|
Newton–Wigner Localization
Newton–Wigner localization (named after Theodore Duddell Newton and Eugene Wigner) is a scheme for obtaining a position operator for massive relativistic quantum particle In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy \Sigma, and represents the contribution to the particle's energy, or effective mass, due to interactions between ...s. It is known to largely conflict with the Reeh–Schlieder theorem outside of a very limited scope. The Newton–Wigner position operators 1, 2, 3, are the premier notion of position in relativistic quantum mechanics of a single particle. They enjoy the same commutation relations with the 3 space momentum operators and transform under rotations in the same way as the , , in ordinary QM. Though formally they have the same properties with respect to 1, 2, 3, as the position in ordinary QM, they have additional properties: One of these is that : _i \, , p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugene Wigner
Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles". A graduate of the Technical University of Berlin, Wigner worked as an assistant to Karl Weissenberg and Richard Becker at the Kaiser Wilhelm Institute in Berlin, and David Hilbert at the University of Göttingen. Wigner and Hermann Weyl were responsible for introducing group theory into physics, particularly the theory of symmetry in physics. Along the way he performed ground-breaking work in pure mathematics, in which he authored a number of mathematical theorems. In particular, Wigner's theorem is a cornerstone in the mathematical formulation of quantum mechanics. He is also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Position Operator
In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle. When the position operator is considered with a wide enough domain (e.g. the space of tempered distributions), its eigenvalues are the possible position vectors of the particle. In one dimension, if by the symbol , x \rangle we denote the unitary eigenvector of the position operator corresponding to the eigenvalue x, then, , x \rangle represents the state of the particle in which we know with certainty to find the particle itself at position x. Therefore, denoting the position operator by the symbol X in the literature we find also other symbols for the position operator, for instance Q (from Lagrangian mechanics), \hat \mathrm x and so on we can write X, x\rangle = x , x\rangle, for every real position x. One possible realization of the unitary state with position x is the Dirac delta (function) distribution centered at the position x, often denoted by \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy. The theory transformed theoretical physics and astronomy during the 20th century, superseding a 200-year-old Classical mechanics, theory of mechanics created primarily by Isaac Newton. It introduced concepts including 4-dimensional spacetime as a unified entity of space and time in physics, time, relativity of simultaneity, kinematics, kinematic and gravity, gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Particle
In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy \Sigma, and represents the contribution to the particle's energy, or effective mass, due to interactions between the particle and its environment. In electrostatics, the energy required to assemble the charge distribution takes the form of self-energy by bringing in the constituent charges from infinity, where the electric force goes to zero. In a condensed matter context relevant to electrons moving in a material, the self-energy represents the potential felt by the electron due to the surrounding medium's interactions with it. Since electrons repel each other the moving electron polarizes, or causes to displace the electrons in its vicinity and then changes the potential of the moving electron fields. These are examples of self-energy. Characteristics Mathematically, this energy is equal to the so-called on mass shell value of the proper self- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reeh–Schlieder Theorem
The Reeh–Schlieder theorem is a result in relativistic local quantum field theory published by Helmut Reeh and Siegfried Schlieder in 1961. The theorem states that the vacuum state \vert \Omega \rangle is a cyclic vector for the field algebra \mathcal(\mathcal) corresponding to any open set \mathcal in Minkowski space. That is, any state \vert \psi \rangle can be approximated to arbitrary precision by acting on the vacuum with an operator selected from the local algebra, even for \vert \psi \rangle that contain excitations arbitrarily far away in space. In this sense, states created by applying elements of the local algebra to the vacuum state are not localized to the region \mathcal. For practical purposes, however, local operators still generate quasi-local states. More precisely, the long range effects of the operators of the local algebra will diminish rapidly with distance, as seen by the cluster properties of the Wightman functions. And with increasing distance, crea ... [...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] |
Maurice Henry Lecorney Pryce
Maurice Henry Lecorney Pryce (24 January 1913 – 24 July 2003) was a British physicist. Pryce was born in Croydon to an Anglo-Welsh father and French mother, and in his teens attended the Royal Grammar School, Guildford. After a few months in Heidelberg to add German to the French that had been his first language at home, he went to Trinity College, Cambridge. In 1935 he went to Princeton University, supported by a Commonwealth Fund Fellowship (now Harkness Fellowship) where he worked with Wolfgang Pauli and John von Neumann, obtaining his Ph.D. with a thesis on ''The wave mechanics of the photon'' under the supervision of Max Born and Ralph Fowler. In 1937 he returned to England as a Fellow of Trinity, until in 1939 he was appointed Reader in Theoretical Physics at Liverpool University under James Chadwick. In 1941 he joined the Admiralty Signals Establishment (now part of the Admiralty Research Establishment) to work on radar. In 1944 he joined the British atomic energy team i ... [...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] |
.svg "Click for more on -> Theory Of Relativity")
