Related papers: Tutorial on Scale and Conformal Symmetries in Dive…
In this essay we give an introduction to conformal symmetry, based on the example of the Yamabe operator and its use in conformal differential geometry, and in representation theory.
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
Using thermodynamic relations and dimensional analysis we derive a general formula for the thermodynamical trace $2\mathcal{E}-DP$ for non-relativistic systems and $\mathcal{E-DP}$ for relativistic systems, where $D$ is the number of…
Various subtleties and problems associated with nonrelativistic (NR) reduction of a scalar field theory to the Schroedinger theory are discussed. Contrary to the usual approaches that discuss the mapping among the equations of motion or the…
The limitations of three-dimensional semi-classical gravity are explored in the context of a conformally invariant theory for a self-interacting scalar field. The analysis of the theory's scaling behaviour reveals that scalar-loop effects…
I review a number of cognate issues that, taken together, pertain to the creation of a non-reductionistic theory of multiscale coordination and present one candidate theory based on the principle of dynamical similarity.
Inspired by the all-important conformal invariance of harmonic maps on two-dimensional domains, this article studies the relationship between biharmonicity and conformality. We first give a characterization of biharmonic morphisms,…
It is shown that regularisation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.
We introduce a dynamic approach to probabilistic forecast reconciliation at scale. Our model differs from the existing literature in this area in several important ways. Firstly we explicitly allow the weights allocated to the base…
We give an explicit example of a model in D=4-epsilon space-time dimensions that is scale but not conformally invariant, is unitary, and has finite correlators. The invariance is associated with a limit cycle renormalization group (RG)…
Defects in conformal field theories are interesting objects to study from both formal and applied points of view. In this paper, we construct conformal defects in free scalar field CFTs in diverse dimensions. After discussing the possible…
This paper investigates scaling symmetry in thermodynamics by unifying constrained Hamiltonian dynamics with symplectic and contact geometries. Through the mathematical processes of contactization and symplectization, we demonstrate that…
Relational particle models are useful toy models for quantum cosmology and the problem of time in quantum general relativity. This paper shows how to extend existing work on concrete examples of relational particle models in 1-d to include…
This article is a survey of results involving conformal deformation of Riemannian metrics and fully nonlinear equations.
We perform molecular dynamics simulations in order to examine the rheological transition of fluids confined in a small space. By performing finite-size scaling analysis, we demonstrate that this rheological transition results from the…
A brief review is presented of the scaling of complex fluids, polymers and polyelectrolytes in solution and in confined geometry, in thermodynamical, structural and rheology properties using equilibrium and nonequilibrium dissipative…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
We recently proposed a chameleonic solution to the cosmological constant problem - Phys. Rev. D82 (2010) 044006. One of the results of that paper is a non-equivalence of different conformal frames at the quantum level. In this letter we…
Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…
The zoo of two-dimensional conformal models has been supplemented by a series of nonunitary conformal models obtained by cosetting minimal models. Some of them coincide with minimal models, some do not have even Kac spectrum of conformal…