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Infrared Divergence
In physics, an infrared divergence (also IR divergence or infrared catastrophe) is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with very small energy approaching zero, or equivalently, because of physical phenomena at very long distances. Overview The infrared divergence only appears in theories with massless particles (such as photons). They represent a legitimate effect that a complete theory often implies. In fact, in the case of photons, the energy is given by E=h\nu, where \nu is the frequency associated to the particle and as it goes to zero, like in the case of soft photons, there will be an infinite number of particles in order to have a finite amount of energy. One way to deal with it is to impose an infrared cutoff and take the limit as the cutoff approaches zero and/or refine the question. Another way is to assign the massless particle a fictitious mass, and then take the limit as the fictitious mass va ... [...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] |
Bremsstrahlung Radiation
In particle physics, bremsstrahlung (; ; ) is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation (i.e., photons), thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases. Broadly speaking, bremsstrahlung or braking radiation is any radiation produced due to the acceleration (positive or negative) of a charged particle, which includes synchrotron radiation (i.e., photon emission by a relativistic particle), cyclotron radiation (i.e. photon emission by a non-relativistic particle), and the emission of electrons and positrons during be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renormalization Group
In theoretical physics, the renormalization group (RG) is a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying physical laws (codified in a quantum field theory) as the energy (or mass) scale at which physical processes occur varies. A change in scale is called a scale transformation. The renormalization group is intimately related to ''scale invariance'' and ''conformal invariance'', symmetries in which a system appears the same at all scales ( self-similarity), where under the fixed point of the renormalization group flow the field theory is conformally invariant. As the scale varies, it is as if one is decreasing (as RG is a semi-group and doesn't have a well-defined inverse operation) the magnifying power of a notional microscope viewing the system. In so-called renormalizable theories, the system at one scale will generally consist of self- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renormalization
Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that is used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian. For example, an electron theory may begin by postulating an electron with an initial mass and charge. In quantum field theory a cloud of virtual particles, such as photons, positrons, and others surrounds and interacts with the initial electron. Accounting for the interactions of the surrounding particles (e.g. collisions at different energies) shows that the electron-system behaves as if it had a different mass and charge than initially postulated. Renormalization, in this example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cutoff (physics)
In theoretical physics, cutoff (AE: cutoff, BE: cut-off) is an arbitrary maximal or minimal value of energy, momentum, or length, used in order that objects with larger or smaller values than these physical quantities are ignored in some calculation. It is usually represented within a particular energy or length scale, such as Planck units. When used in this context, the traditional terms "infrared" and "ultraviolet" are not literal references to specific regions of the spectrum, but rather refer by analogy to portions of a calculation for low energies (infrared) and high energies (ultraviolet), respectively. Infrared and ultraviolet cutoff An infrared cutoff (long-distance cutoff) is the minimal value of energy – or, equivalently, the maximal wavelength (usually a very large distance) – that will be taken into account in a calculation, typically an integral. At the opposite end of the energy scale, an ultraviolet cutoff is the maximal allowed energy or the shortest allowed d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unruh Effect
The Unruh effect (also known as the Fulling–Davies–Unruh effect) is a theoretical prediction in quantum field theory that an observer who is uniformly accelerating through empty space will perceive a thermal bath. This means that even in the absence of any external heat sources, an accelerating observer will detect particles and experience a temperature. In contrast, an inertial observer in the same region of spacetime would observe no temperature. In other words, the background appears to be warm from an accelerating reference frame. In layman's terms, an accelerating thermometer in empty space (like one being waved around), without any other contribution to its temperature, will record a non-zero temperature, just from its acceleration. Heuristically, for a uniformly accelerating observer, the ground state of an inertial observer is seen as a mixed state in thermodynamic equilibrium with a non-zero temperature bath. The Unruh effect was first described by Stephen Fulling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
McGraw-Hill
McGraw Hill is an American education science company that provides educational content, software, and services for students and educators across various levels—from K-12 to higher education and professional settings. They produce textbooks, digital learning tools, and adaptive technology to enhance learning experiences and outcomes. It is one of the "big three" educational publishers along with Houghton Mifflin Harcourt and Pearson Education. McGraw Hill also publishes reference and trade publications for the medical, business, and engineering professions. Formerly a division of The McGraw Hill Companies (later renamed McGraw Hill Financial, now S&P Global), McGraw Hill Education was divested and acquired by Apollo Global Management in March 2013 for $2.4 billion in cash. McGraw Hill was sold in 2021 to Platinum Equity for $4.5 billion. History McGraw Hill was founded in 1888, when James H. McGraw, co-founder of McGraw Hill, purchased the ''American Journal of Railway ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transition Amplitude
In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The square of the modulus of this quantity at a point in space represents a probability density at that point. Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that system, a link that was first proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding, and the probability thus calculated is sometimes called the "Born probability". These probabilistic concepts, namely ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Electrodynamic
In particle physics, quantum electrodynamics (QED) is the Theory of relativity, relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomenon, phenomena involving electric charge, electrically charged particles interacting by means of exchange of photons and represents the quantum mechanics, quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. In technical terms, QED can be described as a perturbation theory (quantum mechanics), perturbation theory of the electromagnetic Quantum vacuum state, quantum vacuum. Richard Feynman called it "the jewel of physics" for its precision tests of QED, extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Theory
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, which are distinct but closely intertwined phenomena. Electromagnetic forces occur between any two charged particles. Electric forces cause an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs between charged particles in relative motion. These two forces are described in terms of electromagnetic fields. Macroscopic charged objects are described in terms of Coulomb's law for electricity and Ampère's force law for magnetism; the Lorentz force describes microscopic charged particles. The electromagnetic force is responsible for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Charge
Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and unlike charges attract each other. An object with no net charge is referred to as neutral particle, electrically neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum mechanics, quantum effects. In an isolated system, the total charge stays the same - the amount of positive charge minus the amount of negative charge does not change over time. Electric charge is carried by subatomic particles. In ordinary matter, negative charge is carried by electrons, and positive charge is carried by the protons in the atomic nucleus, nuclei of atoms. If there are more electrons than protons in a piece of matter, it will have a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. the other being Derivative, differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Usage of integration expanded to a wide variety of scientific fields thereafter. A definite integral computes the signed area of the region in the plane that is bounded by the Graph of a function, graph of a given Function (mathematics), function between two points in the real line. Conventionally, areas above the horizontal Coordinate axis, axis of the plane are positive while areas below are n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
