69 research outputs found
Extension of the Poincar\'e Symmetry and Its Field Theoretical Implementation
We define a new algebraic extension of the Poincar\'e symmetry; this algebra
is used to implement a field theoretical model. Free Lagrangians are explicitly
constructed; several discussions regarding degrees of freedom, compatibility
with Abelian gauge invariance etc. are done. Finally we analyse the
possibilities of interaction terms for this model.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Asymptotic expansion of the multi-orientable random tensor model
Three-dimensional random tensor models are a natural generalization of the
celebrated matrix models. The associated tensor graphs, or 3D maps, can be
classified with respect to a particular integer or half-integer, the degree of
the respective graph. In this paper we analyze the general term of the
asymptotic expansion in N, the size of the tensor, of a particular random
tensor model, the multi-orientable tensor model. We perform their enumeration
and we establish which are the dominant configurations of a given degree.Comment: 27 pages, 24 figures, several minor modifications have been made, one
figure has been added; accepted for publication in "Electronic Journal of
Combinatorics
Using Grassmann calculus in combinatorics: Lindstr\"om-Gessel-Viennot lemma and Schur functions
Grassmann (or anti-commuting) variables are extensively used in theoretical
physics. In this paper we use Grassmann variable calculus to give new proofs of
celebrated combinatorial identities such as the Lindstr\"om-Gessel-Viennot
formula for graphs with cycles and the Jacobi-Trudi identity. Moreover, we
define a one parameter extension of Schur polynomials that obey a natural
convolution identity.Comment: 10 pages, contribution to GASCom 2016; v2: minor correction
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