Related papers: Is There An Ultimate Symmetry in Physics?
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
Astrophysical paradoxes are the paradoxes of physics. The main motivation of a formulated paradox is clearly recognized in the scientific environment because the phenomenon of a paradox itself has become interesting. There is an explanation…
This thesis is focused on some solvable quantum mechanical models and their associated symmetries.
In this paper, we argue that there are foundational dilemmas in theoretical physics related to the concept of reality and the nature of mathematics in physics. Physical theory is treated as a conceptual organism which develops under the…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…
In this talk, some aspects of duality symmetries are presented.
I give an overview of the motivations for and theory/phenomenology of supersymmetry.
An algorithm is proposed for research into the symmetrical properties of theoretical and mathematical physics equations. The application of this algorithm to the free Schrodinger equation permited us to establish that in addition to the…
Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used…
Is speculative mathematics dangerous? Recent interactions between physics and mathematics pose the question with some force: traditional mathematical norms discourage speculation, but it is the fabric of theoretical physics. In practice…
Perhaps the most important aspect of symmetry in physics is the idea that a state does not need to have the same symmetries as the theory that describes it. This phenomenon is known as spontaneous symmetry breaking. In these lecture notes,…
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.
These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…
Symmetries for wave equation with additional conditions are found. Some conditions yield infinite-dimensional symmetry algebra for the nonlinear equation. Ansatzes and solutions corresponding to the new symmetries were constructed.
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…
One of the interesting aspects in the study of atomic nuclei is the strikingly regular behaviour many display in spite of being complex quantum-mechanical systems, prompting the universal question of how regularity emerges out of…
We give a brief survey of some of the geometry of mirror symmetry, written in 2004 for the "Encyclopaedia of Mathematical Physics". Probably a little bit out of date now in a few places, but hey.
I will sketchily illustrate how the theory of symmetry helps in determining solutions of (deterministic) differential equations, both ODEs and PDEs, staying within the classical theory. I will then present a quick discussion of some more…