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Hubbard–Stratonovich Transformation
The Hubbard–Stratonovich (HS) transformation is an exact mathematical transformation invented by Russian physicist Ruslan L. Stratonovich and popularized by British physicist John Hubbard. It is used to convert a particle theory into its respective field theory by linearizing the density operator in the many-body interaction term of the Hamiltonian and introducing an auxiliary scalar field. It is defined via the integral identity : \exp \left\ = \sqrt \; \int_^\infty \exp \left - \frac - i x y \right\, dy, where the real constant a > 0. The basic idea of the HS transformation is to reformulate a system of particles interacting through two-body potentials into a system of independent particles interacting with a fluctuating field. The procedure is widely used in polymer physics, classical particle physics, spin glass theory, and electronic structure theory. Calculation of resulting field theories The resulting field theories are well-suited for the application of effective ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transformation (geometry)
In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both \mathbb^2 or both \mathbb^3 — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Classifications Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations). They can also be classified according to the properties they preserve: * Displacements preserve distances and oriented angles (e.g., translations); * Isometries preserve angles and distances (e.g., Euclidean transformations); * Similarities preserve angles and ratios between distances (e.g., resizing); * Affine transformations preserve parallelism (e.g., scaling, shear); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruslan L
Ruslan may refer to: * ''Ruslan'' (film), a 2009 film starring Steven Segal * Ruslan (given name), male name used mainly in Slavic countries, with list of people * Antonov An-124 ''Ruslan'', large Soviet cargo aircraft, later built in Ukraine and Russia * SS ''Ruslan'', a Russian cargo ship in the Third Aliyah in 1919 See also * Rusian (other) Rusian may refer to: * Old East Slavic, a language which some scholars refer to as ''Rusian'' * Ruthenian language, also known as ''Rusian'' * Rusian, a fictional character in '' And You Thought There Is Never a Girl Online?'' See also * Rus' ... * Ruslan and Ludmila (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Hubbard (physicist)
John Hubbard (27 October 1931 – 27 November 1980) was a British physicist, best known for the Hubbard model for interacting electrons, the Hubbard–Stratonovich transformation, and the Hubbard approximations. He graduated from Imperial College London, receiving a B.Sc. (1955) and a Ph.D. degree (1958). He was the Head of the Solid State Theory Group at the Atomic Energy Research Establishment in Harwell (England), and worked at the IBM Research Laboratory IBM Research is the research and development division for IBM, an American multinational information technology company headquartered in Armonk, New York, with operations in over 170 countries. IBM Research is the largest industrial research org ... in San Jose, California (1976–1980). References External links Biographyby A. L. Kuzemsky, 2006. * John Hubbard 1931–1980by David Thouless, 18 June 2013 {{DEFAULTSORT:Hubbard, John 1931 births 1980 deaths Alumni of Imperial College London IBM employees B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 hundredt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scalar Field Theory
In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation. The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a pseudoscalar. Since they do not involve polarization complications, scalar fields are often the easiest to appreciate second quantization through. For this reason, scalar field theories are often used for purposes of introduction of novel concepts and techniques. The signature of the metric employed below is . Classical scalar field theory A general reference for this section is Ramond, Pierre (2001-12-21). Field Theory: A Modern Primer (Second Edition). USA: Westview Press. , Ch 1. Linear (free) theory The most basic scalar field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density Matrix
In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using the Born rule. It is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent ''mixed states''. Mixed states arise in quantum mechanics in two different situations: first when the preparation of the system is not fully known, and thus one must deal with a statistical ensemble of possible preparations, and second when one wants to describe a physical system which is entangled with another, without describing their combined state. Density matrices are thus crucial tools in areas of quantum mechanics that deal with mixed states, such as quantum statistical mechanics, open quantum systems, quantum decoherence, and quantum information. Definition an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Rowan Hamilton
Sir William Rowan Hamilton LL.D, DCL, MRIA, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the Andrews Professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Ireland, living at Dunsink Observatory. Hamilton's scientific career included the study of geometrical optics, ideas from Fourier analysis, and his work on quaternions which made him one of the founders of modern linear algebra. He made major contributions in optics, classical mechanics and abstract algebra. His work was fundamental to modern theoretical physics, particularly his reformulation of Newtonian mechanics, now called Hamiltonian mechanics. It is now central both to electromagnetism and to quantum mechanics. Early life Hamilton was the fourth of nine children born to Sarah Hutton (1780–1817) and Archibald Hamilton (1778–1819),Bruno (2003) who lived in Dublin at 29 Dominick Street, later renumbered to 36. Hamilton's father, who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scalar (physics)
In physics, scalars (or scalar quantities) are physical quantities that are unaffected by changes to a vector space basis (i.e., a coordinate system transformation). Scalars are often accompanied by units of measurement, as in "10 cm". Examples of scalar quantities are mass, distance, charge, volume, time, speed, and the magnitude of physical vectors in general (such as velocity). A change of a vector space basis changes the description of a vector in terms of the basis used but does not change the vector itself, while a scalar has nothing to do with this change. In classical physics, like Newtonian mechanics, rotations and reflections preserve scalars, while in relativity, Lorentz transformations or space-time translations preserve scalars. The term "scalar" has origin in the multiplication of vectors by a unitless scalar, which is a ''uniform scaling'' transformation. Relationship with the mathematical concept A scalar in physics is also a scalar in mathematics, as an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soviet Physics Doklady
''Doklady Physics: A Journal of the Russian Academy of Sciences'' is a monthly peer-reviewed scientific journal published by MAIK Nauka/Interperiodica and Springer Science+Business Media. This journal covers Russian to English translations of physics, technical physics, astronomy, and mechanics articles from '' Doklady Akademii Nauk'' (English: ''Proceedings of the Russian Academy of Sciences''). The editor-in-chief is Sergey V. Garnov (Prokhorov General Physics Institute). The journal was established in 1956 as ''Soviet Physics-Doklady'' and renamed ''Physics-Doklady'' in 1993, before obtaining its current title in 1998. Abstracting and indexing This journal is abstracted and indexed in: * Current Contents/Physical, Chemical and Earth Sciences * Science Citation Index * Chemical Abstracts Service * Compendex * Scopus * Inspec * Current Mathematical Publications * Zentralblatt Math According to the ''Journal Citation Reports'', the journal has a 2013 impact factor The impac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review Letters
''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journal Citation Reports'' impact factor and the journal ''h''-index proposed by Google Scholar, many physicists and other scientists consider ''Physical Review Letters'' to be one of the most prestigious journals in the field of physics. ''According to Google Scholar, PRL is the journal with the 9th journal h-index among all scientific journals'' ''PRL'' is published as a print journal, and is in electronic format, online and CD-ROM. Its focus is rapid dissemination of significant, or notable, results of fundamental research on all topics related to all fields of physics. This is accomplished by rapid publication of short reports, called "Letters". Papers are published and available electronically one article at a time. When published in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer Physics
Polymer physics is the field of physics that studies polymers, their fluctuations, mechanical properties, as well as the kinetics of reactions involving degradation and polymerisation of polymers and monomers respectively.P. Flory, ''Principles of Polymer Chemistry'', Cornell University Press, 1953. .Pierre Gilles De Gennes, ''Scaling Concepts in Polymer Physics'' CORNELL UNIVERSITY PRESS Ithaca and London, 1979M. Doi and S. F. Edwards, ''The Theory of Polymer Dynamics'' Oxford University Inc NY, 1986 While it focuses on the perspective of condensed matter physics, polymer physics is originally a branch of statistical physics. Polymer physics and polymer chemistry are also related with the field of polymer science, where this is considered the applicative part of polymers. Polymers are large molecules and thus are very complicated for solving using a deterministic method. Yet, statistical approaches can yield results and are often pertinent, since large polymers (i.e., polymers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
