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Majorana Fermion
A Majorana fermion (, uploaded 19 April 2013, retrieved 5 October 2014; and also based on the pronunciation of physicist's name.), also referred to as a 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 a Dirac fermion, which describes fermions that are not their own antiparticles. With the exception of neutrinos, all of the Standard Model 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 the neutrinos is not settled – they may turn out to be either Dirac or Majorana fermions. In condensed matter physics, quasiparticle excitations can appear like bound Majorana fermions. However, instead of a single fundamental particle, they are the collective movement of several individual particles (themselves composite) which are governed by non-Abelian statistics. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ettore Majorana
Ettore Majorana (,, uploaded 19 April 2013, retrieved 14 December 2019 ; born on 5 August 1906 – possibly dying after 1959) was an Italian theoretical physicist who worked on neutrino masses. On 25 March 1938, he disappeared under mysterious circumstances after purchasing a ticket to travel by ship from Palermo to Naples. The Majorana equation and Majorana fermions are named after him. In 2006, the Majorana Prize was established in his memory. Life and work In 1938, Enrico Fermi was quoted as saying about Majorana: "There are several categories of scientists in the world; those of second or third rank do their best but never get very far. Then there is the first rank, those who make important discoveries, fundamental to scientific progress. But then there are the geniuses, like Galilei and Newton. Majorana was one of these." Gifted in mathematics Majorana was born in Catania, Sicily. Mathematically gifted, he was very young when he joined Enrico Fermi's team in Rome a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Creation And Annihilation Operators
Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually denoted \hat) lowers the number of particles in a given state by one. A creation operator (usually denoted \hat^\dagger) increases the number of particles in a given state by one, and it is the adjoint of the annihilation operator. In many subfields of physics and chemistry, the use of these operators instead of wavefunctions is known as second quantization. They were introduced by Paul Dirac. Creation and annihilation operators can act on states of various types of particles. For example, in quantum chemistry and many-body theory the creation and annihilation operators often act on electron states. They can also refer specifically to the ladder operators for the quantum harmonic oscillator. In the latter case, the raising operator is in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truly Neutral Particle
In particle physics, a truly neutral particle is a subatomic particle that is its 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 (like 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. Composite particles can also be truly neutral. A system composed of a particle forming a bound state with its antiparticle, such as the neutral pion (), is ''truly neutral''. Such a state is called an “-onium”, another example of which is positronium, the bound state ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sterile Neutrinos
Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that are believed to 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 right-handed neutrino), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weak Isospin
In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol or , with the third component written as or . It can be understood as the eigenvalue of a charge operator. is more important than and typically the term "weak isospin" may refer to the "3rd component of weak isospin". The weak isospin conservation law relates to the conservation of T_3; weak interactions conserve . It is also conserved by the electromagnetic and strong interactions. However, interaction with the Higgs field does ''not'' conserve , as directly seen by propagation of fermions, mixing chiralities by dint of their mass terms resulting from their Higgs couplings. Since the Higgs field vacuum expectation value is nonzero, particles interact with this field all the time even in vacuum. Interaction with the Higgs field changes particles' weak isospin (and weak hypercharge). ... [...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 symmetr ... [...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 the letter ''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 ''q'' of the generator ''Q''. 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 generator of the (local) symmetry group. This charge is sometimes called the Noether charge. Thus, for exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sterile Neutrino
Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that are believed to 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 right-handed neutrino), 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 ... [...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. 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. The most familiar Clifford algebras, the orthogonal Clifford algebras, are also referred to as (''pseudo-'')''Riemannian Clifford algebras'', as distinct from ''symplectic Clifford algebras''.see for ex. Introduction and basic properties A Clifford algebra is a unital associative algebra that contains and is generated by a vector space over a field , where is equipped with a qua ... [...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 = \begin 0 & -2 & 45 \\ 2 & 0 & 4 \\ -45 & -4 & 0 \end = A^\textsf . 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 scala ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutator
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 (from the definition , being equal to the identity 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 other group theorists define the commutator as :. Identities (group theory) Commutator identities are an important tool in group theory. The expr ... [...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 (x \mapsto -x), reciprocation (x \mapsto 1/x), and complex conjugation (z \mapsto \bar z) 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 ''f'' and ''g'' 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_ + ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
