Related papers: Segal's contractions, AdS and conformal groups
The development of the notion of group contraction first introduced by E. In{\"o}n{\"u} and E.P. Wigner in 1953 is briefly reviewed. The fundamental role of the idea of degenerate transformations is stressed. The significance of…
The connection between spin and symmetry was established by Wigner in his 1939 paper on the Poincar\'e group. For a massive particle at rest, the little group is O(3) from which the concept of spin emerges. The little group for a massless…
The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the field of analytic complex functions, the generic…
Degenerations, contractions and deformations of various algebraic structures play an important role in mathematics and physics. There are many different definitions and special cases of these notions. We try to give a general definition…
Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation…
New fundamental physical theories can, so far a posteriori, be seen as emerging from existing ones via some kind of deformation. That is the basis for Flato's ``deformation philosophy", of which the main paradigms are the physics…
This article presents a precise description of the interplay between the symmetries of a quantum or classical theory with spacetime interpretation, and some of its physical properties relating to causality, horizons and positive energy. Our…
The Carroll group arises in the vanishing speed of light limit of the Poincar\'{e} group and was initially discarded as just a mathematical curiosity. However, recent developments have proved otherwise. Carroll and conformal Carroll…
Lie algebra contractions on the classical Drinfel'd Double of a given Lie bialgebra are introduced and compared to the usual Lie bialgebra contraction theory. The connection between both approaches turns out to be intimately linked to…
This paper is the first part of the proof of the conformal bootstrap for Liouville conformal field theory on surfaces with a boundary, devoted to Segal's axioms in this context. We introduce the notion of Segal's amplitudes on surfaces with…
In the first part of the thesis we focus on local symmetries. We review a self-consistent framework that we employed in order to discuss the dynamics of the theories of interest. Its merit lies in that we can make the symmetry group act…
A contribution to the collection of reviews "Introduction to Higher Spin Theory" edited by S. Fredenhagen, this introductory article is a pedagogical account of higher-spin fields and their connections with String Theory. We start with the…
Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…
This text presents some basic notions in symplectic geometry, Poisson geometry, Hamiltonian systems, Lie algebras and Lie groups actions on symplectic or Poisson manifolds, momentum maps and their use for the reduction of Hamiltonian…
We formulate axioms of conformal theory (CT) in dimensions $>2$ modifying Segal's axioms for two-dimensional CFT. (In the definition of higher-dimensional CFT one includes also a condition of existence of energy-momentum tensor.) We use…
Using a rigidity property of the foliations of $S^2 \times [0, 1]$ that are defined by a non-vanishing closed one-form, we give a rather simple proof of a theorem due J. Cerf, going back to 1968, that the group of direct diffeomorphisms of…
This paper is concerned with symmetries of closed multiplicative 2-forms on Lie groupoids and their infinitesimal counterparts. We use them to study Lie group actions on Dirac manifolds by Dirac diffeomorphisms and their lifts to…
These are introductory notes on symmetries in quantum field theory and how they apply to particle physics. The notes cover the fundamentals of group theory, their representations, Lie groups, and Lie algebras, along with an elaborate…
The geometries of spaces having as groups the real orthogonal groups and some of their contractions are described from a common point of view. Their central extensions and Casimirs are explicitly given. An approach to the trigonometry of…
Higher-form symmetries have proved useful in constraining the dynamics of a number of quantum field theories. In the context of the Argyres-Douglas (AD) theories of the $(G,G')$ type, we find that the 1-form symmetries are invariant under…