Effective Field Theory
... low-energy physics, where low is defined with respect to some energy scale
Λ. They only take explicitly into account the relevant degrees of freedom,
i.e. those states with m ≪ Λ, while the heavier excitations with M ≫ Λ
are integrated out from the action. One gets in this way a string of nonrenorma ...
Gravitational Lensing with a Large Deflection Angle as a Probe of
... black hole to loop around it several times before reaching the observer. We move on to discuss recent
developments in the study of ``braneworld" models which present an interesting framework for the effect of
extra dimensions on gravity. We also discuss several potential black hole metrics in the Ra ...
Renormalization group and the Planck scale
... background ﬁeld formalism is used by adding a non-propagating background ﬁeld
ḡmn [21,30,32–34]. This way, the extended effective action Gk [gmn , ḡmn ] becomes
gauge-invariant under the combined symmetry transformations of the physical
and the background ﬁeld. A second beneﬁt of this is that the ...
a 1 - SMU Physics
... Theoretical Advances
In QCD a quark's effective mass
depends on its momentum. The
function describing this can be
calculated and is depicted here.
Numerical simulations of lattice
QCD (data, at two different bare
masses) have confirmed model
predictions (solid curves) that the
vast bulk of the const ...
... is the magnetic permeability of free space. As is well known, Equation (1.1) is equivalent to
Coulomb’s law (for the electric fields generated by point charges), Equation (1.2) is equivalent to
the statement that magnetic monopoles do not exist (which implies that magnetic field-lines can
never begi ...
Collected Scientific Papers - SN Bose National Centre for Basic
... implication of strict identity of photons? In what sense and to what extent can we think
of light a s a collection of photons? All these questions were answered a t one stroke by
Bose, who asked us to consider the many-photon states to be counted as states with
equal probability. Photons were thus p ...
Widening the Axion Window via Kinetic and Stückelberg Mixings
... determined by the kinetic terms, Gij . The matrix f αβ encodes
the coupling constants of and possible mixing among the
Uð1Þ gauge symmetries with gauge potential Aα and field
strength Fα . GA denotes the field strength of the strongly
coupled non-Abelian gauge groups that generate instanton
In physics, Kaluza–Klein theory (KK theory) is a unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time. It is considered to be an important precursor to string theory.The five-dimensional theory was developed in three steps. The original hypothesis came from Theodor Kaluza, who sent his results to Einstein in 1919, and published them in 1921. Kaluza's theory was a purely classical extension of general relativity to five dimensions. The 5-dimensional metric has 15 components. Ten components are identified with the 4-dimensional spacetime metric, 4 components with the electromagnetic vector potential, and one component with an unidentified scalar field sometimes called the ""radion"" or the ""dilaton"". Correspondingly, the 5-dimensional Einstein equations yield the 4-dimensional Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field. Kaluza also introduced the hypothesis known as the ""cylinder condition"", that no component of the 5-dimensional metric depends on the fifth dimension. Without this assumption, the field equations of 5-dimensional relativity are enormously more complex. Standard 4-dimensional physics seems to manifest the cylinder condition. Kaluza also set the scalar field equal to a constant, in which case standard general relativity and electrodynamics are recovered identically.In 1926, Oskar Klein gave Kaluza's classical 5-dimensional theory a quantum interpretation, to accord with the then-recent discoveries of Heisenberg and Schrödinger. Klein introduced the hypothesis that the fifth dimension was curled up and microscopic, to explain the cylinder condition. Klein also calculated a scale for the fifth dimension based on the quantum of charge.It wasn't until the 1940s that the classical theory was completed, and the full field equations including the scalar field were obtained by three independent research groups:Thiry, working in France on his dissertation under Lichnerowicz; Jordan, Ludwig, and Müller in Germany, with critical input from Pauli and Fierz; and Scherrer working alone in Switzerland. Jordan's work led to the scalar-tensor theory of Brans & Dicke; Brans and Dicke were apparently unaware of Thiry or Scherrer. The full Kaluza equations under the cylinder condition are quite complex, and most English-language reviews as well as the English translations of Thiry contain some errors. The complete Kaluza equations were recently evaluated using tensor algebra software.