|
Haag–Łopuszański–Sohnius Theorem
In theoretical physics, the Haag–Łopuszański–Sohnius theorem states that if both commutating and anticommutating generators are considered, then the only way to nontrivially mix spacetime and internal symmetries is through supersymmetry. The anticommutating generators must be spin-1/2 spinors which can additionally admit their own internal symmetry known as R-symmetry. The theorem is a generalization of the Coleman–Mandula theorem to Lie superalgebras. It was proved in 1975 by Rudolf Haag, Jan Łopuszański, and Martin Sohnius as a response to the development of the first supersymmetric field theories by Julius Wess and Bruno Zumino in 1974. History During the 1960s, a set of theorems investigating how internal symmetries can be combined with spacetime symmetries were proved, with the most general being the Coleman–Mandula theorem. It showed that the Lie group symmetry of an interacting theory must necessarily be a direct product of the Poincaré group with some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert Einstein was concerned wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direct Product
In mathematics, one can often define a direct product of objects already known, giving a new one. This generalizes the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one talks about the product in category theory, which formalizes these notions. Examples are the product of sets, groups (described below), rings, and other algebraic structures. The product of topological spaces is another instance. There is also the direct sum – in some areas this is used interchangeably, while in others it is a different concept. Examples * If we think of \R as the set of real numbers, then the direct product \R \times \R is just the Cartesian product \. * If we think of \R as the group of real numbers under addition, then the direct product \R\times \R still has \ as its underlying set. The difference between this and the preceding example is that \R \times \R is now a group, and so we have to also say how to add their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J). Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, and the internal energy contained within a thermodynamic system. All living organisms constantly take in and release energy. Due to mass–energy equivalence, any object that has mass whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle
In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object which can be described by several physical property, physical or chemical property, chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from subatomic particles like the electron, to microscopic scale, microscopic particles like atoms and molecules, to macroscopic scale, macroscopic particles like powder (substance), powders and other granular materials. Particles can also be used to create scientific models of even larger objects depending on their density, such as humans moving in a crowd or celestial bodies in motion (physics), motion. The term ''particle'' is rather general in meaning, and is refined as needed by various scientific fields. Anything that is composed of particles may be referred to as being particulate. However, the noun ''particulates, particulate'' is most frequently ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scattering Amplitude
In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. By Nouredine Zettili, 2nd edition, page 623. Paperback 688 pages January 2009 The plane wave is described by the : where is the position vector; ; is the incoming plane wave with the |
Analytic Function
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions. A function is analytic if and only if its Taylor series about ''x''0 converges to the function in some neighborhood for every ''x''0 in its domain. Definitions Formally, a function f is ''real analytic'' on an open set D in the real line if for any x_0\in D one can write : f(x) = \sum_^\infty a_ \left( x-x_0 \right)^ = a_0 + a_1 (x-x_0) + a_2 (x-x_0)^2 + a_3 (x-x_0)^3 + \cdots in which the coefficients a_0, a_1, \dots are real numbers and the series is convergent to f(x) for x in a neighborhood of x_0. Alternatively, a real analytic function is an infinitely differentiable function such that the Taylor series at any point x_0 in its domain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S-matrix
In physics, the ''S''-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More formally, in the context of QFT, the ''S''-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the ''in-states'' and the ''out-states'') in the Hilbert space of physical states. A multi-particle state is said to be ''free'' (non-interacting) if it transforms under Lorentz transformations as a tensor product, or ''direct product'' in physics parlance, of ''one-particle states'' as prescribed by equation below. ''Asymptotically free'' then means that the state has this appearance in either the distant past or the distant future. While the ''S''-matrix may be defined for any background (spacetime) that is asymptotically solvable and has no event horizons, it has a simple form in the case of the Minkowsk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massless Particle
In particle physics, a massless particle is an elementary particle whose invariant mass is zero. There are two known gauge boson massless particles: the photon (carrier of electromagnetism) and the gluon (carrier of the strong force). However, gluons are never observed as free particles, since they are confined within hadrons. In addition the Weyl semimetal or Weyl fermion discovered in 2015 is also massless. Neutrinos were originally thought to be massless. However, because neutrinos change flavor as they travel, at least two of the types of neutrinos must have mass. The discovery of this phenomenon, known as neutrino oscillation, led to Canadian scientist Arthur B. McDonald and Japanese scientist Takaaki Kajita sharing the 2015 Nobel prize in physics. *Note that although literal Weyl fermions have never been experimentally confirmed to physically exist, certain systems can act collectively such that they seem to contain Weyl fermion quasiparticles. See also *Relativistic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CERN
The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in a northwestern suburb of Geneva, on the France–Switzerland border. It comprises 23 member states, and Israel (admitted in 2013) is currently the only non-European country holding full membership. CERN is an official United Nations General Assembly observer. The acronym CERN is also used to refer to the laboratory; in 2019, it had 2,660 scientific, technical, and administrative staff members, and hosted about 12,400 users from institutions in more than 70 countries. In 2016, CERN generated 49 petabytes of data. CERN's main function is to provide the particle accelerators and other infrastructure needed for high-energy physics research — consequently, numerous experiments have been constructed at CERN through international collaborations. CERN is the site of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wess–Zumino Model
In theoretical physics, the Wess–Zumino model has become the first known example of an interacting four-dimensional quantum field theory with linearly realised supersymmetry. In 1974, Julius Wess and Bruno Zumino studied, using modern terminology, dynamics of a single chiral superfield (composed of a complex scalar and a spinor fermion) whose cubic superpotential leads to a renormalizable theory. The treatment in this article largely follows that of Figueroa-O'Farrill's lectures on supersymmetry, and to some extent of Tong. The model is an important model in supersymmetric quantum field theory. It is arguably the simplest supersymmetric field theory in four dimensions, and is ungauged. The Wess–Zumino action Preliminary treatment Spacetime and matter content In a preliminary treatment, the theory is defined on flat spacetime (Minkowski space). For this article, the metric has ''mostly plus'' signature. The matter content is a real scalar field S, a real pseudoscala ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wrocław
Wrocław (; german: Breslau, or . ; Silesian German: ''Brassel'') is a city in southwestern Poland and the largest city in the historical region of Silesia. It lies on the banks of the River Oder in the Silesian Lowlands of Central Europe, roughly from the Baltic Sea to the north and from the Sudeten Mountains to the south. , the official population of Wrocław is 672,929, with a total of 1.25 million residing in the metropolitan area, making it the third largest city in Poland. Wrocław is the historical capital of Silesia and Lower Silesia. Today, it is the capital of the Lower Silesian Voivodeship. The history of the city dates back over a thousand years; at various times, it has been part of the Kingdom of Poland, the Kingdom of Bohemia, the Kingdom of Hungary, the Habsburg monarchy of Austria, the Kingdom of Prussia and Germany. Wrocław became part of Poland again in 1945 as part of the Recovered Territories, the result of extensive border changes and expulsions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
