Musical Modulation by Symmetries
... • Using the model of musical modulation by symmetries developed by Mazzola and Muzzulini an analogy is made to modern physics, where symmetries are used to explain forces of transition. • This modulation model provides direct modulations between all tonalities in C12 in 12 tempered tuning, and the r ...
... • Using the model of musical modulation by symmetries developed by Mazzola and Muzzulini an analogy is made to modern physics, where symmetries are used to explain forces of transition. • This modulation model provides direct modulations between all tonalities in C12 in 12 tempered tuning, and the r ...
Infrared and ultraviolet cutoffs of quantum field theory
... to have a modification of Lorentz transformations compatible with the presence of an observer-independent scale of length has been only recently initiated to be explored [13]. In order for the dispersion relation Eq. (5) to be compatible with the very stringent limits on CPT violation [14] it is ne ...
... to have a modification of Lorentz transformations compatible with the presence of an observer-independent scale of length has been only recently initiated to be explored [13]. In order for the dispersion relation Eq. (5) to be compatible with the very stringent limits on CPT violation [14] it is ne ...
Numerical Renormalization Group Study of Random Transverse
... quantum phase transition is much stronger than on classical systems at temperature driven phase transitions. As first observed by McCoy 1) in a somewhat disguised version of a random transverse Ising chain, non-conventional scaling and off-critical singularities that lead to divergent susceptibilities ...
... quantum phase transition is much stronger than on classical systems at temperature driven phase transitions. As first observed by McCoy 1) in a somewhat disguised version of a random transverse Ising chain, non-conventional scaling and off-critical singularities that lead to divergent susceptibilities ...
3. Liquid crystals
... Definition of orientational order parameter should be one in ordered phase and zero in isotropic phase only polar angle β relevant → use a function of cos(β) nematic phase: β and π-β are equally likely → use a function of cos 2(β) average of cos 2(β) for isotropic distribution is 1/3 ...
... Definition of orientational order parameter should be one in ordered phase and zero in isotropic phase only polar angle β relevant → use a function of cos(β) nematic phase: β and π-β are equally likely → use a function of cos 2(β) average of cos 2(β) for isotropic distribution is 1/3 ...
Cosmological Singularities in String Theory
... Since SYM is strongly coupled, you produce a complicated excited state involving all N2 degrees of freedom. Locality probably breaks down: Away from the singularity, locality can be measured by scalar eigenvalues. Near the singularity, all of the eigenvalues interact strongly with off-diagonal mode ...
... Since SYM is strongly coupled, you produce a complicated excited state involving all N2 degrees of freedom. Locality probably breaks down: Away from the singularity, locality can be measured by scalar eigenvalues. Near the singularity, all of the eigenvalues interact strongly with off-diagonal mode ...
Transport through interacting quantum wires and nanotubes
... QGL action, coefficients from full model ...
... QGL action, coefficients from full model ...
Supersymmetry as a probe of the topology of manifolds
... weak coupling limit of N=2 supersymmetric Yang-Mills. Seiberg and Witten’s result implied that we could also study the theory in its strong coupling limit too[8]. It turns out that this theory is a lot simpler because one ends up dealing with abelian gauge fields rather than something non-abelian li ...
... weak coupling limit of N=2 supersymmetric Yang-Mills. Seiberg and Witten’s result implied that we could also study the theory in its strong coupling limit too[8]. It turns out that this theory is a lot simpler because one ends up dealing with abelian gauge fields rather than something non-abelian li ...
Continuous Matrix Product States for Quantum Fields
... be adopted to describe quantum field theories. We will define a new family of states that we call continuous MPS (CMPS) that describe field theories in 1 spatial dimension. We will also show that CMPS can be understood as the continuous limit of standard MPS. Those CMPS can be used as variational st ...
... be adopted to describe quantum field theories. We will define a new family of states that we call continuous MPS (CMPS) that describe field theories in 1 spatial dimension. We will also show that CMPS can be understood as the continuous limit of standard MPS. Those CMPS can be used as variational st ...
GeoSym-QFT
... geometry) and groups (quantum groups). Several problems in renormalization theory can be studied using algebraic methods, which also allow us to consider geometric aspects of non-perturbative Yang-Mills theory. A variety of quantization schemes as well as tools from statistical field theory applied ...
... geometry) and groups (quantum groups). Several problems in renormalization theory can be studied using algebraic methods, which also allow us to consider geometric aspects of non-perturbative Yang-Mills theory. A variety of quantization schemes as well as tools from statistical field theory applied ...
quantum field theory, effective potentials and determinants of elliptic
... of more than one Higgs fields, known as extended Higgs sectors such as the minimal supersymmetric Standard Model (MSSM). The Standard Model can be thought of as a limit to such theories with limits obtained by supersymmetry breaking of which there are many ways, and even more with introduction of D- ...
... of more than one Higgs fields, known as extended Higgs sectors such as the minimal supersymmetric Standard Model (MSSM). The Standard Model can be thought of as a limit to such theories with limits obtained by supersymmetry breaking of which there are many ways, and even more with introduction of D- ...
1821 Navier "Navier-Stokes equations" for an
... analysis, PDE and math physics; Probability theory Number Theory: 1823-24 Fermat's last theorem for the case n=5, brought immediate fame, (Fermat proved for n=4 and Euler for n=3), in 1825 he lectured at the French Acad. of Sci. on his proof, later proved for n=14. 1827-28 biquadratic reciprocity la ...
... analysis, PDE and math physics; Probability theory Number Theory: 1823-24 Fermat's last theorem for the case n=5, brought immediate fame, (Fermat proved for n=4 and Euler for n=3), in 1825 he lectured at the French Acad. of Sci. on his proof, later proved for n=14. 1827-28 biquadratic reciprocity la ...
Introduction to Renormalization Group Alex Kovner Valparaiso, December 12-14, 2013
... Introduction to Renormalization Group December ...
... Introduction to Renormalization Group December ...
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.