Andrei Dmitriyevich Linde is a Russian-American theoretical physicist and the Harald Trap Friis Professor of Physics at Stanford University. Linde is one of the main authors of the inflationary universe theory, as well as the theory of eternal inflation and inflationary multiverse, he received his Bachelor of Science degree from Moscow State University. In 1975, Linde was awarded a Ph. D. from the Lebedev Physical Institute in Moscow. He worked at CERN since 1989 and moved to the United States in 1990, where he became professor of physics at Stanford University. Among the various awards he has received for his work on inflation, in 2002 he was awarded the Dirac Medal, along with Alan Guth of MIT and Paul Steinhardt of Princeton University. In 2004 he received, along with Alan Guth, the Gruber Prize in Cosmology for the development of inflationary cosmology. In 2012 he, along with Alan Guth, was an inaugural awardee of the Fundamental Physics Prize. In 2014 he received the Kavli Prize in Astrophysics "for pioneering the theory of cosmic inflation", together with Alan Guth and Alexei Starobinsky.
In 2018 he received the Gamow Prize. During 1972 to 1976, David Kirzhnits and Andrei Linde developed a theory of cosmological phase transitions. According to this theory, there was not much difference between weak and electromagnetic interactions in the early universe; these interactions became different from each other only after the cosmological phase transitions which happened when the temperature in the expanding Universe's became sufficiently small. In 1974, Linde found that the energy density of scalar fields that break the symmetry between different interactions can play the role of the vacuum energy density in the Einstein equations. Between 1976 and 1978, Linde demonstrated that the release of this energy during the cosmological phase transitions may be sufficient to heat up the universe; these observations became the main ingredients of the first version of the inflationary universe theory proposed by Alan Guth in 1980. This theory, now called the "Old inflation theory", was based on the assumption that the universe was hot.
It experienced the cosmological phase transitions and was temporarily stuck in a supercooled metastable vacuum state. The universe expanded exponentially – "inflated" – until the false vacuum decayed and the universe became hot again; this idea attracted much attention because it could provide a unique solution to many difficult problems of the standard Big Bang theory. In particular, it could explain why the universe is so uniform. However, as Guth realized, this scenario did not quite work as intended: the decay of the false vacuum would make the universe inhomogeneous. In 1981, Linde developed another version of inflationary theory which he called "New inflation", he demonstrated that the exponentially rapid expansion of the universe could occur not only in the false vacuum but during a slow transition away from the false vacuum. This theory resolved the problems of the original model proposed by Guth while preserving most of its attractive features. A few months a similar scenario was proposed by Andreas Albrecht and Paul Steinhardt which referenced Linde's paper.
Soon after that, it was realized that the new inflationary scenario suffered from some problems. Most of them arose because of the standard assumption that the early universe was hot, inflation occurred during the cosmological phase transitions. In 1983, Linde abandoned some of the key principles of old and new inflation and proposed a more general inflationary theory, chaotic inflation. Chaotic inflation occurs in a much broader class of theories, without any need for the assumption of initial thermal equilibrium; the basic principles of this scenario became incorporated in most of the presently existing realistic versions of inflationary theory. Chaotic inflation changed the way. On, Linde proposed a possible modification of the way in which inflation may end, by developing the hybrid inflation scenario. In that model, inflation ends due to the "waterfall" instability. According to the inflationary theory, all elementary particles in the universe emerged after the end of inflation, in a process called reheating.
The first version of the theory of reheating, the theory of creation of matter in the universe, was developed in 1982 by Alexander Dolgov and Linde, by L. F. Abbott, Edward Farhi and Mark B. Wise. In 1994, this theory was revised by L. A. Kofman and Alexei Starobinsky, they have shown that the process of creation of matter after inflation may be much more efficient due to the effect of parametric resonance. The most far-reaching prediction made by Linde was related to what is now called the theory of inflationary multiverse, or string theory landscape. In 1982-1983, Steinhardt and Alexander Vilenkin realized that exponential expansion in the new inflation scenario, once it begins, continues without end in some parts of the universe. On the basis of this scenario, Linde proposed a model of a self-reproducing inflationary universe consisting of different parts; these parts are exponentially uniform, because of inflation. Therefore, for all practical purposes each of these parts looks like a separate mini-universe, or pocket universe, independent of what happens in other parts of the universe.
Inhabitants of each of these parts might think that the universe everywhere looks the same, masses of elementary particles, as well as the laws of their interactions, must be the same all over the world. However, in the contex
Willy Fischler is a theoretical physicist. He is the Jane and Roland Blumberg Centennial Professor of Physics at the University of Texas at Austin, where he is affiliated with the Weinberg theory group, his contributions to physics include: Early computation of the force between heavy quarks. The invisible axion, as a solution to the strong CP problem; the cosmological effects of the invisible axion and its role as a candidate for dark matter. Pioneering work on the use of supersymmetry to solve outstanding problems in the standard model of particle physics; the first formulation of what became known as the "moduli problem in cosmology". The Fischler-Susskind mechanism in string theory; the original formulation of the holographic entropy bound in the context of cosmology. The discovery of M theory, or BFSS Matrix Theory. M theory is an example of a gauge/gravity duality. Black Hole production in colliders, he is a Licensed Paramedic with Marble Falls Area EMS and was a volunteer EMT with the Westlake Fire Department.
Prof. Fischler's homepage Medic MFAEMS
Bosonic string theory
Bosonic string theory is the original version of string theory, developed in the late 1960s. It is so called. In the 1980s, supersymmetry was discovered in the context of string theory, a new version of string theory called superstring theory became the real focus. Bosonic string theory remains a useful model to understand many general features of perturbative string theory, many theoretical difficulties of superstrings can already be found in the context of bosonic strings. Although bosonic string theory has many attractive features, it falls short as a viable physical model in two significant areas. First, it predicts only the existence of bosons. Second, it predicts the existence of a mode of the string with imaginary mass, implying that the theory has an instability to a process known as "tachyon condensation". In addition, bosonic string theory in a general spacetime dimension displays inconsistencies due to the conformal anomaly. But, as was first noticed by Claud Lovelace, in a spacetime of 26 dimensions, the critical dimension for the theory, the anomaly cancels.
This high dimensionality is not a problem for string theory, because it can be formulated in such a way that along the 22 excess dimensions spacetime is folded up to form a small torus or other compact manifold. This would leave only the familiar four dimensions of spacetime visible to low energy experiments; the existence of a critical dimension where the anomaly cancels is a general feature of all string theories. There are four possible bosonic string theories, depending on whether open strings are allowed and whether strings have a specified orientation. Recall that a theory of open strings must include closed strings. A specific orientation of the string means that only interaction corresponding to an orientable worldsheet are allowed. A sketch of the spectra of the four possible theories is as follows: Note that all four theories have a negative energy tachyon and a massless graviton; the rest of this article applies to the closed, oriented theory, corresponding to borderless, orientable worldsheets.
Bosonic string theory can be said to be defined by the path integral quantization of the Polyakov action: I 0 = T 8 π ∫ M d 2 ξ g g m n ∂ m x μ ∂ n x ν G μ ν x μ is the field on the worldsheet describing the embedding of the string in 25+1 spacetime. G is the metric on the target spacetime, taken to be the Minkowski metric in the perturbative theory. Under a Wick rotation, this is brought to a Euclidean metric G μ ν = δ μ ν. M is the worldsheet as a topological manifold parametrized by the ξ coordinates. T is the string tension and related to the Regge slope as T = 1 2 π α ′. I 0 has Weyl invariance. Weyl symmetry is broken upon quantization and therefore this action has to be supplemented with a counterterm, along with a hypothetical purely topological term, proportional to the Euler characteristic: I = I 0 + λ χ + μ 0 2 ∫ M d 2 ξ g The explicit breaking of Weyl invariance by the counterterm can be cancelled away in the critical dimension 26. Physical quantities are constructed from the partition function and N-point function: Z = ∑ h = 0 ∞ ∫ D g m n D X μ N exp ⟨ V i 1 ⋯ V i p ( k
Maxim Lvovich Kontsevich is a Russian and French mathematician. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami, he received the Henri Poincaré Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Fundamental Physics Prize in 2012, the Breakthrough Prize in Mathematics in 2014. He was born into the family of Lev Rafailovich Kontsevich, Soviet orientalist and author of the Kontsevich system. After ranking second in the All-Union Mathematics Olympiads, he attended Moscow State University but left without a degree in 1985 to become a researcher at the Institute for Information Transmission Problems in Moscow. While at the institute he published papers that caught the interest of the Max Planck institute in Bonn and was invited for 3 months. Just before the end of his time there, he attended a 5 day international meeting, the Arbeitstagung, where he sketched a proof of the Witten conjecture to the amazement of Michael Atiyah and other mathematicians and his invitation to the institute was subsequently extended to 3 years.
The next year he finished the proof and worked on various topics on mathematical physics and in 1992 received his Ph. D. at the University of Bonn under Don Bernard Zagier. His thesis outlines a proof of a conjecture by Edward Witten that two quantum gravitational models are equivalent, his work concentrates on geometric aspects of mathematical physics, most notably on knot theory and mirror symmetry. One of his results is a formal deformation quantization, he introduced knot invariants defined by complicated integrals analogous to Feynman integrals. In topological field theory, he introduced the moduli space of stable maps, which may be considered a mathematically rigorous formulation of the Feynman integral for topological string theory. In 1998, he won the Fields Medal for his "contributions to four problems of Geometry". In July 2012, he was an inaugural awardee of the Fundamental Physics Prize, the creation of physicist and internet entrepreneur, Yuri Milner. In 2014, he was awarded Breakthrough Prize in Mathematics.
Kontsevich integral Homological mirror symmetry Motivic integration Kontsevich quantization formula Ring of periods Fields Medal citation at the website of the 2002 International Congress of Mathematicians held in Beijing. Taubes, Clifford Henry "The work of Maxim Kontsevich". In Proceedings of the International Congress of Mathematicians, Vol. I. Doc. Math. Extra Vol. I, 119–126. O'Connor, John J.. "Maxim Kontsevich", MacTutor History of Mathematics archive, University of St Andrews. Maxim Kontsevich at the Mathematics Genealogy Project AMS Profile of Maxim Kontsevich Official Homepage of Maxim Kontsevich Stankova, Zvezdelina. "Pebbling a Chessboard". YouTube: Brady Haran. Retrieved 19 December 2013. Videos of Maxim Konzewitsch in the AV-Portal of the German National Library of Science and Technology
The brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. The brain is located in the head close to the sensory organs for senses such as vision; the brain is the most complex organ in a vertebrate's body. In a human, the cerebral cortex contains 14–16 billion neurons, the estimated number of neurons in the cerebellum is 55–70 billion; each neuron is connected by synapses to several thousand other neurons. These neurons communicate with one another by means of long protoplasmic fibers called axons, which carry trains of signal pulses called action potentials to distant parts of the brain or body targeting specific recipient cells. Physiologically, the function of the brain is to exert centralized control over the other organs of the body; the brain acts on the rest of the body both by generating patterns of muscle activity and by driving the secretion of chemicals called hormones. This centralized control allows coordinated responses to changes in the environment.
Some basic types of responsiveness such as reflexes can be mediated by the spinal cord or peripheral ganglia, but sophisticated purposeful control of behavior based on complex sensory input requires the information integrating capabilities of a centralized brain. The operations of individual brain cells are now understood in considerable detail but the way they cooperate in ensembles of millions is yet to be solved. Recent models in modern neuroscience treat the brain as a biological computer different in mechanism from an electronic computer, but similar in the sense that it acquires information from the surrounding world, stores it, processes it in a variety of ways; this article compares the properties of brains across the entire range of animal species, with the greatest attention to vertebrates. It deals with the human brain insofar; the ways in which the human brain differs from other brains are covered in the human brain article. Several topics that might be covered here are instead covered there because much more can be said about them in a human context.
The most important is brain disease and the effects of brain damage, that are covered in the human brain article. The shape and size of the brain varies between species, identifying common features is difficult. There are a number of principles of brain architecture that apply across a wide range of species; some aspects of brain structure are common to the entire range of animal species. The simplest way to gain information about brain anatomy is by visual inspection, but many more sophisticated techniques have been developed. Brain tissue in its natural state is too soft to work with, but it can be hardened by immersion in alcohol or other fixatives, sliced apart for examination of the interior. Visually, the interior of the brain consists of areas of so-called grey matter, with a dark color, separated by areas of white matter, with a lighter color. Further information can be gained by staining slices of brain tissue with a variety of chemicals that bring out areas where specific types of molecules are present in high concentrations.
It is possible to examine the microstructure of brain tissue using a microscope, to trace the pattern of connections from one brain area to another. The brains of all species are composed of two broad classes of cells: neurons and glial cells. Glial cells come in several types, perform a number of critical functions, including structural support, metabolic support and guidance of development. Neurons, are considered the most important cells in the brain; the property that makes neurons unique is their ability to send signals to specific target cells over long distances. They send these signals by means of an axon, a thin protoplasmic fiber that extends from the cell body and projects with numerous branches, to other areas, sometimes nearby, sometimes in distant parts of the brain or body; the length of an axon can be extraordinary: for example, if a pyramidal cell of the cerebral cortex were magnified so that its cell body became the size of a human body, its axon magnified, would become a cable a few centimeters in diameter, extending more than a kilometer.
These axons transmit signals in the form of electrochemical pulses called action potentials, which last less than a thousandth of a second and travel along the axon at speeds of 1–100 meters per second. Some neurons emit action potentials at rates of 10–100 per second in irregular patterns. Axons transmit signals to other neurons by means of specialized junctions called synapses. A single axon may make as many as several thousand synaptic connections with other cells; when an action potential, traveling along an axon, arrives at a synapse, it causes a chemical called a neurotransmitter to be released. The neurotransmitter binds to receptor molecules in the membrane of the target cell. Synapses are the key functional elements of the brain; the essential function of the brain is cell-to-cell communication, synapses are the points at which communication occurs. The human brain has been estimated to contain 100 trillion synapses; the functions of these synapses are diverse: some are excitatory.
In theoretical physics, T-duality is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories describes strings propagating in an imaginary spacetime shaped like a circle of some radius R, while the other theory describes strings propagating on a spacetime shaped like a circle of radius proportional to 1 / R; the idea of T-duality was first noted by Bala Sathiapalan in an obscure paper in 1987. The two T-dual theories are equivalent in the sense that all observable quantities in one description are identified with quantities in the dual description. For example, momentum in one description takes discrete values and is equal to the number of times the string winds around the circle in the dual description; the idea of T-duality can be extended including superstring theories. The existence of these dualities implies that different superstring theories are physically equivalent; this led to the realization, in the mid-1990s, that all of the five consistent superstring theories are just different limiting cases of a single eleven-dimensional theory called M-theory.
In general, T-duality relates two theories with different spacetime geometries. In this way, T-duality suggests a possible scenario in which the classical notions of geometry break down in a theory of Planck scale physics; the geometric relationships suggested by T-duality are important in pure mathematics. Indeed, according to the SYZ conjecture of Andrew Strominger, Shing-Tung Yau, Eric Zaslow, T-duality is related to another duality called mirror symmetry, which has important applications in a branch of mathematics called enumerative algebraic geometry. T-duality is a particular example of a general notion of duality in physics; the term duality refers to a situation where two different physical systems turn out to be equivalent in a nontrivial way. If two theories are related by a duality, it means that one theory can be transformed in some way so that it ends up looking just like the other theory; the two theories are said to be dual to one another under the transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena.
Like many of the dualities studied in theoretical physics, T-duality was discovered in the context of string theory. In string theory, particles are modeled not as zero-dimensional points but as one-dimensional extended objects called strings; the physics of strings can be studied in various numbers of dimensions. In addition to three familiar dimensions from everyday experience, string theories may include one or more compact dimensions which are curled up into circles. A standard analogy for this is to consider multidimensional object such as a garden hose. If the hose is viewed from a sufficient distance, it appears to have its length. However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Thus, an ant crawling inside it would move in two dimensions; such extra dimensions are important in T-duality, which relates a theory in which strings propagate on a circle of some radius R to a theory in which strings propagate on a circle of radius 1 / R.
In mathematics, the winding number of a curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point. The notion of winding number is important in the mathematical description of T-duality where it is used to measure the winding of strings around compact extra dimensions. For example, the image below shows several examples of curves in the plane, illustrated in red; each curve is assumed to be closed, meaning it has no endpoints, is allowed to intersect itself. Each curve has an orientation given by the arrows in the picture. In each situation, there is a distinguished point in the plane, illustrated in black; the winding number of the curve around this distinguished point is equal to the total number of counterclockwise turns that the curve makes around this point. When counting the total number of turns, counterclockwise turns count as positive, while clockwise turns counts as negative. For example, if the curve first circles the origin four times counterclockwise, circles the origin once clockwise the total winding number of the curve is three.
According to this scheme, a curve that does not travel around the distinguished point at all has winding number zero, while a curve that travels clockwise around the point has negative winding number. Therefore, the winding number of a curve may be any integer; the pictures above show curves with winding numbers between −2 and 3: The simplest theories in which T-duality arises are two-dimensional sigma models with circular target spaces. These are simple quantum field theories that describe propagation of strings in an imaginary spacetime shaped like a circle; the strings can thus be modeled as curves in the plane that are confined to lie in a circle, say of radius R, about the origin. In what follows, the strings are assumed to be closed. Denote this circle by S R 1. One can think of this circle as a copy of the real line with two points identified if they differ by a multiple of the circle's circumference 2 π R, it follows that the state of a string at any given time can be represe
David Jonathan Gross is an American theoretical physicist and string theorist. Along with Frank Wilczek and David Politzer, he was awarded the 2004 Nobel Prize in Physics for their discovery of asymptotic freedom. Gross is the Chancellor’s Chair Professor of Theoretical Physics at the Kavli Institute for Theoretical Physics of the University of California, Santa Barbara, was the KITP director and holder of their Frederick W. Gluck Chair in Theoretical Physics, he is a faculty member in the UC Santa Barbara Physics Department and is affiliated with the Institute for Quantum Studies at Chapman University in California. He is a foreign member of the Chinese Academy of Sciences. Gross was born to a Jewish family in Washington, D. C. in February 1941. His parents were Bertram Myron Gross. Gross received his bachelor's degree and master's degree from the Hebrew University of Jerusalem, Israel, in 1962, he received his Ph. D. in physics from the University of California, Berkeley, in 1966, under the supervision of Geoffrey Chew.
He was a Junior Fellow at Harvard University, a Eugene Higgins Professor of Physics at Princeton University until 1997, when he began serving as Princeton's Thomas Jones Professor of Mathematical Physics Emeritus. He has received many honors, including a MacArthur Foundation Fellowship in 1987, the Dirac Medal in 1988 and the Harvey Prize in 2000, he has been a central figure in particle physics and string theory. In 1973, Professor Gross, working with his first graduate student, Frank Wilczek, at Princeton University, discovered asymptotic freedom—the primary feature of non-Abelian gauge theories—led Gross and Wilczek to the formulation of quantum chromodynamics, the theory of the strong nuclear force. Asymptotic freedom is a phenomenon where the nuclear force weakens at short distances, which explains why experiments at high energy can be understood as if nuclear particles are made of non-interacting quarks; the flip side of asymptotic freedom is that the force between quarks grows stronger as one tries to separate them.
Therefore, the closer quarks are to each other, the less the strong interaction is between them. This is the reason. QCD completed the Standard Model, which details the three basic forces of particle physics—the electromagnetic force, the weak force, the strong force. Gross was awarded the 2004 Nobel Prize in Physics, for this discovery, he has made seminal contributions to the theory of Superstrings, a burgeoning enterprise that brings gravity into the quantum framework. With collaborators he originated the "Heterotic String Theory," the prime candidate for a unified theory of all the forces of nature, he continues to do research in this field at a world center of physics. Gross, with Jeffrey A. Harvey, Emil Martinec, Ryan Rohm formulated the theory of the heterotic string; the four were whimsically nicknamed the "Princeton String Quartet."In 2003, Gross was one of 22 Nobel Laureates who signed the Humanist Manifesto. Gross is an atheist. In 2015, Gross signed the Mainau Declaration 2015 on Climate Change on the final day of the 65th Lindau Nobel Laureate Meeting.
The declaration was signed by a total of 76 Nobel Laureates and handed to then-President of the French Republic, François Hollande, as part of the successful COP21 climate summit in Paris. David's first wife was Shulamith, they have two children. His second wife is Jacquelyn Savani, he has a stepdaughter in California. He has three brothers including, Samuel R. Gross, professor of law, Theodore Gross, a playwright. NSF Graduate Fellowship Alfred P. Sloan Foundation Fellow J. J. Sakurai Prize of the American Physical Society MacArthur Foundation Fellowship Prize Dirac Medal, International Center for Theoretical Physics Oscar Klein Medal, Royal Swedish Academy Harvey Prize, Technion-Israel Institute of Technology High Energy and Particle Physics Prize, European Physical Society Grande Médaille d'Or de l'Académie des sciences, France Nobel Prize in Physics Recipient Golden Plate Award, Academy of Achievement San Carlos Boromero Award, University of San Carlos, Philippines Honorary Doctorate in Science, the University of Cambodia Richard E. Prange Prize, University of Maryland Medal of Honor, Joint Institute for Nuclear Research, Russia Nobel citation ArXiv papers Webpage at the Kavli Institute David Gross on INSPIRE-HEP BBC synopsis on the award Interviews