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Electromagnetic Fields
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified ''as'' light) and interacts with charges and currents. Its quantum counterpart is one of the four fundamental forces of nature (the others are gravitation, weak interaction and strong interaction.) The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is described ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Field (physics)
In physics, a field is a physical quantity, represented by a scalar (mathematics), scalar, vector (mathematics and physics), vector, or tensor, that has a value for each Point (geometry), point in Spacetime, space and time. For example, on a weather map, the surface temperature is described by assigning a real number, number to each point on the map; the temperature can be considered at a certain point in time or over some interval of time, to study the dynamics of temperature change. A surface wind map, assigning an vector (mathematics and physics), arrow to each point on a map that describes the wind velocity, speed and direction at that point, is an example of a vector field, i.e. a 1-dimensional (rank-1) tensor field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another rank-1 tensor field, while electrodynamics can be formulated in terms of Mathematical descriptions of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Force Law
Lorentz is a name derived from the Roman surname, Laurentius, which means "from Laurentum". It is the German form of Laurence. Notable people with the name include: Given name * Lorentz Aspen (born 1978), Norwegian heavy metal pianist and keyboardist * Lorentz Dietrichson (1834–1917), Norwegian poet and historian of art and literature * Lorentz Eichstadt (1596–1660), German mathematician and astronomer * Lorentz Harboe Ree (1888–1962), Norwegian architect * Lorentz Lange (1783–1860), Norwegian judge and politician * Lorentz Reige (born 1990), Swedish dancer * Lorentz Reitan (born 1946), Norwegian musicologist Mononym * Lorentz (rapper), real name Lorentz Alexander, Swedish singer and rapper Surname * Dominique Lorentz, French investigative journalist who has written books on nuclear proliferation * Friedrich Lorentz, author of works on the Pomeranian language * Hendrik Antoon Lorentz (1853–1928), Dutch physicist and Nobel Prize winner * Hendrikus Albertus Lorentz ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Onde Electromagnetique
Onde means ''wave'' in French and ''the same'' (ಒಂದೇ) in Kannada language. It may refer to *Onde, Vikramgad, a village in India *''Onde Balliya Hoogalu'', a 1967 Indian Kannada film *''Onde Roopa Eradu Guna'', a 1975 Indian Kannada film *''Onde Guri'', a 1983 Indian Kannada film *''Le Onde'', a 1996 album by the Italian pianist Ludovico Einaudi *Mille Lune Mille Onde, a single from Andrea Bocelli's 2001 album ''Cieli di Toscana'' *''Onde (film)'', a 2005 Italian film *Onde 2000, a motorcycle racing team based in Spain See also *Ondes (other) Ondes is a commune in southwestern France. Ondes or Öndeş may also refer to *ondes Martenot, an early electronic musical instrument * Selen Öndeş (born 1988), Turkish volleyball player * Saint-Benoît-des-Ondes, a commune in northwestern Franc ... * Onde-onde (other) {{disambiguation, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Creation 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] |
Photons
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always move at the speed of light in vacuum, (or about ). The photon belongs to the class of bosons. As with other elementary particles, photons are best explained by quantum mechanics and exhibit wave–particle duality, their behavior featuring properties of both waves and particles. The modern photon concept originated during the first two decades of the 20th century with the work of Albert Einstein, who built upon the research of Max Planck. While trying to explain how matter and electromagnetic radiation could be in thermal equilibrium with one another, Planck proposed that the energy stored within a material object should be regarded as composed of an integer number of discrete, equal-sized parts. To explain the photoelectric effect, Ein ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Diagrams
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory. Frank Wilczek wrote that the calculations that won him the 2004 Nobel Prize in Physics "would have been literally unthinkable without Feynman diagram ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time-evolution Operator
Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state (also called ''stateful systems''). In this formulation, ''time'' is not required to be a continuous parameter, but may be discrete or even finite. In classical physics, time evolution of a collection of rigid bodies is governed by the principles of classical mechanics. In their most rudimentary form, these principles express the relationship between forces acting on the bodies and their acceleration given by Newton's laws of motion. These principles can also be equivalently expressed more abstractly by Hamiltonian mechanics or Lagrangian mechanics. The concept of time evolution may be applicable to other stateful systems as well. For instance, the operation of a Turing machine can be regarded as the time evolution of the machine's control state together with the state of the tape (or possibly multiple tapes) including the position of the machine's read-write he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation Function (quantum Field Theory)
In quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products of field operators. They are a key object of study in quantum field theory where they can be used to calculate various observables such as S-matrix elements. Definition For a scalar field theory with a single field \phi(x) and a vacuum state , \Omega\rangle at every event (x) in spacetime, the n-point correlation function is the vacuum expectation value of the time-ordered products of n field operators in the Heisenberg picture G_n(x_1,\dots, x_n) = \langle \Omega, T\, \Omega\rangle. Here T\ is the time-ordering operator for which orders the field operators so that earlier time field operators appear to the right of later time field operators. By transforming the fields and states into the interaction picture, this is rewritten as G_n(x_1, \dots, x_n) = \frac, where , 0\rangle is the ground state of the free theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wick's Theorem
Wick's theorem is a method of reducing high-order derivatives to a combinatorics problem. It is named after Italian physicist Gian-Carlo Wick. It is used extensively in quantum field theory to reduce arbitrary products of creation and annihilation operators to sums of products of pairs of these operators. This allows for the use of Green's function methods, and consequently the use of Feynman diagrams in the field under study. A more general idea in probability theory is Isserlis' theorem. In perturbative quantum field theory, Wick's theorem is used to quickly rewrite each time ordered summand in the Dyson series as a sum of normal ordered terms. In the limit of asymptotically free ingoing and outgoing states, these terms correspond to Feynman diagrams. Definition of contraction For two operators \hat and \hat we define their contraction to be :\hat^\bullet\, \hat^\bullet \equiv \hat\,\hat\, - \mathopen \hat\,\hat \mathclose where \mathopen \hat \mathclose denotes the n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyson Series
In scattering theory, a part of mathematical physics, the Dyson series, formulated by Freeman Dyson, is a perturbative expansion of the time evolution operator in the interaction picture. Each term can be represented by a sum of Feynman diagrams. This series diverges asymptotically, but in quantum electrodynamics (QED) at the second order the difference from experimental data is in the order of 10−10. This close agreement holds because the coupling constant (also known as the fine-structure constant) of QED is much less than 1. 10^-5, so how does it follow that second order approximation in alpha is good to 10^-10? --> Notice that in this article Planck units are used, so that ''ħ'' = 1 (where ''ħ'' is the reduced Planck constant). The Dyson operator Suppose that we have a Hamiltonian , which we split into a ''free'' part and an ''interacting part'' , i.e. . We will work in the interaction picture here, that is, :V_(t) = \mathrm^ V_(t) \mathrm^, where H ... [...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] |
Perturbation Theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of \varepsilon usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
