-volume of some D-... more We study a class of type I string models with supersymmetry broken on the world-volume of some D-branes and vanishing tree-level potential. Despite the non-supersymmetric spectrum, supersymmetry is non-linearly realized on these D-branes, while it is spontaneously broken in the bulk by Scherk-Schwarz boundary conditions. These models can easily accommodate 3-branes with interesting gauge groups and chiral fermions. We also study the effective field theory and in particular we compute the four-fermion couplings of the localized Goldstino with the matter fermions on the brane. * On leave of absence from CPHT, Ecole Polytechnique, UMR du CNRS 7644. 1 The parameter C f is related to the parametrisation of other authors by C f = − α 4 [17] = C f f 2 [18].