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Majorana Particle
In particle physics a Majorana fermion (, uploaded 19 April 2013, retrieved 5 October 2014; and also based on Ettore Majorana, the pronunciation of physicist's name.) or Majorana particle is a fermion that is its own antiparticle. They were hypothesised by Ettore Majorana in 1937. The term is sometimes used in opposition to Dirac fermion, which describes fermions that are not their own antiparticles. With the exception of neutrinos, all of the Standard Model elementary fermions are known to behave as Dirac fermions at low energy (lower than the electroweak symmetry breaking temperature), and none are Majorana fermions. The nature of neutrinos is not settled – they may be either Dirac or Majorana fermions. In condensed matter physics, quasiparticle Excited state, excitations can appear like bound Majorana states. However, instead of a single fundamental particle, they are the collective movement of several individual particles (themselves composite) which are governed by Anyon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Physics
Particle physics or high-energy physics is the study of Elementary particle, fundamental particles and fundamental interaction, forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the scale of protons and neutrons, while the study of combinations of protons and neutrons is called nuclear physics. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three Generation (particle physics), generations of fermions, although ordinary matter is made only from the first fermion generation. The first generation consists of Up quark, up and down quarks which form protons and neutrons, and electrons and electron neutrinos. The three fundamental interactions known to be mediated by bosons are electromagnetism, the weak interaction, and the strong interaction. Quark, Quarks cannot exist on their own but form hadrons. Hadrons that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a and b are real numbers, then the complex conjugate of a + bi is a - bi. The complex conjugate of z is often denoted as \overline or z^*. In polar form, if r and \varphi are real numbers then the conjugate of r e^ is r e^. This can be shown using Euler's formula. The product of a complex number and its conjugate is a real number: a^2 + b^2 (or r^2 in polar coordinates). If a root of a univariate polynomial with real coefficients is complex, then its complex conjugate is also a root. Notation The complex conjugate of a complex number z is written as \overline z or z^*. The first notation, a vinculum, avoids confusion with the notation for the conjugate transpose of a matrix, which can be thought of as a generalization of the complex conjugate. The second is preferred in physics, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truly Neutral Particle
In particle physics, a truly neutral particle is a subatomic particle that has no charge quantum number; they are their own antiparticle. In other words, it remains itself under the charge conjugation, which replaces particles with their corresponding antiparticles. All charges of a ''truly neutral particle'' must be equal to zero. This requires particles to not only be electrically neutral, but also requires that all of their other charges (such as the colour charge) be neutral. Examples Known examples of such elementary particles include photons, Z bosons, and Higgs bosons, along with the hypothetical neutralinos, sterile neutrinos, and gravitons. For a spin-½ particle such as the neutralino, being ''truly neutral'' implies being a Majorana fermion. By way of contrast, neutrinos are not ''truly neutral'' since they have a weak isospin of , or equivalently, a non-zero weak hypercharge In the Standard Model (mathematical formulation), Standard Model of electroweak interact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weak Isospin
In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with half-integer weak isospin can interact with the bosons; particles with zero weak isospin do not. Weak isospin is a construct parallel to the idea of isospin under the strong interaction. Weak isospin is usually given the symbol or , with the third component written as or is more important than ; typically "weak isospin" is used as short form of the proper term "3rd component of weak isospin". It can be understood as the eigenvalue of a charge operator. Notation This article uses and for weak isospin and its projection. Regarding ambiguous notation, is also used to represent the 'normal' (strong force) isospin, same for its third component a.k.a. or . Aggravating the confusion, is also used as the symbol for the Topness quantum number. Conservation law The weak isospin conservation law relates to the conservation of \ T_3\ ; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majorana Mass
In physics, the Majorana equation is a relativistic wave equation. It is named after the Italian physicist Ettore Majorana, who proposed it in 1937 as a means of describing fermions that are their own antiparticle. Particles corresponding to this equation are termed Majorana particles, although that term now has a more expansive meaning, referring to any (possibly non-relativistic) fermionic particle that is its own anti-particle (and is therefore electrically neutral). There have been proposals that massive neutrinos are described by Majorana particles; there are various extensions to the Standard Model that enable this. The article on Majorana particles presents status for the experimental searches, including details about neutrinos. This article focuses primarily on the mathematical development of the theory, with attention to its discrete and continuous symmetries. The discrete symmetries are charge conjugation, parity transformation and time reversal; the continuous symmetry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charge (physics)
In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian. Charges are often denoted by Q, and so the invariance of the charge corresponds to the vanishing commutator ,H0, where H is the Hamiltonian. Thus, charges are associated with conserved quantum numbers; these are the eigenvalues of the generator Q. A "charge" can also refer to a point-shaped object with an electric charge and a position, such as in the method of image charges. Abstract definition Abstractly, a charge is any generator of a continuous symmetry of the physical system under study. When a physical system has a symmetry of some sort, Noether's theorem implies the existence of a conserved current. The thing that "flows" in the current is the "charge"; the charge is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sterile Neutrino
Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that interact only via gravity and not via any of the other fundamental interactions of the Standard Model. The term ''sterile neutrino'' is used to distinguish them from the known, ordinary ''active neutrinos'' in the Standard Model, which carry an isospin charge of and engage in the weak interaction. The term typically refers to neutrinos with right-handed chirality (see '), which may be inserted into the Standard Model. Particles that possess the quantum numbers of sterile neutrinos and masses great enough such that they do not interfere with the current theory of Big Bang nucleosynthesis are often called neutral heavy leptons (NHLs) or heavy neutral leptons (HNLs). The existence of right-handed neutrinos is theoretically well-motivated, because the known active neutrinos are left-handed and all other known fermions have been observed with both left and right chirality. They could ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Algebra
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished subspace. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing. They are named after the English mathematician William Kingdon Clifford (1845–1879). The most familiar Clifford algebras, the orthogonal Clifford algebras, are also referred to as (''pseudo-'')''Riemannian Clifford algebras'', as distinct from ''symplectic Clifford algebras''. Introduction and basic properties A Clifford algebra is a unital associative algebra that contains and is generated by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew-symmetric Matrix
In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the condition In terms of the entries of the matrix, if a_ denotes the entry in the i-th row and j-th column, then the skew-symmetric condition is equivalent to Example The matrix A = \begin 0 & 2 & -45 \\ -2 & 0 & -4 \\ 45 & 4 & 0 \end is skew-symmetric because A^\textsf = \begin 0 & -2 & 45 \\ 2 & 0 & 4 \\ -45 & -4 & 0 \end = -A . Properties Throughout, we assume that all matrix entries belong to a field \mathbb whose characteristic is not equal to 2. That is, we assume that , where 1 denotes the multiplicative identity and 0 the additive identity of the given field. If the characteristic of the field is 2, then a skew-symmetric matrix is the same thing as a symmetric matrix. * The sum of two skew-symmetric matrices is skew-symmetric. * A scalar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anticommutator
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. Group theory The commutator of two elements, and , of a group , is the element : . This element is equal to the group's identity if and only if and commute (that is, if and only if ). The set of all commutators of a group is not in general closed under the group operation, but the subgroup of ''G'' generated by all commutators is closed and is called the ''derived group'' or the ''commutator subgroup'' of ''G''. Commutators are used to define nilpotent and solvable groups and the largest abelian quotient group. The definition of the commutator above is used throughout this article, but many group theorists define the commutator as : . Using the first definition, this can be expressed as . Identities (group theory) Commutator identities are an important tool in group theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Involution (mathematics)
In mathematics, an involution, involutory function, or self-inverse function is a function that is its own inverse, : for all in the domain of . Equivalently, applying twice produces the original value. General properties Any involution is a bijection. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (), reciprocation (), and complex conjugation () in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the Beaufort polyalphabetic cipher. The composition of two involutions and is an involution if and only if they commute: . Involutions on finite sets The number of involutions, including the identity involution, on a set with elements is given by a recurrence relation found by Heinrich August Rothe in 1800: : a_0 = a_1 = 1 and a_n = a_ + (n - 1)a_ for n > 1. The first few terms of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutralino
In supersymmetry, the neutralino is a hypothetical particle. In the Minimal Supersymmetric Standard Model (MSSM), a popular model of realization of supersymmetry at a low energy, there are four neutralinos that are fermions and are electrically neutral, the lightest of which is stable in an R-parity conserved scenario of MSSM. They are typically labeled (the lightest), , and (the heaviest) although sometimes \tilde_1^0, \ldots, \tilde_4^0 is also used when \tilde_i^\pm is used to refer to charginos. : These four states are composites of the bino and the neutral wino (which are the neutral electroweak gauginos), and the neutral higgsinos. As the neutralinos are Majorana fermions, each of them is identical to its antiparticle. Expected behavior If they exist, these particles would only interact with the weak vector bosons, so they would not be directly produced at hadron colliders in copious numbers. They would primarily appear as particles in cascade decays (dec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
