Optical Response in Infinite Dimensions
... • DMFT (IPT) captures both sides: Insulating and Metallic • DMFT clarifies the nature of MIT transition ...
... • DMFT (IPT) captures both sides: Insulating and Metallic • DMFT clarifies the nature of MIT transition ...
Gravity Duals for Nonrelativistic Conformal Field
... coupling. Not many of these are accessible experimentally. However, there are many nonrelativistic conformal field theories which govern physical systems. Such examples arise in condensed matter physics [2], atomic physics [3], and nuclear physics [4]. In the first situation, these are called ‘‘quan ...
... coupling. Not many of these are accessible experimentally. However, there are many nonrelativistic conformal field theories which govern physical systems. Such examples arise in condensed matter physics [2], atomic physics [3], and nuclear physics [4]. In the first situation, these are called ‘‘quan ...
The Quantum Space-Time - Institute for Advanced Study
... • There is great deal of evidence that there exists a full quantum theory, ``string theory’’, describing the quantum mechanics of spacetime. • It passes many physical consistency checks: Lorentz invariance, unitarity, reproduces the low energy effective field theory approximation, etc. • Mathematica ...
... • There is great deal of evidence that there exists a full quantum theory, ``string theory’’, describing the quantum mechanics of spacetime. • It passes many physical consistency checks: Lorentz invariance, unitarity, reproduces the low energy effective field theory approximation, etc. • Mathematica ...
slides - 7th MATHEMATICAL PHYSICS MEETING
... At this stage, the Universe was in a quantum state, which should be described by a wave function (complex valued and depends on some real parameters). But, QC is related to Planck scale phenomena - it is natural to reconsider its foundations. We maintain here the standard point of view that the wave ...
... At this stage, the Universe was in a quantum state, which should be described by a wave function (complex valued and depends on some real parameters). But, QC is related to Planck scale phenomena - it is natural to reconsider its foundations. We maintain here the standard point of view that the wave ...
Quantum field theory and knot invariants
... V : L → Z[t±1/2 ], L 7→ VL (t), defined by the condition V (t) = 1, where denotes the oriented unknot, and the linear skein relations t−1 VL+ (t) − tVL− (t) = (t1/2 − t−1/2 )VL0 (t) for any L ∈ L. Here, L+ , L− , and L0 are three oriented links with diagrams identical to L except at one crossing, ...
... V : L → Z[t±1/2 ], L 7→ VL (t), defined by the condition V (t) = 1, where denotes the oriented unknot, and the linear skein relations t−1 VL+ (t) − tVL− (t) = (t1/2 − t−1/2 )VL0 (t) for any L ∈ L. Here, L+ , L− , and L0 are three oriented links with diagrams identical to L except at one crossing, ...
Note 1
... electrons are not gauge invariant. The reason is that the states used to define the S-matrix have particles at infinity, and gauge transformations acting at infinity are true symmetries. They take one physical state to a di↵erent physical state — unlike local gauge transformations, which map a physi ...
... electrons are not gauge invariant. The reason is that the states used to define the S-matrix have particles at infinity, and gauge transformations acting at infinity are true symmetries. They take one physical state to a di↵erent physical state — unlike local gauge transformations, which map a physi ...
superstring theory: past, present, and future john h. schwarz
... 2. Understand empty space The vacuum energy density, called dark energy, is observed to be about 70% of the total energy of the present Universe. It causes the expansion of the Universe to accelerate. This energy density is only about 10-122 when expressed in Planck units. Anthropic explanation: If ...
... 2. Understand empty space The vacuum energy density, called dark energy, is observed to be about 70% of the total energy of the present Universe. It causes the expansion of the Universe to accelerate. This energy density is only about 10-122 when expressed in Planck units. Anthropic explanation: If ...
kavic_Poster0216
... Observable quantities and physical states must be gauge-invariant as a consequence of Gauss’ law ...
... Observable quantities and physical states must be gauge-invariant as a consequence of Gauss’ law ...
Noncommutative space-time and Dirac constraints - Indico
... As the dispersion relations used by these models are quadratic in while the spatial momentum scale as z the models are in principle renormalizable by power counting arguments at least for z 3 . ...
... As the dispersion relations used by these models are quadratic in while the spatial momentum scale as z the models are in principle renormalizable by power counting arguments at least for z 3 . ...
On matrix theory, graph theory, and finite geometry
... typical problem demands a characterizations of all maps on a certain set of matrices that preserve some function, subset or a relation. If the studied maps are bijective by the assumption, then the characterization of the maps involved is often easier to obtain. In the case of certain preservers of ...
... typical problem demands a characterizations of all maps on a certain set of matrices that preserve some function, subset or a relation. If the studied maps are bijective by the assumption, then the characterization of the maps involved is often easier to obtain. In the case of certain preservers of ...
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.