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The su(2) Lie algebra is a mathematical structure used in physics to describe symmetries in quantum systems. It consists of matrices that satisfy certain properties, such as being traceless and anti-Hermitian. The su(2) algebra is commonly used in the study of angular momentum and spin in quantum mechanics. Its applications include describing the behavior of particles in magnetic fields, understanding the structure of atomic nuclei, and studying the properties of elementary particles.
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What is unitary symmetry?
A type of symmetry law, an important example of which is flavor symmetry, one of the approximate internal symmetry laws obeyed by the strong interactions of elementary particles. According to the successful theory of strong interactions, quantum chromodynamics, flavor symmetry is the consequence of the fact that the so-called glue force (mediated by the SU3color gauge field) is the same between all the kinds (flavors) of quarks. If the quarks all had the same mass, they then would be dynamically equivalent constituents of hadrons, and hadrons would occur as degenerate multiplets of the group SUN, where N is the number of quark flavors. The lightest quarks (u and d) have similar masses, so the lightest hadrons, made of u and d quarks, do exhibit an SU2flavor symmetry known as i-spin invariance. The mass of the next heavier quark (s) is much larger than the masses of the u and d quarks, but much smaller than the masses of the yet heavier quarks (c, b, …); consequently the hadrons that contain no quarks heavier than the s quark clearly may be grouped into SU3flavor multiplets. See Color (quantum mechanics), Flavor, Hadron, Quantum chromodynamics, QuarksAn example of unitary symmetry is the approximate spin independence of the forces on electrons (as in an atom): There is a fundamental doublet, comprising the spin-up electron and the spin-down electron. Denoting these two states by |u⟩ and |d⟩, all physical properties (energy eigenvalues, charge density, and so on) are unchanged by the replacements shown in the equations below,where α and β are complex numbers. The group of all the transformations of two states that preserves their hermitean scalar products [⟨u|d⟩ = 0, ⟨u|u⟩ = ⟨d|d⟩ = 1] is known as the two-dimensional unitary group, U2; the transformations of the equations above form a subgroup SU2 which merely lacks the uninteresting transformations of the form |u⟩ → eiϕ|u⟩ and |d⟩→eiϕ|d⟩, that is, an equal change of phase of the two states.The strong interactions are approximately invariant to an SU2 group; the fundamental doublet can be taken to be the nucleon, with the up and down states proton and neutron. This SU2 symmetry is known as charge independence, or, loosely, as i-spin conservation, the analog to the electron spin being known as i-spin I . See I-spinWhen a sufficient number of strange particles had been observed, it was seen that they, together with the old nonstrange particles, were grouped into multiplets of particles with the same space-time quantum numbers (except for mass; the masses of the members are only similar, not equal). This suggested the existence of a yet larger symmetry; it has turned out that this symmetry is the group of all unitary transformations of a triplet of fundamental particles, U3, or SU3 if the uninteresting equal phase change of all particles is omitted. This symmetry is often loosely called unitary symmetry. See Strange particlesA striking difference in the manifestations of SU2 and SU3 is that whereas all possible multiplets of the former appear in nature, only those multiplets of the latter appear that can be regarded as compounds of the fundamental triplet in which the net number of component fundamental particles (number of particles minus number of antiparticles) is an integral multiple of 3. In particular, no particle that could be regarded as the fundamental triplet is found. Despite this nonappearance, it turns out that a great deal about the strongly interacting particles (hadrons) is at least qualitatively explained if they are regarded as physical compounds of a fundamental triplet of particles, to which the name quark has been given. The color theory (quantum chromodynamics) of strong interactions explains why single quarks are never observed.According to the argument given above, hadrons have the approximate symmetry SUN, where N is the number of kinds of quarks, or flavors. Six flavors of quark are known; in addition to the quarks with the flavors up, down, and strange described above, three more quarks, charm, bottom, and top, have been found. See Charm, Elementary particle, J/psi particle, Upsilon particles
What BMX brand is better Blackeye or United?
Well, both United and Blackeye have a full line of bikes. Blackeye comes in cheaper with their Mack at only $190. United's start at $290 with their Recruit RN1. For $10 more, you can get a bike from Blackeye that's equivalent component wise, but has a cromoly top and downtube and cromoly fork steerer (the United Recruit is all hi-tensile steel). The Blackeye is also slightly longer in the front for taller riders. If you're comparing top of the line models, then you're putting the $500 Blackeye Killarado up against the $520 United Supreme SU2. Both are VERY similar in build quality and specs and both come with a 21" long top tube. The Blackeye comes with smaller frame size options for smaller riders, but if you need the longer 21" frame, I'd still say go with the Blackeye and save yourself $20.
What BMX is better United or Blackeye?
Well, both United and Blackeye have a full line of bikes. Blackeye comes in cheaper with their Mack at only $190. United's start at $290 with their Recruit RN1. For $10 more, you can get a bike from Blackeye that's equivalent component wise, but has a cromoly top and downtube and cromoly fork steerer (the United Recruit is all hi-tensile steel). The Blackeye is also slightly longer in the front for taller riders. If you're comparing top of the line models, then you're putting the $500 Blackeye Killarado up against the $520 United Supreme SU2. Both are VERY similar in build quality and specs and both come with a 21" long top tube. The Blackeye comes with smaller frame size options for smaller riders, but if you need the longer 21" frame, I'd still say go with the Blackeye and save yourself $20.
What are facts about the USSR?
Soviet UnionFrom Wikipedia, the free encyclopediaJump to: navigation, search This article is about the socialist state. For the ship with this name, see SS Albert Ballin."USSR" and "CCCP" redirect here. For other uses, see USSR (disambiguation) and CCCP (disambiguation).Союз Советских Социалистических РеспубликSoyuz Sovetskikh Sotsialisticheskikh RespublikUnion of Soviet Socialist RepublicsOther names ↓ 1922-1991 ↓ Flag Coat of arms MottoПролетарии всех стран, соединяйтесь!(Translit.: Proletarii vsekh stran, soyedinyaytes'!)English: Workers of the world, unite! AnthemThe Internationale (1922-1944)Hymn of the Soviet Union (1944-1991) CapitalMoscow Language(s) Russian, many others GovernmentFederal socialist republic, Single-party communist state General Secretary - 1922-1953 (first) Joseph Stalin - 1985-1991 (last) Mikhail Gorbachev Premier - 1923-1924 (first) Vladimir Lenin - 1991 (last) Ivan Silayev History - Established December 30, 1922 - Disestablished December 26, 19911 1991 Area - 1991 22,402,200 km² (8,649,538 sq mi) Population - 1991 est. 293,047,571 Density 13.1 /km² (33.9 /sq mi) Currency Ruble (SUR) Internet TLD .su2 Calling code +7Preceded by Succeeded by Russian Socialist Federative Soviet Republic Transcaucasian Socialist Federative Soviet Republic Ukrainian Soviet Socialist Republic Byelorussian Soviet Socialist Republic Tuvan People's Republic Kresy Bessarabia Finnish Karelia Estonia3 Latvia3 Lithuania3 Russia Belarus Ukraine Moldova Georgia Armenia Azerbaijan Kazakhstan Uzbekistan Turkmenistan Kyrgyzstan Tajikistan Estonia3 Lithuania3 Latvia3 1On December 21, 1991, eleven of the former socialist republics declared in Alma-Ata (with the twelfth republic - Georgia - attending as an observer) that with the formation of the Commonwealth of Independent States the Union of Soviet Socialist Republics ceases to exist.2Assigned on September 19, 1990, existing onwards.3The governments of Estonia, Latvia, and Lithuania view themselves as continuous and unrelated to the respective Soviet republics.Russia views the Estonian, Latvian, and Lithuanian SSRs as legal constituent republics of the USSR and predecessors of the modern Baltic states.The Government of the United States and a number of other countries did not recognize the legal inclusion of Estonia, Latvia, and Lithuania in the USSR. "Soviet" redirects here. For the term itself, see Soviet (council). For other uses, see Soviet (disambiguation).The Union of Soviet Socialist Republics (USSR) was a constitutionally socialist state that existed in Eurasia from 1922 to 1991. The name is a translation of the Russian: Союз Советских Социалистических Республик​ (help·info), tr. Soyuz Sovetskikh Sotsialisticheskikh Respublik, abbreviated СССР, SSSR. The common short name is Soviet Union,[1] from Советский Союз, Sovetskiy Soyuz. A soviet is a council, the theoretical basis for the socialist society of the USSR.Emerging from the Russian Empire following the Russian Revolution of 1917 and the Russian Civil War of 1918-1921, the USSR was a union of several Soviet republics, but the synecdoche Russia-after the Russian SFSR, its largest and most populous constituent state-continued to be commonly used throughout the country's existence. The geographic boundaries of the USSR varied with time, but after the last major territorial annexations of the Baltic states, eastern Poland, Bessarabia, and certain other territories during World War II, from 1945 until dissolution, the boundaries approximately corresponded to those of late Imperial Russia, with the notable exclusions of Poland and most of Finland.As the largest and oldest constitutionally communist state in existence, the Soviet Union became the primary model for future communist nations during the Cold War; the government and the political organization of the country were defined by the only political party, the Communist Party of the Soviet Union.From 1945 until dissolution in 1991-a period known as the Cold War-the Soviet Union and the United States of America were the two world superpowers that dominated the global agenda of economic policy, foreign affairs, military operations, cultural exchange, scientific advancements including the pioneering of space exploration, and sports (including the Olympic Games and various world championships).Initially established as a union of four Soviet Socialist Republics, the USSR grew to contain 15 constituent or "union republics" by 1956: Armenian SSR, Azerbaijan SSR, Byelorussian SSR, Estonian SSR, Georgian SSR, Kazakh SSR, Kirghiz SSR, Latvian SSR, Lithuanian SSR, Moldavian SSR, Russian SFSR, Tajik SSR, Turkmen SSR, Ukrainian SSR and Uzbek SSR. (From annexation of the Estonian SSR on August 6, 1940 up to the reorganization of the Karelo-Finnish SSR into the Karelian ASSR on July 16, 1956, the count of "union republics" was sixteen.)The Russian Federation is the successor state to the USSR. Russia is the leading member of the Commonwealth of Independent States.
