Soft Photon
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Soft Photon
In particle physics, soft photons are photons having photon energies much smaller than the energies of the particles participating in a particular scattering process, and they are not energetic enough to be detected. Such photons can be emitted from (or absorbed by) the external (incoming and outgoing) lines of charged particles of the Feynman diagram for the process. Even though soft photons are not detected, the possibility of their emission must be taken into account in the calculation of the scattering amplitude In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process.
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Particle Physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three generations of fermions, but ordinary matter is made only from the first fermion generation. The first generation consists of 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. Quarks cannot exist on their own but form hadrons. Hadrons that contain an odd number of quarks are called baryons and those that contain an even number are called mesons. Two baryons, the proton and the neutron, make up most of the mass of ordinary matter. Mesons are unstable and the longest-lived last for only a few hundredths of ...
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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 ...
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Photon Energy
Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy. Photon energy can be expressed using any unit of energy. Among the units commonly used to denote photon energy are the electronvolt (eV) and the joule (as well as its multiples, such as the microjoule). As one joule equals 6.24 × 1018 eV, the larger units may be more useful in denoting the energy of photons with higher frequency and higher energy, such as gamma rays, as opposed to lower energy photons as in the optical and radio frequency regions of the electromagnetic spectrum. Formulas Physics Photon energy is directly proportional to frequency. E = hf where *E is energy *h is the Planck constant * f is frequency This equation is known ...
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Scattering
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections of radiation that undergo scattering are often called ''diffuse reflections'' and unscattered reflections are called ''specular'' (mirror-like) reflections. Originally, the term was confined to light scattering (going back at least as far as Isaac Newton in the 17th century). As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" (not then recognized as electromagnetic in nature) in 1800. John Tyndall, a pioneer in light scattering researc ...
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Feynman Diagram
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 diagra ...
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Scattering Amplitude
In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process.''Quantum Mechanics: Concepts and Applications''
By Nouredine Zettili, 2nd edition, page 623. Paperback 688 pages January 2009 The plane wave is described by the : \psi(\mathbf) = e^ + f(\theta)\frac \;, where \mathbf\equiv(x,y,z) is the position vector; r\equiv, \mathbf, ; e^ is the incoming plane wave with the

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 van ...
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Virtual Particle
A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturbation theory of quantum field theory where interactions between ordinary particles are described in terms of exchanges of virtual particles. A process involving virtual particles can be described by a schematic representation known as a Feynman diagram, in which virtual particles are represented by internal lines. Virtual particles do not necessarily carry the same mass as the corresponding real particle, although they always conserve energy and momentum. The closer its characteristics come to those of ordinary particles, the longer the virtual particle exists. They are important in the physics of many processes, including particle scattering and Casimir forces. In quantum field theory, forces—such as the electromagnetic repulsion or a ...
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Steven Weinberg
Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles. He held the Josey Regental Chair in Science at the University of Texas at Austin, where he was a member of the Physics and Astronomy Departments. His research on elementary particles and physical cosmology was honored with numerous prizes and awards, including the 1979 Nobel Prize in physics and the 1991 National Medal of Science. In 2004, he received the Benjamin Franklin Medal of the American Philosophical Society, with a citation that said he was "considered by many to be the preeminent theoretical physicist alive in the world today." He was elected to the U.S. National Academy of Sciences, Britain's Royal Society, the American Philosophical Society, and the American Academy of Arts and Sciences. Weinb ...
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Soft Graviton Theorem
In physics, the soft graviton theorem, first formulated by Steven Weinberg in 1965, allows calculation of the S-matrix, used in calculating the outcome of collisions between particles, when low-energy (soft) gravitons come into play. Specifically, if in a collision between ''n'' incoming particles from which ''m'' outgoing particles arise, the outcome of the collision depends on a certain ''S'' matrix, by adding one or more gravitons to the ''n'' + ''m'' particles, the resulting ''S'' matrix (let it be ''S''') differs from the initial ''S'' only by a factor that does not depend in any way, except for the momentum, on the type of particles to which the gravitons couple. The theorem also holds by putting photons in place of gravitons, thus obtaining a corresponding soft photon theorem. The theorem is used in the context of attempts to formulate a theory of quantum gravity in the form of a perturbative quantum theory, that is, as an approximation of a possible, as yet unknown, ...
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Gauge Theories
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 boso ...
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