Symmetry Symmetry *Yuh-Nung Jan and Lily Yeh Jan, 1999. Asymmetry across species. Nature Cell Biology 1, E42 - E44 ...more on Wikipedia about "Asymmetry"
In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object. ...more on Wikipedia about "Automorphism"
Broken symmetry is a concept used in mathematics and physics when an object breaks either rotational symmetry or translational symmetry. That is, when one can only rotate an object in certain angles or when one is able to tell if the object has been shifted sideways (unless one shifts by a whole number of lattice units). ...more on Wikipedia about "Broken symmetry"
In physics, C-symmetry means the symmetry of physical laws under a charge-conjugation transformation. Electromagnetism, gravity and the strong interaction all obey C-symmetry, but weak interactions violate C-symmetry maximally. (Some postulated extensions of the Standard Model, like left-right models, restore this symmetry.) ...more on Wikipedia about "C-symmetry"
Chirality ( Greek handedness, derived from the word stem χειρ~, ch[e]ir~ - hand~) is an asymmetry property important in several branches of science. An object or a system is called chiral if it differs from its mirror image. Such objects then come in two forms, which are mirror images of each other, and these pairs of mirror image objects are called enantiomorphs (Greek opposite forms) or, when referring to molecules, enantiomers. A non-chiral object is called achiral (sometimes also amphichiral). ...more on Wikipedia about "Chirality"
In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or more particularly if it cannot be mapped to its mirror image by rotations and translations alone. Such objects come in two forms, called enantiomorphs. ...more on Wikipedia about "Chirality (mathematics)"
Circular symmetry in mathematical physics applies to a 2-dimensional field which can be expressed as a function of distance from a central point only. This means that all points on each circle take the same value. ...more on Wikipedia about "Circular symmetry"
In mathematics, especially abstract algebra, a binary operation on a set S is commutative if ...more on Wikipedia about "Commutative operation"
In mathematics, continuous symmetry is an intuitive idea corresponding to the concept of viewing some symmetries as motions, as opposed to e.g. reflection symmetry, which is invariance under a kind of flip from one state to another. It has largely and successfully been formalised in the mathematical notions of topological group, Lie group and group action. For most practical purposes continuous symmetry is modelled by a group action of a topological group. ...more on Wikipedia about "Continuous symmetry"
(CP-violation) In physics, and specifically particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics. It plays an important role in theories of cosmology that attempt to explain the dominance of matter over antimatter in the present Universe. The discovery of CP violation in 1964 in the decays of neutral kaons resulted in the Nobel Prize in Physics in 1980 for its discoverers James Cronin and Val Fitch. The study of CP violation remains a vibrant area of theoretical and experimental work today. ...more on Wikipedia about "CP-violation"
Category:Quantum field theoryCPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously. Efforts in the late 1950s revealed the violation of P-symmetry by some phenomena that involve weak nuclear force fields, and there are well known violations of C-symmetry and T-symmetry as well. For a short time, the CP-symmetry was believed to be preserved by all physical phenomena, but that was later found to be false too. There is a theorem that derives the preservation of CPT symmetry for all of physical phenomena assuming the correctness of quantum laws. ...more on Wikipedia about "CPT symmetry"
A crystal system is a category of space groups, which characterize symmetry of structures in three dimensions with translational symmetry in three directions, having a discrete symmetry group. A major application is in crystallography, to categorize crystals, but by itself the topic is one of 3D Euclidean geometry. ...more on Wikipedia about "Crystal system"
In crystallography, a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a point fixed while moving each atom of the crystal to the position of an atom of the same kind. That is, an infinite crystal would look exactly the same before and after any of the operations in its point group. In the classification of crystals, each point group corresponds to a crystal class. ...more on Wikipedia about "Crystallographic point group"
(Cyclic symmetries) This article deals with the four infinite series of point groups in three dimensions (n≥1) with n-fold rotational symmetry about one axis ( rotation by an angle of 360°/n does not change the object), and no other rotational symmetry (n=1 covers the cases of no rotational symmetry at all): ...more on Wikipedia about "Cyclic symmetries"
(Dihedral symmetry in three dimensions) Chiral: ...more on Wikipedia about "Dihedral symmetry in three dimensions"
An influential research programme and manifesto was published in 1872 by Felix Klein, under the title Vergleichende Betrachtungen über neuere geometrische Forschungen. This Erlangen Program (Erlanger Programm) — Klein was then at Erlangen — proposed a new kind of solution to the problems of geometry of the time. ...more on Wikipedia about "Erlangen program"
In theoretical physics, explicit symmetry breaking is the act of breaking symmetry of a theory by adding terms to its defining equations of motion (most typically, to the Lagrangian or the Hamiltonian) that do not respect the symmetry. ...more on Wikipedia about "Explicit symmetry breaking"
Facial symmetry is one of a number of traits associated with health, physical attractiveness and beauty of a person or animal. It is also hypothesized as a factor in interpersonal attraction. ...more on Wikipedia about "Facial symmetry"
Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. Gauge theories with non- abelian symmetry groups are also sometimes known as Yang-Mills theories. Most physical theories are described by Lagrangians which are invariant under certain transformations, when the transformations are identically performed at every space-time point—they have global symmetries. Gauge theory extends this idea by requiring that the Lagrangians must possess local symmetries as well—it should be possible to perform these symmetry transformations in a particular region of space-time without affecting what happens in another region. This requirement is a generalized version of the equivalence principle of general relativity. ...more on Wikipedia about "Gauge theory"
A global symmetry is a symmetry that holds for all points in the spacetime under consideration, as opposed to a local symmetry that only holds for an open subset of points. ...more on Wikipedia about "Global symmetry"
In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. For example, the set of integers is a group under the operation of addition. The branch of mathematics which studies groups is called group theory. ...more on Wikipedia about "Group (mathematics)"
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The Higgs mechanism or Anderson-Higgs mechanism, originally proposed by the British physicist Peter Higgs based on a suggestion by Philip Anderson, is the mechanism that gives mass to all elementary particles in particle physics. It makes the W boson different from the photon, for example. It can be understood as an elementary case of tachyon condensation where the role of the tachyon is played by a scalar field called the Higgs field. The massive quantum excitation of the Higgs field is also called the Higgs boson. ...more on Wikipedia about "Higgs mechanism"
Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich. It seeks a systematic mathematical explanation for a phenomenon called mirror symmetry first observed by physicists studying string theory. ...more on Wikipedia about "Homological mirror symmetry"
Apart from the two infinite series of prismatic and antiprismatic symmetry, rotational icosahedral symmetry or chiral icosahedral symmetry of chiral objects and full icosahedral symmetry or achiral icosahedral symmetry are the discrete point symmetries (or equivalently, symmetries on the sphere) with the largest symmetry groups. ...more on Wikipedia about "Icosahedral symmetry"
*In the case of n-fold rotational symmetry about an axis (n≥2), all vectors and pseudovectors at the axis are directed along it (or zero); a fortiori this applies for cylindrical symmetry. ...more on Wikipedia about "Isometries in physics"
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