89, 053618 (2014)
... atomic systems tantalizingly close. The cold-atom system may be a better platform for the observation of Majorana fermions because of the lack of disorder and impurity [10,37,41–45], an issue that has led to intensive debates in the condensed-matter community on the zero-bias peak signature of Major ...
... atomic systems tantalizingly close. The cold-atom system may be a better platform for the observation of Majorana fermions because of the lack of disorder and impurity [10,37,41–45], an issue that has led to intensive debates in the condensed-matter community on the zero-bias peak signature of Major ...
The AdS/CFT Correspondence arXiv:1501.00007
... the nature of space and time has popularized the theory to the extent that it would be hard to find a scientific-minded person who has not heard of Einstein’s theory of gravity. Yet, despite its universally recognized elegance, until recently general relativity has been used by a relatively small su ...
... the nature of space and time has popularized the theory to the extent that it would be hard to find a scientific-minded person who has not heard of Einstein’s theory of gravity. Yet, despite its universally recognized elegance, until recently general relativity has been used by a relatively small su ...
9 Quantum Phases and Phase Transitions of Mott
... precisely, they have an even number of S = 1/2 spins per unit cell [13]. In such cases, the spin gap can be understood by adiabatic continuation from the simple limiting case in which the spins form local spin singlets within each unit cell. A simple approach that can be used for a theoretical descr ...
... precisely, they have an even number of S = 1/2 spins per unit cell [13]. In such cases, the spin gap can be understood by adiabatic continuation from the simple limiting case in which the spins form local spin singlets within each unit cell. A simple approach that can be used for a theoretical descr ...
Regents Pathways - Think Through Math
... where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key feat ...
... where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key feat ...
Wu_Y_H
... flat Euclidean 3-space and one dimensional Euclidean time line t, i.e., four dimensional fiber bundle. Each fiber t contains a Euclidean (contravariant) flat metric γ. ...
... flat Euclidean 3-space and one dimensional Euclidean time line t, i.e., four dimensional fiber bundle. Each fiber t contains a Euclidean (contravariant) flat metric γ. ...
Vladimirov A.A., Diakonov D. Diffeomorphism
... lattice vertices, where the ˇeld derivatives are replaced by the ˇnite differences of the ˇelds between neighboring lattice points. In this way, the construction of the diffeomorphism-invariant lattice action is hardly possible. We propose to replace the action over a manifold by a sum over the latt ...
... lattice vertices, where the ˇeld derivatives are replaced by the ˇnite differences of the ˇelds between neighboring lattice points. In this way, the construction of the diffeomorphism-invariant lattice action is hardly possible. We propose to replace the action over a manifold by a sum over the latt ...
Quantization of Relativistic Free Fields
... Gravitational interactions, for example, couple to zero-point energy. The infinity creates a problem when trying to construct quantum field theories in the presence of a classical gravitational field, since the vacuum energy gives rise to an infinite cosmological constant, which can be determined ex ...
... Gravitational interactions, for example, couple to zero-point energy. The infinity creates a problem when trying to construct quantum field theories in the presence of a classical gravitational field, since the vacuum energy gives rise to an infinite cosmological constant, which can be determined ex ...
Haag`s Theorem in Renormalisable Quantum Field Theories
... • First, all approaches to construct quantum field models in a way seen as mathematically sound and rigorous employ methods from operator theory and stochastic analysis, the latter only in the Euclidean case. This is certainly natural given the corresponding heuristically very successful notions use ...
... • First, all approaches to construct quantum field models in a way seen as mathematically sound and rigorous employ methods from operator theory and stochastic analysis, the latter only in the Euclidean case. This is certainly natural given the corresponding heuristically very successful notions use ...
LHC Theory Lecture 1: Calculation of Scattering Cross Sections
... Particles are represented by fields. What is meant by this? → Discuss below! QFT’s are commonly formulated in so-called natural units featuring ~ = c = 1. → Mass, Energy, momentum, inverse time and length scales have the same physical dimension, known as mass dimension: [m] = [E ] = [p] = [t −1 ] = ...
... Particles are represented by fields. What is meant by this? → Discuss below! QFT’s are commonly formulated in so-called natural units featuring ~ = c = 1. → Mass, Energy, momentum, inverse time and length scales have the same physical dimension, known as mass dimension: [m] = [E ] = [p] = [t −1 ] = ...
String Theory - damtp - University of Cambridge
... real world. At low-energies it naturally gives rise to general relativity, gauge theories, scalar fields and chiral fermions. In other words, it contains all the ingredients that make up our universe. It also gives the only presently credible explanation for the value of the cosmological constant al ...
... real world. At low-energies it naturally gives rise to general relativity, gauge theories, scalar fields and chiral fermions. In other words, it contains all the ingredients that make up our universe. It also gives the only presently credible explanation for the value of the cosmological constant al ...
Mathematisches Forschungsinstitut Oberwolfach Subfactors and
... The idea of obtaining a “continuum limit” by letting the number of boundary points on the discs fill out the circle has been around for over 20 years but this paper is the first one to take a concrete, though by no means big enough, step in that direction. Planar algebra is an abstraction of the not ...
... The idea of obtaining a “continuum limit” by letting the number of boundary points on the discs fill out the circle has been around for over 20 years but this paper is the first one to take a concrete, though by no means big enough, step in that direction. Planar algebra is an abstraction of the not ...
XXZ Dao-Xin Yao, Y. L. Loh, and E. W. Carlson Michael Ma
... which correspond to small trimers and large trimers, respectively. Each spin has four nearest neighbors. The unit cell contains a total of nine spins 共six on the a sublattice and three on the b sublattice兲. The space group of the TKL is the same as that of the hexagonal lattice, p6m, in Hermann– Mau ...
... which correspond to small trimers and large trimers, respectively. Each spin has four nearest neighbors. The unit cell contains a total of nine spins 共six on the a sublattice and three on the b sublattice兲. The space group of the TKL is the same as that of the hexagonal lattice, p6m, in Hermann– Mau ...
Scale invariance
In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilatations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity.In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale.In quantum field theory, scale invariance has an interpretation in terms of particle physics. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved.In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical point, fluctuations occur at all length scales, and thus one should look for an explicitly scale-invariant theory to describe the phenomena. Such theories are scale-invariant statistical field theories, and are formally very similar to scale-invariant quantum field theories.Universality is the observation that widely different microscopic systems can display the same behaviour at a phase transition. Thus phase transitions in many different systems may be described by the same underlying scale-invariant theory.In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.