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Quantum field theory

Quantum field theory
For example, quantum electrodynamics (QED) has one electron field and one photon field; quantum chromodynamics (QCD) has one field for each type of quark; and, in condensed matter, there is an atomic displacement field that gives rise to phonon particles. Edward Witten describes QFT as "by far" the most difficult theory in modern physics.[1] In QFT, quantum mechanical interactions between particles are described by interaction terms between the corresponding underlying fields. QFT interaction terms are similar in spirit to those between charges with electric and magnetic fields in Maxwell's equations. However, unlike the classical fields of Maxwell's theory, fields in QFT generally exist in quantum superpositions of states and are subject to the laws of quantum mechanics. Because the fields are continuous quantities over space, there exist excited states with arbitrarily large numbers of particles in them, providing QFT systems with an effectively infinite number of degrees of freedom.

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Classical mechanics Diagram of orbital motion of a satellite around the earth, showing perpendicular velocity and acceleration (force) vectors. In physics, classical mechanics and quantum mechanics are the two major sub-fields of mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology. The Wicker Man (1973 Edit Storyline Sgt. Howie travels to Summerisle to investigate the disappearance of a young girl. He discovers that the locals are weird and unhelpful, and becomes determined to get to the bottom of the disappearance. Written by Sean Taylor <>

Quantum mechanics Solution to Schrödinger's equation for the hydrogen atom at different energy levels. The brighter areas represent a higher probability of finding an electron Quantum mechanics gradually arose from Max Planck's solution in 1900 to the black-body radiation problem (reported 1859) and Albert Einstein's 1905 paper which offered a quantum-based theory to explain the photoelectric effect (reported 1887). Early quantum theory was significantly reformulated in the mid-1920s.

Category theory « The Unapologetic Mathematician Comma Categories Another useful example of a category is a comma category. The term comes from the original notation which has since fallen out of favor because, as Saunders MacLane put it, “the comma is already overworked”. We start with three categories Classical field theory A physical field can be thought of as the assignment of a physical quantity at each point of space and time. For example, in a weather forecast, the wind velocity during a day over a country is described by assigning a vector to each point in space. Each vector represents the direction of the movement of air at that point. As the day progresses, the directions in which the vectors point change as the directions of the wind change. From the mathematical viewpoint, classical fields are described by sections of fiber bundles (covariant classical field theory). The term 'classical field theory' is commonly reserved for describing those physical theories that describe electromagnetism and gravitation, two of the fundamental forces of nature.

Scattering theory Top: the real part of a plane wave travelling upwards. Bottom: The real part of the field after inserting in the path of the plane wave a small transparent disk of index of refraction higher than the index of the surrounding medium. This object scatters part of the wave field, although at any individual point, the wave's frequency and wavelength remain intact. In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Prosaically, wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow.

HomeschoolScientist Upload Subscription preferences Loading... Working... Subatomic Particles Paul Davies, a cosmologist at Arizona State University in Tempe, admires the fact that Aharonov’s team has always striven to verify its claims experimentally. “This isn’t airy-fairy philosophy—these are real experiments,” he says. Davies has now joined forces with the group to investigate the framework’s implications for the origin of the cosmos (See “Does the Universe Have a Destiny?” below). Algebraic structure The properties of specific algebraic structures are studied in abstract algebra. The general theory of algebraic structures has been formalized in universal algebra. Category theory is used to study the relationships between two or more classes of algebraic structures, often of different kinds.

First quantization A first quantization of a physical system is a semi-classical treatment of quantum mechanics, in which particles or physical objects are treated using quantum wave functions but the surrounding environment (for example a potential well or a bulk electromagnetic field or gravitational field) is treated classically. First quantization is appropriate for studying a single quantum-mechanical system being controlled by a laboratory apparatus that is itself large enough that classical mechanics is applicable to most of the apparatus. Theoretical background[edit]