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Wick's Theorem Wick's theorem Wick's theorem is a method of reducing highorder derivatives to a combinatorics problem.[1] It is named after GianCarlo 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 [...More...]  "Wick's Theorem" on: Wikipedia Yahoo Parouse 

Quantum Chromodynamics In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a nonabelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years. QCD exhibits two main properties: Color Color confinement, plasmas. This is a consequence of the constant force between two color charges as they are separated: In order to increase the separation between two quarks within a hadron, everincreasing amounts of energy are required [...More...]  "Quantum Chromodynamics" on: Wikipedia Yahoo Parouse 

Parity (physics) In quantum mechanics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate. In three dimensions, it is also often described by the simultaneous flip in the sign of all three spatial coordinates (a point reflection): P : ( x y z ) ↦ ( − x − y − z ) . displaystyle mathbf P : begin pmatrix x\y\zend pmatrix mapsto begin pmatrix x\y\zend pmatrix . It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. A parity transformation on something achiral, on the other hand, can be viewed as an identity transformation [...More...]  "Parity (physics)" on: Wikipedia Yahoo Parouse 

Regularization (physics) In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called regulator. The regulator, also known as a "cutoff", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for (and requires) the possibility that "new physics" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an "effective theory" within its intended scale of use. It is distinct from renormalization, another technique to control infinities without assuming new physics, by adjusting for selfinteraction feedback. Regularization was for many decades controversial even amongst its inventors, as it combines physical and epistemological claims into the same equations [...More...]  "Regularization (physics)" on: Wikipedia Yahoo Parouse 

Klein–Gordon Equation The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second order in space and time and manifestly Lorentz covariant. It is a quantized version of the relativistic energy–momentum relation. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. Its theoretical relevance is similar to that of the Dirac equation.[1] Electromagnetic interactions can be incorporated, forming the topic of scalar electrodynamics, but because common spinless particles like the pi mesons are unstable and also experience the strong interaction (with unknown interaction term in the Hamiltonian[2]), the practical utility is limited. The equation can be put into the form of a Schrödinger equation [...More...]  "Klein–Gordon Equation" on: Wikipedia Yahoo Parouse 

Topological Charge In physics, a topological quantum number (also called topological charge) is any quantity, in a physical theory, that takes on only one of a discrete set of values, due to topological considerations. Most commonly, topological quantum numbers are topological invariants associated with topological defects or solitontype solutions of some set of differential equations modeling a physical system, as the solitons themselves owe their stability to topological considerations. The specific "topological considerations" are usually due to the appearance of the fundamental group or a higherdimensional homotopy group in the description of the problem, quite often because the boundary, on which the boundary conditions are specified, has a nontrivial homotopy group that is preserved by the differential equations [...More...]  "Topological Charge" on: Wikipedia Yahoo Parouse 

Noether Charge Noether's (first)[1] theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether Emmy Noether in 1915 and published in 1918.[2], although a special case was proven by E. Cosserat & F. Cosserat in 1909.[3] The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action. Noether's theorem Noether's theorem is used in theoretical physics and the calculus of variations. A generalization of the formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g [...More...]  "Noether Charge" on: Wikipedia Yahoo Parouse 

Explicit Symmetry Breaking In theoretical physics, explicit symmetry breaking is the breaking of a symmetry of a theory by terms in its defining equations of motion (most typically, to the Lagrangian or the Hamiltonian) that do not respect the symmetry. Usually this term is used in situations where these symmetrybreaking terms are small, so that the symmetry is approximately respected by the theory. An example is the spectral line splitting in the Zeeman effect, due to a magnetic interaction perturbation in the Hamiltonian of the atoms involved. Explicit symmetry breaking differs from spontaneous symmetry breaking. In the latter, the defining equations respect the symmetry but the ground state (vacuum) of the theory breaks it.[1] Explicit symmetry breaking is also associated with electromagnetic radiation [...More...]  "Explicit Symmetry Breaking" on: Wikipedia Yahoo Parouse 

Gauge Symmetry (mathematics) In mathematics, any Lagrangian system generally admits gauge symmetries, though it may happen that they are trivial. In theoretical physics, the notion of gauge symmetries depending on parameter functions is a cornerstone of contemporary field theory. A gauge symmetry of a Lagrangian L displaystyle L is defined as a differential operator on some vector bundle E displaystyle E taking its values in the linear space of (variational or exact) symmetries of L displaystyle L [...More...]  "Gauge Symmetry (mathematics)" on: Wikipedia Yahoo Parouse 

Poincaré Symmetry The Poincaré group, named after Henri Poincaré Henri Poincaré (1906),[1] was first defined by Minkowski (1908) as the group of Minkowski spacetime isometries.[2][3] It is a tengenerator nonabelian Lie group Lie group of fundamental importance in physics.Contents1 Overview 2 Poincaré symmetry 3 Poincaré group 4 Poincaré algebra 5 Other dimensions 6 SuperPoincaré algebra 7 See also 8 Notes 9 ReferencesOverview[edit] A Minkowski spacetime isometry has the property that the interval between events is left invariant. For example, if everything was postponed by two hours, including the two events and the path you took to go from one to the other, then the time interval between the events recorded by a stopwatch you carried with you would be the same. Or if everything was shifted five kilometres to the west, or turned 60 degrees to the right, you would also see no change in the interval [...More...]  "Poincaré Symmetry" on: Wikipedia Yahoo Parouse 

Lorentz Symmetry In relativistic physics, Lorentz symmetry, named for Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".[1] Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance Lorentz covariance has two distinct, but closely related meanings:A physical quantity is said to be Lorentz covariant Lorentz covariant if it transforms under a given representation of the Lorentz group. According to the representation theory of the Lorentz group, these quantities are built out of scalars, fourvectors, fourtensors, and spinors [...More...]  "Lorentz Symmetry" on: Wikipedia Yahoo Parouse 

Rotation Symmetry Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks the same.Contents1 Formal treatment1.1 Discrete rotational symmetry 1.2 Examples 1.3 Multiple symmetry axes through the same point 1.4 Rotational symmetry Rotational symmetry with respect to any angle 1.5 Rotational symmetry Rotational symmetry with translational symmetry2 See also 3 References 4 External linksFormal treatment[edit] See also: Rotational invariance Formally the rotational symmetry is symmetry with respect to some or all rotations in mdimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation [...More...]  "Rotation Symmetry" on: Wikipedia Yahoo Parouse 

Time Translation Symmetry Time Time translation symmetry or temporal translation symmetry (TTS) is a mathematical transformation in physics that moves the times of events through a common interval. Time Time translation symmetry is the hypothesis that the laws of physics are unchanged, (i.e. invariant) under such a transformation. Time Time translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time Time translation symmetry is closely connected via the Noether theorem, to conservation of energy.[1] In mathematics, the set of all time translations on a given system form a Lie group. There are many symmetries in nature besides time translation, such as spacial translation or rotational symmetries [...More...]  "Time Translation Symmetry" on: Wikipedia Yahoo Parouse 

Tsymmetry Tsymmetry Tsymmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal: T : t ↦ − t . displaystyle T:tmapsto t. Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics [...More...]  "Tsymmetry" on: Wikipedia Yahoo Parouse 

Space Translation Symmetry In geometry, a translation "slides" a thing by a: Ta(p) = p + a. In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation. Discrete translational symmetry is invariant under discrete translation. Analogously an operator A on functions is said to be translationally invariant with respect to a translation operator T δ displaystyle T_ delta if the result after applying A doesn't change if the argument function is translated [...More...]  "Space Translation Symmetry" on: Wikipedia Yahoo Parouse 

Charge Conjugation Charge conjugation is a transformation that switches all particles with their corresponding antiparticles, and thus changes the sign of all charges: not only electric charge but also the charges relevant to other forces. In physics, Csymmetry means the symmetry of physical laws under a chargeconjugation transformation. Electromagnetism, gravity and the strong interaction all obey Csymmetry, but weak interactions violate Csymmetry.Contents1 Charge reversal in electroweak theory 2 Combination of charge and parity reversal 3 Charge definition 4 See also 5 ReferencesCharge reversal in electroweak theory[edit] The laws of electromagnetism (both classical and quantum) are invariant under this transformation: if each charge q were to be replaced with a charge −q, and thus the directions of the electric and magnetic fields were reversed, the dynamics would preserve the same form [...More...]  "Charge Conjugation" on: Wikipedia Yahoo Parouse 