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Symplectic Action
In physics, action is a scalar quantity describing how a physical system has dynamics (physics), changed over time. Action is significant because the equations of motion of the system can be derived through the principle of stationary action. In the simple case of a single particle moving with a constant velocity (uniform linear motion), the action is the momentum of the particle times the distance it moves, integral (mathematics), added up along its path; equivalently, action is twice the particle's kinetic energy times the duration for which it has that amount of energy. For more complicated systems, all such quantities are combined. More formally, action is a functional (mathematics), mathematical functional which takes the trajectory (also called path or history) of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths. Action has dimensional analysis, dimensions of energy × time or momentu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joule-second
The joule-second (symbol J⋅s or J s) is the unit of action and of angular momentum in the International System of Units (SI) equal to the product of an SI derived unit, the joule (J), and an SI base unit, the second (s). The joule-second is a unit of action or of angular momentum. The joule-second also appears in quantum mechanics within the definition of Planck's constant.Schlamminger, S.; Haddad, D.; Seifert, F.; Chao, L. S.; Newell, D. B.; Liu, R.; Steiner, R. L.; Pratt, J. R. (2014). "Determination of the Planck constant using a watt balance with a superconducting magnet system at the National Institute of Standards and Technology." Metrologia. 51 (2): S15. arXiv:1401.8160 . Bibcode:2014Metro..51S..15S. doi:10.1088/0026-1394/51/2/S15. ISSN 0026-1394. Angular momentum is the product of an object’s moment of inertia, in units of kg⋅m2 and its angular velocity in units of rad⋅s−1. This product of moment of inertia and angular velocity yields kg⋅m2⋅s−1 or the jo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Length
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre. Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in. Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, and width, breadth or depth. Height is used when there is a base from which vertical measurements can be taken. Width or breadth usually refer to a shorter dimension when length is the longest one. Depth is used for the third dimension of a three dimensional object. Length is the measure of one spatial dimension, whereas area is a measure of two dimensions (length square ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path Integral Formulation
The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization. Unlike previous methods, the path integral allows one to easily change coordinates between very different canonical descriptions of the same quantum system. Another advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals (for interactions of a certain type, these are ''coordinat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called Quantum, quanta) of their underlying quantum field (physics), fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian (field theory), Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory (quantum mechanics), perturbation theory in quantum mechanics. History Quantum field theory emerged from the wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...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] |
Gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light. On Earth, gravity gives weight to physical objects, and the Moon's gravity is responsible for sublunar tides in the oceans (the corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another). Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electricity and magnetism, two distinct but closely intertwined phenomena. In essence, electric forces occur between any two charged particles, causing an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs exclusively between ''moving'' charged particles. These two effects combine to create electromagnetic fields in the vicinity of charge particles, which can exert influence on other particles via the Lorentz force. At high energy, the weak force and electromagnetic force are unified as a single electroweak force. The electromagnetic force is responsible for many o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Field
In physics, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. For example, on a weather map, the surface temperature is described by assigning a 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 arrow to each point on a map that describes the wind 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 two interacting vector fields at each point in spacetime, or as a single-rank 2-tensor field. In the modern framework of the quantum theory of fields, even without refer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances, ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral Equation
In mathematics, integral equations are equations in which an unknown Function (mathematics), function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,...,x_n ; u(x_1,x_2,x_3,...,x_n) ; I^1 (u), I^2(u), I^3(u), ..., I^m(u)) = 0where I^i(u) is an integral operator acting on ''u.'' Hence, integral equations may be viewed as the analog to differential equations where instead of the equation involving derivatives, the equation contains integrals. A direct comparison can be seen with the mathematical form of the general integral equation above with the general form of a differential equation which may be expressed as follows:f(x_1,x_2,x_3,...,x_n ; u(x_1,x_2,x_3,...,x_n) ; D^1 (u), D^2(u), D^3(u), ..., D^m(u)) = 0where D^i(u) may be viewed as a differential operator of order ''i''. Due to this close connection between differential and integral equations, one can often convert between the two. For examp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamilton's Principle
In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action. It states that the dynamics of a physical system are determined by a variational problem for a functional based on a single function, the Lagrangian, which may contain all physical information concerning the system and the forces acting on it. The variational problem is equivalent to and allows for the derivation of the '' differential'' equations of motion of the physical system. Although formulated originally for classical mechanics, Hamilton's principle also applies to classical fields such as the electromagnetic and gravitational fields, and plays an important role in quantum mechanics, quantum field theory and criticality theories. Mathematical formulation Hamilton's principle states that the true evolution of a system described by generalized coordinates between two specified states and at two specified times and is a stationary point (a point where th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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