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Ginsparg–Wilson Equation
In lattice field theory, the Ginsparg–Wilson equation generalizes chiral symmetry on the lattice in a way that approaches the continuum formulation in the continuum limit. The class of fermions whose Dirac operators satisfy this equation are known as Ginsparg–Wilson fermions, with notable examples being overlap, domain wall and fixed point fermions. They are a means to avoid the fermion doubling problem, widely used for instance in lattice QCD calculations. The equation was discovered by Paul Ginsparg and Kenneth Wilson in 1982, however it was quickly forgotten about since there were no known solutions. It was only in 1997 and 1998 that the first solutions were found in the form of the overlap and fixed point fermions, at which point the equation entered prominence. Ginsparg–Wilson fermions do not contradict the Nielsen–Ninomiya theorem because they explicitly violate chiral symmetry. More precisely, the continuum chiral symmetry relation D\gamma_5+\gamma_5 D=0 (where D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice Field Theory
In physics, lattice field theory is the study of lattice models of quantum field theory. This involves studying field theory on a space or spacetime that has been discretised onto a lattice. Details Although most lattice field theories are not exactly solvable, they are immensely appealing due to their feasibility for computer simulation, often using Markov chain Monte Carlo methods. One hopes that, by performing simulations on larger and larger lattices, while making the lattice spacing smaller and smaller, one will be able to recover the behavior of the continuum theory as the continuum limit is approached. Just as in all lattice models, numerical simulation provides access to field configurations that are not accessible to perturbation theory, such as solitons. Similarly, non-trivial vacuum states can be identified and examined. The method is particularly appealing for the quantization of a gauge theory using the Wilson action. Most quantization approaches maintain Po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Ginsparg
Paul Henry Ginsparg is an American physicist. He developed the arXiv.org e-print archive. Education He is a graduate of Syosset High School in Syosset, New York, on Long Island. He graduated from Harvard University with a Bachelor of Arts in physics and from Cornell University with a Doctor of Philosophy in theoretical particle physics with a thesis titled ''Aspects of symmetry behavior in quantum field theory''. Career in physics Ginsparg was a junior fellow and taught in the physics department at Harvard University until 1990. The pre-print archive was developed while he was a member of staff of Los Alamos National Laboratory, 1990–2001. Since 2001, Ginsparg has been a professor of Physics and Computing & Information Science at Cornell University. He has published physics papers in the areas of quantum field theory, string theory, conformal field theory, and quantum gravity. He often comments on the changing world of physics in the Information Age. Awards He has bee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zeros And Poles
In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. It is the simplest type of non- removable singularity of such a function (see essential singularity). Technically, a point is a pole of a function if it is a zero of the function and is holomorphic (i.e. complex differentiable) in some neighbourhood of . A function is meromorphic in an open set if for every point of there is a neighborhood of in which at least one of and is holomorphic. If is meromorphic in , then a zero of is a pole of , and a pole of is a zero of . This induces a duality between ''zeros'' and ''poles'', that is fundamental for the study of meromorphic functions. For example, if a function is meromorphic on the whole complex plane plus the point at infinity, then the sum of the multiplicities of its poles equals the sum of the multiplicities of its zeros. Definitions A function of a complex variable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermion Doubling
In lattice field theory, fermion doubling occurs when naively putting fermionic fields on a lattice (group), lattice, resulting in more fermionic states than expected. For the naively discretized Dirac fermions in d Euclidean space, Euclidean dimensions, each fermionic field results in 2^d identical fermion species, referred to as different tastes of the fermion. The fermion doubling problem is intractably linked to chirality (physics), chiral invariance by the Nielsen–Ninomiya theorem. Most strategies used to solve the problem require using modified fermions which reduce to the Dirac fermion only in the continuum limit. Naive fermion discretization For simplicity we will consider a four-dimensional theory of a free fermion, although the fermion doubling problem remains in arbitrary dimensions and even if lattice gauge theory, interactions are included. Lattice field theory is usually carried out in Euclidean spacetime arrived at from Minkowski spacetime after a Wick rotation, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilson Fermion
In lattice field theory, Wilson fermions are a fermion discretization that allows to avoid the fermion doubling problem proposed by Kenneth Wilson in 1974. They are widely used, for instance in lattice QCD calculations. An additional so-called Wilson term : S_W = -a^\sum_\frac\left(\bar\psi_x\psi_+\bar\psi_\psi_-2\bar\psi_x\psi_x\right) is introduced supplementing the naively discretized Dirac action in d-dimensional Euclidean spacetime with lattice spacing a, Dirac fields \psi_x at every lattice point x, and the vectors \hat \mu being unit vectors in the \mu direction. The inverse free fermion propagator in momentum space now reads : D(p) = m + \frac ia\sum_\mu \gamma_\mu\sin\left(p_\mu a\right)+\frac1a\sum_\mu\left(1-\cos\left(p_\mu a\right)\right)\, where the last addend corresponds to the Wilson term again. It modifies the mass m of the doublers to : m+\frac\, where l is the number of momentum components with p_\mu = \pi/a. In the continuum limit a\rightarr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. Chirality and helicity The helicity of a particle is positive ("right-handed") if the direction of its spin is the same as the direction of its motion. It is negative ("left-handed") if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards. Mathematically, ''helicity'' is the sign of the projection of the spin vector onto the momentum vector: "left" is negative, "right" is positive. The chirality of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nielsen–Ninomiya Theorem
In lattice field theory, the Nielsen–Ninomiya theorem is a no-go theorem about placing chiral fermions on a lattice. In particular, under very general assumptions such as locality, hermiticity, and translational symmetry, any lattice formulation of chiral fermions necessarily leads to fermion doubling, where there are the same number of left-handed and right-handed fermions. It was first proved by Holger Bech Nielsen and Masao Ninomiya in 1981 using two methods, one that relied on homotopy theory and another that relied on differential topology. Another proof provided by Daniel Friedan uses differential geometry. The theorem was also generalized to any regularization scheme of chiral theories. One consequence of the theorem is that the Standard Model cannot be put on a lattice. Common methods for overcoming the fermion doubling problem is to use modified fermion formulations such as staggered fermions, Wilson fermions, or Ginsparg–Wilson fermions, among others. Lattice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kenneth G
Kenneth Geoffrey Oudejans (born Amsterdam, Netherlands ), better known by his stage name Kenneth G, is a Dutch DJ and record producer A record producer or music producer is a music creating project's overall supervisor whose responsibilities can involve a range of creative and technical leadership roles. Typically the job involves hands-on oversight of recording sessions; ensu .... He became known in 2013 with his releases on the Dutch label Hysteria Records before joining Revealed Recordings the following year. Discography Charting singles Singles * 2008: ''Wobble'' lub Generation* 2009: ''Konichiwa Bitches!'' (with Nicky Romero) ade In NL (Spinnin')* 2010: ''Are U Serious'' elekted Music* 2011: ''Tjoppings'' ade In NL (Spinnin')* 2012: ''Bazinga'' ysteria Recs* 2012: ''Wobble'' ig Boss Records* 2013: ''Duckface'' (with Bassjackers) ysteria Recs* 2013: ''Basskikker'' nes To Watch Records (Mixmash)* 2013: ''Stay Weird'' ysteria Recs* 2013: ''Rage-Aholics'' ev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice QCD
Lattice QCD is a well-established non- perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD is recovered. Analytic or perturbative solutions in low-energy QCD are hard or impossible to obtain due to the highly nonlinear nature of the strong force and the large coupling constant at low energies. This formulation of QCD in discrete rather than continuous spacetime naturally introduces a momentum cut-off at the order 1/''a'', where ''a'' is the lattice spacing, which regularizes the theory. As a result, lattice QCD is mathematically well-defined. Most importantly, lattice QCD provides a framework for investigation of non-perturbative phenomena such as confinement and quark–gluon plasma formation, which are intractable by mean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiral Symmetry
A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity transformation. Invariance under parity transformation by a Dirac fermion is called chiral symmetry. Chirality and helicity The helicity of a particle is positive ("right-handed") if the direction of its spin is the same as the direction of its motion. It is negative ("left-handed") if the directions of spin and motion are opposite. So a standard clock, with its spin vector defined by the rotation of its hands, has left-handed helicity if tossed with its face directed forwards. Mathematically, ''helicity'' is the sign of the projection of the spin vector onto the momentum vector: "left" is negative, "right" is positive. The chirality of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermion Doubling
In lattice field theory, fermion doubling occurs when naively putting fermionic fields on a lattice (group), lattice, resulting in more fermionic states than expected. For the naively discretized Dirac fermions in d Euclidean space, Euclidean dimensions, each fermionic field results in 2^d identical fermion species, referred to as different tastes of the fermion. The fermion doubling problem is intractably linked to chirality (physics), chiral invariance by the Nielsen–Ninomiya theorem. Most strategies used to solve the problem require using modified fermions which reduce to the Dirac fermion only in the continuum limit. Naive fermion discretization For simplicity we will consider a four-dimensional theory of a free fermion, although the fermion doubling problem remains in arbitrary dimensions and even if lattice gauge theory, interactions are included. Lattice field theory is usually carried out in Euclidean spacetime arrived at from Minkowski spacetime after a Wick rotation, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fixed Point Fermion
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Fixed may refer to: * ''Fixed'' (EP), EP by Nine Inch Nails * ''Fixed'' (film), an upcoming animated film directed by Genndy Tartakovsky * Fixed (typeface), a collection of monospace bitmap fonts that is distributed with the X Window System * Fixed, subjected to neutering * Fixed point (mathematics), a point that is mapped to itself by the function * Fixed line telephone, landline See also * * * Fix (other) * Fixer (other) * Fixing (other) * Fixture (other) A fixture can refer to: * Test fixture, used to control and automate testing * Light fixture * Plumbing fixture * Fixture (tool), a tool used in manufacturing * Fixture (property law) * A type of sporting event See also * * * Fixed (disambiguat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
