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Källén Function
The Källén function, also known as triangle function, is a polynomial function in three variables, which appears in geometry and particle physics. In the latter field it is usually denoted by the symbol \lambda. It is named after the theoretical physicist Gunnar Källén, who introduced it as a short-hand in his textbook ''Elementary Particle Physics''.G. Källén, ''Elementary Particle Physics'', (Addison-Wesley, 1964) Definition The function is given by a quadratic polynomial in three variables :\lambda(x,y,z) \equiv x^2 + y^2 + z^2 - 2xy - 2yz - 2zx. Applications In geometry the function describes the area A of a triangle with side lengths a,b,c: :A=\frac \sqrt. See also Heron's formula. The function appears naturally in the kinematics of relativistic particles, e.g. when expressing the energy and momentum components in the center of mass frame by Mandelstam variables In theoretical physics, the Mandelstam variables are numerical quantities that encode the energy, moment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gunnar Källén
Anders Olof Gunnar Källén (13 February 1926 in Kristianstad, Sweden – 13 October 1968 in Hanover, West Germany in a plane accident) was a leading Swedish theoretical physicist and a professor at Lund University until his death at the age of 42. Biography Källén earned his doctorate at Lund in 1950 and worked from 1952 to 1957 at CERN's theoretical division in Copenhagen, which then became the Niels Bohr Institute. He also worked at Nordita 1957–1958 and then began a professorship at Lund University. Källén's research focused on quantum field theory and elementary particle physics. His developments included the so-called Källén–Lehmann representation of correlation functions in quantum field theory, and he made contributions to quantum electrodynamics, especially in renormalizing. He also worked with the axiomatic formulation of quantum field theory, which led to contributions to the theory of functions of several complex variables. He collaborated on the Pauli–Käll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heron's Formula
In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths , , . If s = \tfrac12(a + b + c) is the semiperimeter of the triangle, the area is, :A = \sqrt. It is named after first-century engineer Heron of Alexandria (or Hero) who proved it in his work ''Metrica'', though it was probably known centuries earlier. Example Let be the triangle with sides , and . This triangle’s semiperimeter is :s=\frac=\frac=16 and so the area is : \begin A &= \sqrt = \sqrt\\ &= \sqrt = \sqrt = 24. \end In this example, the side lengths and area are integers, making it a Heronian triangle. However, Heron's formula works equally well in cases where one or more of the side lengths are not integers. Alternate expressions Heron's formula can also be written in terms of just the side lengths instead of using the semiperimeter, in several ways, :\begin A &=\tfrac\sqrt \\ mu&=\tfrac\sqrt \\ mu&=\tfrac\sqrt \\ mu&=\tfrac\sqrt \\ mu&=\tfra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinematics
Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics (physics), kinetics, not kinematics. For further details, see analytical dynamics. Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration). # The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or the observer. Origins and significance Special relativity was originally proposed by Albert Einstein in a paper published on 26 September 1905 titled "On the Electrodynamics of Moving Bodies".Albert Einstein (1905)''Zur Elektrodynamik bewegter Körper'', ''Annalen der Physik'' 17: 891; English translatioOn the Electrodynamics of Moving Bodiesby George Barker Jeffery and Wilfrid Perrett (1923); Another English translation On the Electrodynamics of Moving Bodies by Megh Nad Saha (1920). The incompa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mandelstam Variables
In theoretical physics, the Mandelstam variables are numerical quantities that encode the energy, momentum, and angles of particles in a scattering process in a Lorentz-invariant fashion. They are used for scattering processes of two particles to two particles. The Mandelstam variables were first introduced by physicist Stanley Mandelstam in 1958. If the Minkowski metric is chosen to be \mathrm(1, -1,-1,-1), the Mandelstam variables s,t,u are then defined by :*s=(p_1+p_2)^2 c^2 =(p_3+p_4)^2 c^2 :*t=(p_1-p_3)^2 c^2 =(p_4-p_2)^2 c^2 :*u=(p_1-p_4)^2 c^2 =(p_3-p_2)^2 c^2, where ''p''1 and ''p''2 are the four-momenta of the incoming particles and ''p''3 and ''p''4 are the four-momenta of the outgoing particles. s is also known as the square of the center-of-mass energy (invariant mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinematics (particle Physics)
Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics. Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics kinematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
