|
Helicity (particle Physics)
In physics, helicity is the projection of the spin onto the direction of momentum. Mathematically, ''helicity'' is the sign of the projection of the spin vector onto the momentum vector: "left" is negative, "right" is positive. Overview The angular momentum J is the sum of an orbital angular momentum L and a spin S. The relationship between orbital angular momentum L, the position operator r and the linear momentum (orbit part) p is : \mathbf = \mathbf\times\mathbf , so L's component in the direction of p is zero. Thus, helicity is just the projection of the spin onto the direction of linear momentum. The helicity of a particle is positive ("right-handed") if the direction of its spin is the same as the direction of its motion and negative ("left-handed") if opposite. Helicity is conserved. That is, the helicity commutes with the Hamiltonian, and thus, in the absence of external forces, is time-invariant. It is also rotationally invariant, in that a rotation applied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." It is one of the most fundamental scientific disciplines. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spin-1/2
In quantum mechanics, spin is an intrinsic property of all elementary particles. All known fermions, the particles that constitute ordinary matter, have a spin of . The spin number describes how many symmetrical facets a particle has in one full rotation; a spin of means that the particle must be rotated by two full turns (through 720°) before it has the same configuration as when it started. Particles with net spin include the proton, neutron, electron, neutrino, and quarks. The dynamics of spin- objects cannot be accurately described using classical physics; they are among the simplest systems whose description requires quantum mechanics. As such, the study of the behavior of spin- systems forms a central part of quantum mechanics. Stern–Gerlach experiment The necessity of introducing half-integer spin goes back experimentally to the results of the Stern–Gerlach experiment. A beam of atoms is run through a strong heterogeneous magnetic field, which then splits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gyroball
A gyroball is a rare type of pitch (baseball), baseball pitch used primarily by players in Japan. It is thrown with a spiral-like spin, similar to bullet from a rifle, or an American football pass. This spin stabilizes the ball in flight, minimizing its deviation from a straight-line path to home plate. The gyroball is sometimes confused with the shuuto, another pitch used in Japan. Overview The gyroball pitch was first developed by Ryutaro Himeno, a scientist who used computer simulations to model baseball flight paths, and Kazushi Tezuka, a baseball instructor who developed a throwing technique to pitch a gyroball. The pitch is thrown with a Anatomical_terms_of_motion#Pronation_and_supination, pronated motion of the arm and from a Submarine (baseball), low arm angle, which Himeno and Tezuka argue reduces arm strain. This delivery creates a bullet-like spin on the ball, similar to the way an American football spins when thrown. The effect of this spin, which minimizes the Magnus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helicity Basis
In the Standard Model, using quantum field theory it is conventional to use the helicity basis to simplify calculations (of cross sections, for example). In this basis, the spin is quantized along the axis in the direction of motion of the particle. Spinors The two-component helicity eigenstates \xi_\lambda satisfy :\sigma \cdot \hat \xi_\lambda\left(\hat\right) = \lambda \xi_\lambda\left(\hat\right) \, :where ::\sigma \, are the Pauli matrices, ::\hat \, is the direction of the fermion momentum, ::\lambda = \pm 1 \, depending on whether spin is pointing in the same direction as \hat \, or opposite. To say more about the state, \xi_\lambda \, we will use the generic form of fermion four-momentum: :p^\mu = \left(E, \left, \vec\ \sin \cos, \left, \vec\ \sin \sin, \left, \vec\ \cos \right) \, Then one can say the two helicity eigenstates are :\xi_(\vec) = \frac \begin \left, \vec\ + p_z\\ p_x + i p_y \end = \begin \cos \\ e^\sin \end\, and : \xi_(\vec) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. Chirality and helicity The helicity of a particle is positive ("right-handed") if the direction of its spin is the same as the direction of its motion. It is negative ("left-handed") if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards. Mathematically, ''helicity'' is the sign of the projection of the spin vector onto the momentum vector: "left" is negative, "right" is positive. The chirality of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pauli–Lubanski Pseudovector
In physics, the Pauli–Lubanski pseudovector is an operator defined from the momentum and angular momentum, used in the quantum-relativistic description of angular momentum. It is named after Wolfgang Pauli and Józef Lubański. It describes the spin states of moving particles. It is the generator of the little group of the Poincaré group, that is the maximal subgroup (with four generators) leaving the eigenvalues of the four-momentum vector invariant. Definition It is usually denoted by (or less often by ) and defined by: where * \varepsilon_ is the four-dimensional totally antisymmetric Levi-Civita symbol; * J^ is the relativistic angular momentum tensor operator (M^); * P^ is the four-momentum operator. In the language of exterior algebra, it can be written as the Hodge dual of a trivector, \mathbf = \star(\mathbf \wedge \mathbf). Note W_0 = \vec \cdot \vec, and \vec = E \vec- \vec \times \vec where \vec is the generator of rotations and \vec is the generator of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anyon
In physics, an anyon is a type of quasiparticle so far observed only in two-dimensional physical system, systems. In three-dimensional systems, only two kinds of elementary particles are seen: fermions and bosons. Anyons have statistical properties intermediate between fermions and bosons. In general, the operation of exchange symmetry, exchanging two identical particles, although it may cause a global phase shift, cannot affect observables. Anyons are generally classified as ''abelian'' or ''non-abelian''. Abelian anyons, detected by two experiments in 2020, play a major role in the fractional quantum Hall effect. Introduction The statistical mechanics of large many-body systems obeys laws described by Maxwell–Boltzmann statistics. Quantum statistics is more complicated because of the different behaviors of two different kinds of particles called fermions and bosons. In two-dimensional systems, however, there is a third type of particle, called an anyon. In a two-dimens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unitary Representation
In mathematics, a unitary representation of a group ''G'' is a linear representation π of ''G'' on a complex Hilbert space ''V'' such that π(''g'') is a unitary operator for every ''g'' ∈ ''G''. The general theory is well-developed in the case that ''G'' is a locally compact ( Hausdorff) topological group and the representations are strongly continuous. The theory has been widely applied in quantum mechanics since the 1920s, particularly influenced by Hermann Weyl's 1928 book '' Gruppentheorie und Quantenmechanik''. One of the pioneers in constructing a general theory of unitary representations, for any group ''G'' rather than just for particular groups useful in applications, was George Mackey. Context in harmonic analysis The theory of unitary representations of topological groups is closely connected with harmonic analysis. In the case of an abelian group ''G'', a fairly complete picture of the representation theory of ''G'' is given by Pontryagin duality. In genera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Group
In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space \mathbb^n; that is, the transformations of that space that preserve the Euclidean distance between any two points (also called Euclidean transformations). The group depends only on the dimension ''n'' of the space, and is commonly denoted E(''n'') or ISO(''n''), for ''inhomogeneous special orthogonal'' group. The Euclidean group E(''n'') comprises all translations, rotations, and reflections of \mathbb^n; and arbitrary finite combinations of them. The Euclidean group can be seen as the symmetry group of the space itself, and contains the group of symmetries of any figure (subset) of that space. A Euclidean isometry can be ''direct'' or ''indirect'', depending on whether it preserves the handedness of figures. The direct Euclidean isometries form a subgroup, the special Euclidean group, often denoted SE(''n'') and E+(''n''), whose elements are called rigid motions or Euclidean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Covering Group
In mathematics, a covering group of a topological group ''H'' is a covering space ''G'' of ''H'' such that ''G'' is a topological group and the covering map is a continuous group homomorphism. The map ''p'' is called the covering homomorphism. A frequently occurring case is a double covering group, a topological double cover in which ''H'' has index 2 in ''G''; examples include the spin groups, pin groups, and metaplectic groups. Roughly explained, saying that for example the metaplectic group Mp2''n'' is a ''double cover'' of the symplectic group Sp2''n'' means that there are always two elements in the metaplectic group representing one element in the symplectic group. Properties Let ''G'' be a covering group of ''H''. The kernel ''K'' of the covering homomorphism is just the fiber over the identity in ''H'' and is a discrete normal subgroup of ''G''. The kernel ''K'' is closed in ''G'' if and only if ''G'' is Hausdorff (and if and only if ''H'' is Hausdorff). Going i ... [...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. At present the only confirmed massless particle is the photon. Other particles and quasiparticles Standard Model gauge bosons The photon (carrier of electromagnetism) is one of two known gauge bosons thought to be massless. The photon is well-known from direct observation to exist and be massless. The other massless gauge boson is the gluon (carrier of the strong force) whose existence has been inferred from particle collision decay products; it is expected to be massless, but a zero mass has not been confirmed by experiment. Although there are compelling theoretical reasons to believe that gluons are massless, they can never be observed as free particles due to being confined within hadrons, and hence their presumed lack of rest mass cannot be confirmed by any feasible experiment. The only other observed gauge bosons are the W and Z bosons, which are known from experiments to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Little Group
In mathematics, a group action of a group G on a set (mathematics), set S is a group homomorphism from G to some group (under function composition) of functions from S to itself. It is said that G acts on S. Many sets of transformation (function), transformations form a group (mathematics), group under function composition; for example, the rotation (mathematics), rotations around a point in the plane. It is often useful to consider the group as an abstract group, and to say that one has a group action of the abstract group that consists of performing the transformations of the group of transformations. The reason for distinguishing the group from the transformations is that, generally, a group of transformations of a mathematical structure, structure acts also on various related structures; for example, the above rotation group also acts on triangles by transforming triangles into triangles. If a group acts on a structure, it will usually also act on objects built from that st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
