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Tadpole (physics)
In quantum field theory, a tadpole is a one-loop Feynman diagram with one external leg, giving a contribution to a one-point correlation function (i.e., the field's vacuum expectation value). One-loop diagrams with a propagator that connects back to its originating vertex are often also referred as tadpoles. For many massless theories, these graphs vanish in dimensional regularization (by dimensional analysis and the absence of any inherent mass scale in the loop integral). Tadpole corrections are needed if the corresponding external field has a non-zero vacuum expectation value, such as the Higgs field. Tadpole diagrams were first used in the 1960s. An early example was published by Abdus Salam in 1961, though he did not take credit for the name. Physicists Sidney Coleman and Sheldon Glashow Sheldon Lee Glashow (, ; born December 5, 1932) is a Nobel Prize-winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University an ... [...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] |
Feynman Diagram
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory. Frank Wilczek wrote that the calculations that won him the 2004 Nobel Prize in Physics "would have been literally unthinkable without Feynman diagra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation Function (quantum Field Theory)
In quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products of field operators. They are a key object of study in quantum field theory where they can be used to calculate various observables such as S-matrix elements. Definition For a scalar field theory with a single field \phi(x) and a vacuum state , \Omega\rangle at every event (x) in spacetime, the n-point correlation function is the vacuum expectation value of the time-ordered products of n field operators in the Heisenberg picture G_n(x_1,\dots, x_n) = \langle \Omega, T\, \Omega\rangle. Here T\ is the time-ordering operator for which orders the field operators so that earlier time field operators appear to the right of later time field operators. By transforming the fields and states into the interaction picture, this is rewritten as G_n(x_1, \dots, x_n) = \frac, where , 0\rangle is the ground state of the free theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacuum Expectation Value
In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum. The vacuum expectation value of an operator O is usually denoted by \langle O\rangle. One of the most widely used examples of an observable physical effect that results from the vacuum expectation value of an operator is the Casimir effect. This concept is important for working with correlation functions in quantum field theory. It is also important in spontaneous symmetry breaking. Examples are: *The Higgs field has a vacuum expectation value of 246 GeV. This nonzero value underlies the Higgs mechanism of the Standard Model. This value is given by v = 1/\sqrt = 2M_W/g \approx 246.22\, \rm, where ''MW'' is the mass of the W Boson, G_F^0 the reduced Fermi constant, and the weak isospin coupling, in natural units. It is also near the limit of the most massive nuclei, at v = 264.3 Da. *The chiral condensate in quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propagator
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum. In Feynman diagrams, which serve to calculate the rate of collisions in quantum field theory, virtual particles contribute their propagator to the rate of the scattering event described by the respective diagram. These may also be viewed as the inverse of the wave operator appropriate to the particle, and are, therefore, often called ''(causal) Green's functions'' (called "''causal''" to distinguish it from the elliptic Laplacian Green's function). Non-relativistic propagators In non-relativistic quantum mechanics, the propagator gives the probability amplitude for a particle to travel from one spatial point (x') at one time (t') to another spatial point (x) at a later time (t). Consider a system with Hamiltonian . The Green's function (fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensional Regularization
__NOTOC__ In theoretical physics, dimensional regularization is a method introduced by Giambiagi and Bollini as well as – independently and more comprehensively – by 't Hooft and Veltman for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of a complex parameter ''d'', the analytic continuation of the number of spacetime dimensions. Dimensional regularization writes a Feynman integral as an integral depending on the spacetime dimension ''d'' and the squared distances (''x''''i''−''x''''j'')2 of the spacetime points ''x''''i'', ... appearing in it. In Euclidean space, the integral often converges for −Re(''d'') sufficiently large, and can be analytically continued from this region to a meromorphic function defined for all complex ''d''. In general, there will be a pole at the physical value (usually 4) of ''d'', which needs to be canceled by renormalization to obtain physical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensional Analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often easier within the metric or the SI than in others, due to the regular 10-base in all units. ''Commensurable'' physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are expressed in differing units of measure, e.g. yards and metres, pounds (mass) and kilograms, seconds and years. ''Incommensurable'' physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are expressed in, e.g. metres and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Scale
In physics, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot affect each other and are said to decouple. The decoupling of different length scales makes it possible to have a self-consistent theory that only describes the relevant length scales for a given problem. Scientific reductionism says that the physical laws on the shortest length scales can be used to derive the effective description at larger length scales. The idea that one can derive descriptions of physics at different length scales from one another can be quantified with the renormalization group. In quantum mechanics the length scale of a given phenomenon is related to its de Broglie wavelength \ell = \hbar/p where \hbar is the reduced Planck's constant and p is the momentum that is being probed. In relativistic mechanics time an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loop Integral
In quantum field theory and statistical mechanics, loop integrals are the integrals which appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. These integrals are used to determine counterterms, which in turn allow evaluation of the beta function, which encodes the dependence of coupling g for an interaction on an energy scale \mu. One-loop integral Generic formula A generic one-loop integral, for example those appearing in one-loop renormalization of QED or QCD may be written as a linear combination of terms in the form :\int \frac\frac where the q_i are 4-momenta which are linear combinations of the external momenta, and the m_i are masses of interacting particles. This expression uses Euclidean signature. In Lorentzian signature the denominator would instead be a product of expressions of the form (k+q)^2 - m^2 + i\epsilon. Using Feynman parametrization, this can be rewritten as a linear combination of integrals of the fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Higgs Field
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field, one of the fields in particle physics theory. In the Standard Model, the Higgs particle is a massive scalar boson with zero spin, even (positive) parity, no electric charge, and no colour charge, that couples to (interacts with) mass. It is also very unstable, decaying into other particles almost immediately. The Higgs field is a scalar field, with two neutral and two electrically charged components that form a complex doublet of the weak isospin SU(2) symmetry. Its " Mexican hat-shaped" potential leads it to take a nonzero value ''everywhere'' (including otherwise empty space), which breaks the weak isospin symmetry of the electroweak interaction, and via the Higgs mechanism gives mass to many particles. Both the field and the boson are named after physicist Peter Higgs, who in 1964, alo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tadpole
A tadpole is the larval stage in the biological life cycle of an amphibian. Most tadpoles are fully aquatic, though some species of amphibians have tadpoles that are terrestrial. Tadpoles have some fish-like features that may not be found in adult amphibians such as a lateral line, gills and swimming tails. As they undergo metamorphosis, they start to develop functional lungs for breathing air, and the diet of tadpoles changes drastically. A few amphibians, such as some members of the frog family Brevicipitidae, undergo direct development i.e., they do not undergo a free-living larval stage as tadpoles instead emerging from eggs as fully formed "froglet" miniatures of the adult morphology. Some other species hatch into tadpoles underneath the skin of the female adult or are kept in a pouch until after metamorphosis. Having no hard skeletons, it might be expected that tadpole fossils would not exist. However, traces of biofilms have been preserved and fossil tadpoles have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abdus Salam
Mohammad Abdus Salam Salam adopted the forename "Mohammad" in 1974 in response to the anti-Ahmadiyya decrees in Pakistan, similarly he grew his beard. (; ; 29 January 192621 November 1996) was a Punjabi Pakistani theoretical physicist and a Nobel Prize laureate. He shared the 1979 Nobel Prize in Physics with Sheldon Glashow and Steven Weinberg for his contribution to the electroweak unification theory. He was the first Pakistani and the first from an Islamic country to receive a Nobel Prize in science and the second from an Islamic country to receive any Nobel Prize, after Anwar Sadat of Egypt. Salam was scientific advisor to the Ministry of Science and Technology in Pakistan from 1960 to 1974, a position from which he played a major and influential role in the development of the country's science infrastructure. Salam contributed to numerous developments in theoretical and particle physics in Pakistan. He was the founding director of the Space and Upper Atmosphere Researc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
