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N. Mukunda
Narasimhaiengar Mukunda (born 25 January 1939, New Delhi, India) is an Indian theoretical physicist who is known for his expertise in Particle Physics, Mathematical Physics, Mechanics and Optics. His contributions to physics are many, prominent among them are Representation theory of Lorentz, Poincare and Other non-compact groups, Majorana and other relativistic wave equations, Fourier optics, Hamiltonian theories, quantum mechanics and optics Classical dynamical formalism. Education Mukunda's higher education began at Delhi University, where he graduated with B.Sc. (Hon) degree in 1953. For his Ph.D he studied at University of Rochester with E. C. G. Sudarshan and graduated in 1964. Mukunda’s thesis dealt with Hamiltonian mechanics, symmetry groups and elementary particles..He also studied group theory at Princeton University with Valentine Bargmann, including topological groups and Lie theory. Research Career He was a post-doctoral fellow at Syracuse University be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New Delhi
New Delhi (; ) is the Capital city, capital of India and a part of the Delhi, National Capital Territory of Delhi (NCT). New Delhi is the seat of all three branches of the Government of India, hosting the Rashtrapati Bhavan, New Parliament House, New Delhi, Sansad Bhavan, and the Supreme Court of India, Supreme Court. New Delhi is a Municipal governance in India, municipality within the NCT, administered by the New Delhi Municipal Council (NDMC), which covers mostly Lutyens' Delhi and a few adjacent areas. The municipal area is part of a larger List of districts in India, administrative district, the New Delhi district. Although colloquially ''Delhi'' and ''New Delhi'' are used interchangeably to refer to the National Capital Territory of Delhi, both are distinct entities, with the municipality and the New Delhi district forming a relatively small part within the megacity of Delhi. The National Capital Region (India), National Capital Region is an even larger entity, compris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanics
Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of an object's position relative to its environment. Theoretical expositions of this branch of physics has its origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo Galilei, Johannes Kepler, Christiaan Huygens, and Isaac Newton laid the foundation for what is now known as classical mechanics. As a branch of classical physics, mechanics deals with bodies that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as the physical science that deals with the motion of and forces on bodies not in the quantum realm. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syracuse University
Syracuse University (informally 'Cuse or SU) is a Private university, private research university in Syracuse, New York, United States. It was established in 1870 with roots in the Methodist Episcopal Church but has been nonsectarian since 1920. Located in the city's University Hill, Syracuse, University Hill neighborhood, east and southeast of downtown Syracuse, the large campus features an eclectic mix of architecture, ranging from nineteenth-century Romanesque Revival architecture, Romanesque Revival to contemporary buildings. Syracuse University is organized into 13 schools and colleges and is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". Syracuse University athletic teams, the Syracuse Orange, Orange, participate in 20 intercollegiate sports. SU is a member of the Atlantic Coast Conference (ACC) for all NCAA Division I athletics, except for the College rowing (United States), men's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Theory
In mathematics, the mathematician Sophus Lie ( ) initiated lines of study involving integration of differential equations, transformation groups, and contact (mathematics), contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry. This article addresses his approach to transformation groups, which is one of the areas of mathematics, and was worked out by Wilhelm Killing and Élie Cartan. The foundation of Lie theory is the exponential map (Lie theory), exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie algebra correspondence. The subject is part of differential geometry since Lie groups are differentiable manifolds. Lie groups evolve out of the identity (1) and the tangent vectors to one-parameter group, one-parameter subgroups generate the Lie algebra. The structure of a Lie group is implicit in its algebra, and the structure of the Lie algebra is expressed by root systems and Root datu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valentine Bargmann
Valentine "Valya" Bargmann (April 6, 1908 – July 20, 1989) was a German-American mathematician and theoretical physicist. Biography Born in Berlin, Germany, to a German Jewish The history of the Jews in Germany goes back at least to the year 321 CE, and continued through the Early Middle Ages (5th to 10th centuries CE) and High Middle Ages (c. 1000–1299 CE) when Jewish immigrants founded the Ashkenazi Jewish commu ... family, Bargmann studied there from 1925 to 1933. After the National Socialist Machtergreifung, he moved to Switzerland to the University of Zürich where he received his Ph.D. under Gregor Wentzel. He emigrated to the U.S., barely managing immigration acceptance, as his German passport was to be revoked with only two days of validity left. At the Institute for Advanced Study in Princeton, New Jersey, Princeton (1937–1946) he worked as an assistant to Albert Einstein, publishing with him and Peter Bergmann on classical five-dimensional Kaluza–Klein the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University
Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. The institution moved to Newark, New Jersey, Newark in 1747 and then to its Mercer County, New Jersey, Mercer County campus in Princeton nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate instruction in the hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Particles
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a consequence of Flavour (particle physics), flavor and Quantum chromodynamics, color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number: electrons and other leptons, quarks, and the fundamental bosons. Subatomic particles such as protons or neutrons, which Quark, contain two or more elementary particles, are known as composite particles. Ordinary matter is composed of atoms, themselves once thought to be indivisible elementary particles. The name ''atom'' comes from the Ancient Greek word ''ἄτομος'' (wikt:átomo#:~:text=Learned borrowing from Latin atomus,, "to cut")., atomos) which means ''indivisible'' or ''u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Groups
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object ''X'' is ''G'' = Sym(''X''). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space. This article mainly considers symmetry groups in Euclidean geometry, but the concept may also be studied for more general types of geometric structure. Introduction We consider the "objects" possessing symmetry to be geometric figures, images, and patterns, such as a wallpaper pattern. For symmetry of physical objects, one may also take their physical composition as part of the pattern. (A pattern may be specified formally as a scalar field, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Mechanics
In physics, Hamiltonian mechanics is a reformulation of Lagrangian mechanics that emerged in 1833. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta''. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a Hamilton–Jacobi equation, link between classical and quantum mechanics. Overview Phase space coordinates (''p'', ''q'') and Hamiltonian ''H'' Let (M, \mathcal L) be a Lagrangian mechanics, mechanical system with configuration space (physics), configuration space M and smooth Lagrangian_mechanics#Lagrangian, Lagrangian \mathcal L. Select a standard coordinate system (\boldsymbol,\boldsymbol) on M. The quantities \textstyle p_i(\boldsymbol,\boldsymbol,t) ~\stackrel~ / are called ''m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes the behaviour of visible light, visible, ultraviolet, and infrared light. Light is a type of electromagnetic radiation, and other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for by using the Classical electromagnetism, classical electromagnetic description of light, however complete electromagnetic descriptions of light are often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics, treats light as a collection of Ray (optics), rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Optics
Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination, or '' superposition'', of plane waves. It has some parallels to the Huygens–Fresnel principle, in which the wavefront is regarded as being made up of a combination of spherical wavefronts (also called phasefronts) whose sum is the wavefront being studied. A key difference is that Fourier optics considers the plane waves to be natural modes of the propagation medium, as opposed to Huygens–Fresnel, where the spherical waves originate in the physical medium. A curved phasefront may be synthesized from an infinite number of these "natural modes" i.e., from plane wave phasefronts oriented in different directions in space. When an expanding spherical wave is far from its sources, it is locally tangent to a planar phase front (a single plane wave out of the infinite spectrum), which is transverse to the radial direction of prop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
