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... of gravity. The motivations for invoking it are mainly quantum-theoretical: an opportunity for a renormalizable theory, a better understanding of black hole entropy and perhaps even a step further along the road to a theory of everything. While there are many quantum-theoretical issues to be dealt w ...
... of gravity. The motivations for invoking it are mainly quantum-theoretical: an opportunity for a renormalizable theory, a better understanding of black hole entropy and perhaps even a step further along the road to a theory of everything. While there are many quantum-theoretical issues to be dealt w ...
pptx - Departamento de Matemáticas
... Murray Gell-Mann and Francis E. Low in 1954 restricted the idea to scale transformations in QED,[2] which are the most physically significant, and focused on asymptotic forms of the photon propagator at high energies. They determined the variation of the electromagnetic coupling in QED, by apprecia ...
... Murray Gell-Mann and Francis E. Low in 1954 restricted the idea to scale transformations in QED,[2] which are the most physically significant, and focused on asymptotic forms of the photon propagator at high energies. They determined the variation of the electromagnetic coupling in QED, by apprecia ...
Field Theory on Curved Noncommutative Spacetimes
... Furthermore, pioneered by Schupp and Solodukhin [23], exact solutions of the NC Einstein equations have been found in [23, 24, 25, 26, 27], providing, in particular, explicit models for NC cosmology and NC black hole physics. For a collection of other approaches towards NC cosmology see [28], and fo ...
... Furthermore, pioneered by Schupp and Solodukhin [23], exact solutions of the NC Einstein equations have been found in [23, 24, 25, 26, 27], providing, in particular, explicit models for NC cosmology and NC black hole physics. For a collection of other approaches towards NC cosmology see [28], and fo ...
Continuous Quantum Phase Transitions
... absolute zero of temperature, where crossing the phase boundary means that the quantum ground state of the system changes in some fundamental way. This is accomplished by changing not the temperature, but some parameter in the Hamiltonian of the system. This parameter might be the charging energy in ...
... absolute zero of temperature, where crossing the phase boundary means that the quantum ground state of the system changes in some fundamental way. This is accomplished by changing not the temperature, but some parameter in the Hamiltonian of the system. This parameter might be the charging energy in ...
Quantum field theory and the Jones polynomial
... As in Dirac's famous work on magnetic monopoles, consistency of quantum field theory does not quite require the single-valuedness of 5O, but only of exp (i 5 °). For this purpose, it is necessary and sufficient that the "constant" in (1.4) should be an integral multiple of 2m This gives a quantizati ...
... As in Dirac's famous work on magnetic monopoles, consistency of quantum field theory does not quite require the single-valuedness of 5O, but only of exp (i 5 °). For this purpose, it is necessary and sufficient that the "constant" in (1.4) should be an integral multiple of 2m This gives a quantizati ...
A review of E infinity theory and the mass spectrum of high energy
... 2.4. The string connection and KAM theorem Having mentioned string theory, we should mention that in string theory particles are perceived as highly localised vibration of Planck length strings, so that strictly speaking, within string theory there is no essential difference between a resonance parti ...
... 2.4. The string connection and KAM theorem Having mentioned string theory, we should mention that in string theory particles are perceived as highly localised vibration of Planck length strings, so that strictly speaking, within string theory there is no essential difference between a resonance parti ...
Against Field Interpretations of Quantum Field Theory - Philsci
... Textbooks sometimes note in passing that a free QFT can be generated from a singleparticle Hilbert space H in two ways – second quantization and field quantization – and that the resulting theories are equivalent. As we shall see, this notion can be given a rigorous justification. The result of seco ...
... Textbooks sometimes note in passing that a free QFT can be generated from a singleparticle Hilbert space H in two ways – second quantization and field quantization – and that the resulting theories are equivalent. As we shall see, this notion can be given a rigorous justification. The result of seco ...
Quantum Field Theory and Representation Theory
... Want to consider a different class of example, much closer to what Weyl was studying in 1925. Consider an infinitely massive particle. It can be a non-trivial projective representation of the spatial rotation group SO(3), equivalently a true representation of the spin double-cover Spin(3) = SU (2). ...
... Want to consider a different class of example, much closer to what Weyl was studying in 1925. Consider an infinitely massive particle. It can be a non-trivial projective representation of the spatial rotation group SO(3), equivalently a true representation of the spin double-cover Spin(3) = SU (2). ...
Flipped SU(5) - cosmology - Arizona State University
... Our Primary Tool of Analysis Our primary numerical tools are the programs SUSPECT (Djouadi, Kneur, Moultaka), and micrOMEGAs (Belanger, Boudjema, Pukhov, Semenov), each customized for flipped unification with vectorlike fields by James Maxin • Minimization of the scalar Higgs potential with respect ...
... Our Primary Tool of Analysis Our primary numerical tools are the programs SUSPECT (Djouadi, Kneur, Moultaka), and micrOMEGAs (Belanger, Boudjema, Pukhov, Semenov), each customized for flipped unification with vectorlike fields by James Maxin • Minimization of the scalar Higgs potential with respect ...
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.