New Methods in Computational Quantum Field Theory
... • Pure Einstein gravity is finite at one loop • But not at two (Marcus & Sagnotti; van de Ven) ...
... • Pure Einstein gravity is finite at one loop • But not at two (Marcus & Sagnotti; van de Ven) ...
Lecture 4
... Local Gauge Invariance and Physics consequences of local gauge invariance: ★ For QED local gauge invariance implies that the photon is massless. ★ In theories with local gauge invariance a conserved quantum number implies a long range field. ■ e.g. electric and magnetic field ● There are other ...
... Local Gauge Invariance and Physics consequences of local gauge invariance: ★ For QED local gauge invariance implies that the photon is massless. ★ In theories with local gauge invariance a conserved quantum number implies a long range field. ■ e.g. electric and magnetic field ● There are other ...
perturbative expansion of chern-simons theory with non
... three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly “unitary” format. The one loop contributions (which dif ...
... three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly “unitary” format. The one loop contributions (which dif ...
On-Shell Methods in Quantum Field Theory
... • Short-distance matrix elements to 2-jet production at nextto-leading order: tree level + one-loop amplitudes + real emission ...
... • Short-distance matrix elements to 2-jet production at nextto-leading order: tree level + one-loop amplitudes + real emission ...
Quantum gravitational contributions to quantum electrodynamics
... (The parameter v does occur in the term involving the cosmological constant, but this can play no role in charge renormalisation.) To get the result of the standard background-field method, that must also agree with an analysis using Feynman diagrams and normal Feynman rules, we simply set v = 0. Th ...
... (The parameter v does occur in the term involving the cosmological constant, but this can play no role in charge renormalisation.) To get the result of the standard background-field method, that must also agree with an analysis using Feynman diagrams and normal Feynman rules, we simply set v = 0. Th ...
Spontaneous Symmetry Breaking in Non Abelian Gauge Theories
... All that remains is to come up with dynamics for the gauge field alone, the analogue of the Maxwell Lagrangian − 14 (Fµν )2 . It turns out [10] that the key property of the field tensor that generalizes is that −ieFµν = [Dµ , Dν ]. In the non-abelian case have [Dµ , Dν ] = −ig(∂µ Aν − ∂ν Aµ − g 2 [A ...
... All that remains is to come up with dynamics for the gauge field alone, the analogue of the Maxwell Lagrangian − 14 (Fµν )2 . It turns out [10] that the key property of the field tensor that generalizes is that −ieFµν = [Dµ , Dν ]. In the non-abelian case have [Dµ , Dν ] = −ig(∂µ Aν − ∂ν Aµ − g 2 [A ...
canonical quantum electrodynamics in covariant gauges
... quantum generalizations of the classical Lorentz gauge . The quantization is carried out by mean s of a Lagrange multiplier field. It is shown that there exist generators for four-dimensional translations and rotations in every gauge . A peculiar aspect is that the scalar and longitudinal photon s a ...
... quantum generalizations of the classical Lorentz gauge . The quantization is carried out by mean s of a Lagrange multiplier field. It is shown that there exist generators for four-dimensional translations and rotations in every gauge . A peculiar aspect is that the scalar and longitudinal photon s a ...
Lecture 5 Motion of a charged particle in a magnetic field
... qi ≡ xi = (x1 , x2 , x3 ) and q̇i ≡ vi = (ẋ1 , ẋ2 , ẋ3 ) N.B. form of Lagrangian more natural in relativistic formulation: −qv µ Aµ = −qϕ + qv · A where v µ = (c, v) and Aµ = (ϕ/c, A) Canonical momentum: pi = ∂ẋi L = mvi + qAi no longer given by mass × velocity – there is an extra term! ...
... qi ≡ xi = (x1 , x2 , x3 ) and q̇i ≡ vi = (ẋ1 , ẋ2 , ẋ3 ) N.B. form of Lagrangian more natural in relativistic formulation: −qv µ Aµ = −qϕ + qv · A where v µ = (c, v) and Aµ = (ϕ/c, A) Canonical momentum: pi = ∂ẋi L = mvi + qAi no longer given by mass × velocity – there is an extra term! ...
The Family Problem: Extension of Standard Model with a Loosely
... the eight components of the Higgs triplets are absorbed by the eight gauge fields through the “family” Higgs mechanism via spontaneous symmetry breaking, while the remaining four become massive Higgs particles. (In the previous application, it was referred to as “colored Higgs Mechanism”[1].) ...
... the eight components of the Higgs triplets are absorbed by the eight gauge fields through the “family” Higgs mechanism via spontaneous symmetry breaking, while the remaining four become massive Higgs particles. (In the previous application, it was referred to as “colored Higgs Mechanism”[1].) ...
8. Quantum field theory on the lattice
... The Wilson loops become exponentially small (∼ e−σRT ) as the size increases. However, the statistical noise is ∼ constant in magnitude independent of loop size! Thus, we need to increase the number of measurements exponentially as the loop size increases. ...
... The Wilson loops become exponentially small (∼ e−σRT ) as the size increases. However, the statistical noise is ∼ constant in magnitude independent of loop size! Thus, we need to increase the number of measurements exponentially as the loop size increases. ...
Coupling Charged Particles to the Electromagnetic Field
... In this light, one can understand the Dirac quantization condition for electric charge. We have seen that if monopoles exist, they are described by singular field configurations. This singularity is seemingly a gauge artifact. It can be chosen, for example, to lie in different directions by making ...
... In this light, one can understand the Dirac quantization condition for electric charge. We have seen that if monopoles exist, they are described by singular field configurations. This singularity is seemingly a gauge artifact. It can be chosen, for example, to lie in different directions by making ...
QUANTUM GEOMETRY OF BOSONIC STRINGS
... replacement is necessary, because today gau~e invariance plays the central role in physics. Elementary excitations in gauge theories are formed by the flux lines (closed in the absence of charges) and the time development of these lines forms the world surfaces. All transition amplitude are given by ...
... replacement is necessary, because today gau~e invariance plays the central role in physics. Elementary excitations in gauge theories are formed by the flux lines (closed in the absence of charges) and the time development of these lines forms the world surfaces. All transition amplitude are given by ...
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.