Related papers: About Symmetries in Physics
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…
This is the second in a series of papers intended to provide a basic overview of some of the major ideas in particle physics. Part I [arXiv:0810.3328] was primarily an algebraic exposition of gauge theories. We developed the group theoretic…
It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define…
These notes are an expanded version of lectures given at the 2022 TASI summer school in Boulder, Colorado. One goal of these lecture notes is to (partially) bridge the gap between what one learns in typical introductory quantum field theory…
Examples are presented for appearance of geometric symmetry in the shape of various astronomical objects and phenomena. Usage of these symmetries in astrophysical and extragalactic research is also discussed.
The reader surely knows what particles physics is about: finding building blocks of nature that appear elementary at a given time and study their interactions - so why in the world this essay? The problem is how to arrive at a fundamental…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
Contents of Part 1: 1. Status of the Standard Model(P.H. Frampton), 2. Cosmological Constraints from MBA and Polarization (A. Melchiorri), 3. AdS/CFT Correspondence and Unification at About 4 TeV (P.H. Frampton), 4. New Solutions in String…
This is an introduction to orientifolds with emphasis on applications to duality. Based on lectures given at the 1997 Trieste Summer School on Particle Physics and Cosmology, Italy.
The focus of the present thesis is on the analysis of gauge symmetry and its various impacts on gauge theories. In the first part of this thesis, we have studied different aspects of symmetries in connection with various field and string…
This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…
An attempt is made to present modern hopes to find manifestation of supersymmetry, a new symmetry that relates bosons and fermions, in particle physics from the point of view of renormalization group flow. The Standard Model of particle…
It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…
Symmetry, in particular gauge symmetry, is a fundamental principle in theoretical physics. It is intimately connected to the geometry of fibre bundles. A refinement to the gauge principle, known as ``spontaneous symmetry breaking'', leads…
Introductory lectures on the phenomenology of the minimal supersymmetric Standard Model. The emphasis is on general signatures for supersymmetry and on the motivation for constructing supersymmetric models. These lectures are intended for…
Coherently with the principle of analogy suggested by Dirac, we describe a general setting for reducing a classical dynamics, and the role of the Noether theorem -- connecting symmetries with constants of the motion -- within a reduction.…
The symmetric subpace has many applications in quantum information theory. This review article begins by explaining key background facts about the symmetric subspace from a quantum information perspective. Then we review, and in some places…
In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…
Opening Lecture at the Second Rencontres du Vietnam, October 21-28, 1995.
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how…