Symmetry breaking and the deconstruction of mass
... SU(3)-vector bosons, the gluons, the classical theory is invariant under scaling transformations. Namely, if Aμ represents the gluon fields, and Aμ is a classical solution to the equations of motion, then so is the scaled configuration: λA(λx), for any real parameter λ. Again, the quantum structure ...
... SU(3)-vector bosons, the gluons, the classical theory is invariant under scaling transformations. Namely, if Aμ represents the gluon fields, and Aμ is a classical solution to the equations of motion, then so is the scaled configuration: λA(λx), for any real parameter λ. Again, the quantum structure ...
Geometric Aspects of the Standard Model and the Mysteries
... They are described by geometric theories, i.e. Yang-Mills (YM) theories or, in the case of GR, by semi-Riemannian geometry in dimension four. To a large extent, they are classical theories. Matter, i.e. quarks and leptons and composites thereof, a priori, seems to belong to a different kind of physi ...
... They are described by geometric theories, i.e. Yang-Mills (YM) theories or, in the case of GR, by semi-Riemannian geometry in dimension four. To a large extent, they are classical theories. Matter, i.e. quarks and leptons and composites thereof, a priori, seems to belong to a different kind of physi ...
Basics of Lattice Quantum Field Theory∗
... holds where V (l) is a definition of the potential between heavy quarks due to their interaction with the gluons. One confinement criterion is the linear rise ...
... holds where V (l) is a definition of the potential between heavy quarks due to their interaction with the gluons. One confinement criterion is the linear rise ...
Coherent Exciton Dynamics in Semiconductor Superlattices:A Quasi
... • These considerations apply quite generally, e.g. to optical beam AM. Position and orbital AM related through L=rxp. ...
... • These considerations apply quite generally, e.g. to optical beam AM. Position and orbital AM related through L=rxp. ...
Template for scientific report
... for their quantitative treatment. The basic building blocks of QCD are the Green’s (correlation) functions of the fundamental physical degrees of freedom, gluons and quarks, and of the unphysical ghosts. Even though it is well-known that these quantities are not physical, since they depend on the ga ...
... for their quantitative treatment. The basic building blocks of QCD are the Green’s (correlation) functions of the fundamental physical degrees of freedom, gluons and quarks, and of the unphysical ghosts. Even though it is well-known that these quantities are not physical, since they depend on the ga ...
Слайд 1 - I C R A
... topologically non-trivial universe we would be able to construct a gauge-invariant theory. We have no grounds at all to require for a wave function to satisfy the Wheeler − DeWitt equation. At the same time, independently on our notion about gauge invariance or noninvariance of the theory, the wave ...
... topologically non-trivial universe we would be able to construct a gauge-invariant theory. We have no grounds at all to require for a wave function to satisfy the Wheeler − DeWitt equation. At the same time, independently on our notion about gauge invariance or noninvariance of the theory, the wave ...
Introduction to Strings
... Conformal invariance with respect to world sheet metric Reparametrization invariance with respect to world sheet metric ...
... Conformal invariance with respect to world sheet metric Reparametrization invariance with respect to world sheet metric ...
Lorenz or Coulomb
... (the potentials are the basic quantities) instead of the so-called Heaviside-Hertz formulation (the fields are the basic quantities) in order to describe any experimental fact relative to Classical Electromagnetism [5]. The Riemann-Lorenz procedure consists in using the following postulate : “Any ex ...
... (the potentials are the basic quantities) instead of the so-called Heaviside-Hertz formulation (the fields are the basic quantities) in order to describe any experimental fact relative to Classical Electromagnetism [5]. The Riemann-Lorenz procedure consists in using the following postulate : “Any ex ...
`Holography` without gravity: Phases of matter which are
... Note that the theta angle ϑ here is not the same as the θ in the magnetoelectric resonse. It is topological, like CS theory, in that we didn’t need to introduce the metric to integrate the action covariantly. In D = 3 + 1 we need the form degrees to add up 2 + 1 + 1 = 4. We can add analogs of Maxwel ...
... Note that the theta angle ϑ here is not the same as the θ in the magnetoelectric resonse. It is topological, like CS theory, in that we didn’t need to introduce the metric to integrate the action covariantly. In D = 3 + 1 we need the form degrees to add up 2 + 1 + 1 = 4. We can add analogs of Maxwel ...
Some beautiful equations of mathematical physics
... required to renew his/her professional license by retaking the Ph.D. qualifying exams. Second, I do not wish to be held accountable for any precise definition of terms such as mathematical beauty, simplicity, naturalness, etc. I use these terms in a completely subjective way which is a product of th ...
... required to renew his/her professional license by retaking the Ph.D. qualifying exams. Second, I do not wish to be held accountable for any precise definition of terms such as mathematical beauty, simplicity, naturalness, etc. I use these terms in a completely subjective way which is a product of th ...
Gauge fixing
In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom.Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions ""perpendicular"" to them. Hence there is an enormous amount of freedom involved in taking a ""cross section"" representing each physical configuration by a particular detailed configuration (or even a weighted distribution of them). Judicious gauge fixing can simplify calculations immensely, but becomes progressively harder as the physical model becomes more realistic; its application to quantum field theory is fraught with complications related to renormalization, especially when the computation is continued to higher orders. Historically, the search for logically consistent and computationally tractable gauge fixing procedures, and efforts to demonstrate their equivalence in the face of a bewildering variety of technical difficulties, has been a major driver of mathematical physics from the late nineteenth century to the present.