Related papers: Is symmetry identity?
A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…
In physics, Lie groups represent the algebraic structure that describes symmetry transformations of a given system. Then, the descending Lie algebra of those groups are necessarily real. In most cases, the complexification of those Lie…
The claim that a particle is an irreducible representation of the Poincar\'e group -- what I call \emph{Wigner's identification} -- is now, decades on from Wigner's (1939) original paper, so much a part of particle physics folklore that it…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the…
The concept of emergence, or synergy in its simplest form, is widely used but lacks a rigorous definition. Our work connects information and set theory to uncover the mathematical nature of synergy as the failure of distributivity. It…
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…
We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity.
Biological intelligence is remarkable in its ability to produce complex behaviour in many diverse situations through data efficient, generalisable and transferable skill acquisition. It is believed that learning "good" sensory…
Symmetry is at the heart of much of mathematics, physics, and art. Traditional geometric symmetry groups are defined in terms of isometries of the ambient space of a shape or pattern. If we slightly generalize this notion to allow the…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a…
In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While…
Symmetry arguments are frequently used -- often implicitly -- in mathematical modeling of natural selection. Symmetry simplifies the analysis of models and reduces the number of distinct population states to be considered. Here, I introduce…
Symmetry is conventionally described in a contrariety manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry…
Gauge symmetries are often highlighted as a fundamental cornerstone of modern physics. But at the same time, it is commonly emphasized that gauge symmetries are not a fundamental feature of nature but merely redundancies in our description.…
This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the problem determine different properties of the…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…