
Recent progress in the theory of Anderson localization
... Super spin chain (D.H. Lee, ….) WZNW model (Zirnbauer, Tsvelik et al.,…) (2) Quantum Hall plateau transitions (class C) equivalent to classical percolation (Gruzberg, Ludwig, Read 1999) (3) Symplectic class (spin-orbit scattering) ...
... Super spin chain (D.H. Lee, ….) WZNW model (Zirnbauer, Tsvelik et al.,…) (2) Quantum Hall plateau transitions (class C) equivalent to classical percolation (Gruzberg, Ludwig, Read 1999) (3) Symplectic class (spin-orbit scattering) ...
Document
... dimensions mass raise to power negative dimensions. Coupling constant is multiplied by factor having dimension mass raise to power positive dimensions so that scattering amplitude is dimensionless. This quatitiy will be and When we take theory will Not remain renormalizble. Theory should not have co ...
... dimensions mass raise to power negative dimensions. Coupling constant is multiplied by factor having dimension mass raise to power positive dimensions so that scattering amplitude is dimensionless. This quatitiy will be and When we take theory will Not remain renormalizble. Theory should not have co ...
Introduction to Effective Field Theory
... interactions. 2. The interactions are nonlocal. Replace the nonlocal interactions to local interactions so that the effective theory becomes valid. 3. This modifies the high-energy behavior of the theory. 4. Matching: The physics should be the same at the boundary. (e. g., coupling constant) ...
... interactions. 2. The interactions are nonlocal. Replace the nonlocal interactions to local interactions so that the effective theory becomes valid. 3. This modifies the high-energy behavior of the theory. 4. Matching: The physics should be the same at the boundary. (e. g., coupling constant) ...
Mathematical Tripos, Part III, 2009-2010
... Scaling Limit of the Long-range Contact Process Sorting Networks and the Exclusion Process Birational Geometry in Positive Characteristic Cliques of Primes in Noetherian Rings Braid Groups Groups of Piecewise Linear Homeomorphisms of the Real Line Localization in Relativistic Quantum Theories Decohe ...
... Scaling Limit of the Long-range Contact Process Sorting Networks and the Exclusion Process Birational Geometry in Positive Characteristic Cliques of Primes in Noetherian Rings Braid Groups Groups of Piecewise Linear Homeomorphisms of the Real Line Localization in Relativistic Quantum Theories Decohe ...
Canonical quantization of scalar fields
... and let’s find the equation of motion, Euler-Lagrange equation: ...
... and let’s find the equation of motion, Euler-Lagrange equation: ...
Syllabus : Advanced Quantum Mechanics (Prof
... description of electrons and positrons together and their canonical quantization -- with nonrelativistic approximations being derived. An explicitly covariant description of the S-matrix in terms of Feynman’s diagrams is presented in the latter part of the course and is used to give a short introduc ...
... description of electrons and positrons together and their canonical quantization -- with nonrelativistic approximations being derived. An explicitly covariant description of the S-matrix in terms of Feynman’s diagrams is presented in the latter part of the course and is used to give a short introduc ...
Marvin_Weinstein
... Coupling constant renormalization isn’t required, just a choice of coupling constant. Question: What do we hold fixed ? My choice is the energy of the zero momentum two-particle state. This immediately shows why this theory is trivial in four dimensions. ...
... Coupling constant renormalization isn’t required, just a choice of coupling constant. Question: What do we hold fixed ? My choice is the energy of the zero momentum two-particle state. This immediately shows why this theory is trivial in four dimensions. ...
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.