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Dark Photon
The dark photon (also hidden, heavy, para-, or secluded photon) is a hypothetical hidden sector particle, proposed as a force carrier similar to the photon of electromagnetism but potentially connected to dark matter. In a minimal scenario, this new force can be introduced by extending the gauge group of the Standard Model of Particle Physics with a new abelian U(1) gauge symmetry. The corresponding new spin-1 gauge boson (i.e., the dark photon) can then couple very weakly to electrically charged particles through kinetic mixing with the ordinary photon and could thus be detected. The dark photon can also interact with the Standard Model if some of the fermions are charged under the new abelian group. The possible charging arrangements are restricted by a number of consistency requirements such as anomaly cancellation and constraints coming from Yukawa matrices. Motivation Observations of gravitational effects that cannot be explained by visible matter alone imply the existe ...
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Hidden Sector
In particle physics, the hidden sector, also known as the dark sector, is a hypothetical collection of yet-unobserved quantum fields and their corresponding hypothetical particles. The interactions between the hidden sector particles and the Standard Model particles are weak, indirect, and typically mediated through gravity or other new particles. Examples of new hypothetical mediating particles in this class of theories include the dark photon, sterile neutrino, and axion. In many cases, hidden sectors include a new gauge group that is independent from the Standard Model gauge group. The hidden sectors are commonly predicted by the models from string theory. They may be relevant as a source of dark matter and supersymmetry breaking, solving the Muon g-2 anomaly and beryllium-8 decay anomaly. } See also * Fifth force * Dark energy * Dark matter *Dark radiation *Higgs sector In particle physics, the Higgs sector is the collection of quantum fields and/or particles that are respons ...
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Dirac Equation
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin- massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the fine structure of the hydrogen spectrum in a completely rigorous way. The equation also implied the existence of a new form of matter, ''antimatter'', previously unsuspected and unobserved and which was experimentally confirmed several years later. It also provided a ''theoretical'' justification for the introduction of several component wave functions in Pauli's phenomenological theory of spin. The wave functions in the Dirac theo ...
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Four-current
In special and general relativity, the four-current (technically the four-current density) is the four-dimensional analogue of the electric current density. Also known as vector current, it is used in the geometric context of ''four-dimensional spacetime'', rather than three-dimensional space and time separately. Mathematically it is a four-vector, and is Lorentz covariant. Analogously, it is possible to have any form of "current density", meaning the flow of a quantity per unit time per unit area. see current density for more on this quantity. This article uses the summation convention for indices. See covariance and contravariance of vectors for background on raised and lowered indices, and raising and lowering indices on how to switch between them. Definition Using the Minkowski metric \eta_ of metric signature , the four-current components are given by: :J^\alpha = \left(c \rho, j^1 , j^2 , j^3 \right) = \left(c \rho, \mathbf \right) where ''c'' is the speed of light, ''ρ' ...
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Stueckelberg Action
In field theory, the Stueckelberg action (named after Ernst Stueckelberg) describes a massive spin-1 field as an R (the real numbers are the Lie algebra of U(1)) Yang–Mills theory coupled to a real scalar field φ. This scalar field takes on values in a real 1D affine representation of R with'' m'' as the coupling strength. :\mathcal=-\frac(\partial^\mu A^\nu-\partial^\nu A^\mu)(\partial_\mu A_\nu-\partial_\nu A_\mu)+\frac(\partial^\mu \phi+m A^\mu)(\partial_\mu \phi+m A_\mu) This is a special case of the Higgs mechanism, where, in effect, and thus the mass of the Higgs scalar excitation has been taken to infinity, so the Higgs has decoupled and can be ignored, resulting in a nonlinear, affine representation of the field, instead of a linear representation — in contemporary terminology, a U(1) nonlinear -model. Gauge-fixing φ=0, yields the Proca action. This explains why, unlike the case for non-abelian vector fields, quantum electrodynamics with a massive pho ...
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Higgs Mechanism
In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other being fermions) would be considered massless, but measurements show that the W+, W−, and Z0 bosons actually have relatively large masses of around 80 GeV/''c''2. The Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field (the Higgs field) that permeates all space to the Standard Model. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass. In the Standard Model, the phrase "Higgs mechanism" refers specifically to the generation of masses for the W±, and Z weak gauge bosons through electroweak symmetry breaking. The Large Hadron Coll ...
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Electroweak Symmetry Breaking
In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other being fermions) would be considered massless, but measurements show that the W+, W−, and Z0 bosons actually have relatively large masses of around 80 GeV/''c''2. The Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field (the Higgs field) that permeates all space to the Standard Model. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass. In the Standard Model, the phrase "Higgs mechanism" refers specifically to the generation of masses for the W±, and Z weak gauge bosons through electroweak symmetry breaking. The Large Hadron Coll ...
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Field Strength Tensor
In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written very concisely, and allows for the quantization of the electromagnetic field by Lagrangian formulation described below. Definition The electromagnetic tensor, conventionally labelled ''F'', is defined as the exterior derivative of the electromagnetic four-potential, ''A'', a differential 1-form: :F \ \stackrel\ \mathrmA. Therefore, ''F'' is a differential 2-form—that is, an antisymmetric rank-2 tensor field—on Minkowski space. In component form, :F_ = \partial_\mu A_\nu - \partial_\nu A_\mu. where \partial is the four-gradient and A is the fou ...
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Electroweak Interaction
In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV,The particular number 246 GeV is taken to be the vacuum expectation value v = (G_\text \sqrt)^ of the Higgs field (where G_\text is the Fermi coupling constant). they would merge into a single force. Thus, if the temperature is high enough – approximately 1015  K – then the electromagnetic force and weak force merge into a combined electroweak force. During the quark epoch (shortly after the Big Bang), the electroweak force split into the electromagnetic and weak force. It is thought that the required temperature of 1015 K has not been seen widely throughout the unive ...
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Dirac Fermion
In physics, a Dirac fermion is a spin-½ particle (a fermion) which is different from its antiparticle. The vast majority of fermions – perhaps all – fall under this category. Description In particle physics, all fermions in the standard model have distinct antiparticles (''perhaps'' excepting neutrinos) and hence are Dirac fermions. They are named after Paul Dirac, and can be modeled with the Dirac equation. A Dirac fermion is equivalent to two Weyl fermions. The counterpart to a Dirac fermion is a Majorana fermion, a particle that must be its own antiparticle. Dirac quasi-particles In condensed matter physics, low-energy excitations in graphene and topological insulators, among others, are fermionic quasiparticles described by a pseudo-relativistic Dirac equation. See also * Dirac spinor, a wavefunction-like description of a Dirac fermion * Dirac–Kähler fermion, a geometric formulation of Dirac fermions * Majorana fermion, an alternate category of fermion, possibly de ...
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Gauge Field
In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups). The term ''gauge'' refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called ''gauge transformations'', form a Lie group—referred to as the ''symmetry group'' or the ''gauge group'' of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the ''gauge field''. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called ''gauge invariance''). When such a theory is quantized, the quanta of the gauge fields are called ''gauge bosons' ...
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