In gauge theory with SU2 symmetry, the Slavnov-Taylor identities imply that the counter-term of the mass renormalization vanishes.[6, 7] Nevertheless, the space-time gauge identities in Yang-Mills gravity do not have the exact analog.
Space-time translational gauge identities in Abelian Yang-Mills gravity
Moreover, the BRST-gauge-ﬁxed Hamiltonian is strongly invariant under BRST transformations, which is a rather counter-intuitive property for an ob ject that has been gauge-ﬁxed.
Symmetry Doubling: Doubly General Relativity
However, we only encounter power-law divergences, and the counterterms used to subtract those divergences are completely ﬁxed by demanding that the continuum theory is conformally invariant (in general these counter-terms are not gauge-invariant or Lorentz-invariant).
Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
Notice the gauge ﬁxing terms have no counter terms themselves.
A Kaluza-Klein Model with Spontaneous Symmetry Breaking: Light-Particle Effective Action and its Compactification Scale Dependence
Since the divergences in the symmetric phase can be consistently subtracted, the equality of the counter terms between phases implies that the divergences in the broken phase, with it’s massive gauge boson, can also be consistently subtracted.
A Kaluza-Klein Model with Spontaneous Symmetry Breaking: Light-Particle Effective Action and its Compactification Scale Dependence
Introducing these new counter terms will do violence to the original 5-d gauge and Lorentz invariance since they require us to separate ¯A5 from the rest of the components of the gauge ﬁeld, destroying covariance.
A Kaluza-Klein Model with Spontaneous Symmetry Breaking: Light-Particle Effective Action and its Compactification Scale Dependence
For now we will ignore issues of 5-d gauge and Lorentz invariance and accept that these must be violated in order to make the theory ﬁnite (Lorentz violating counter terms could be sourced by D-brane localized interactions).
A Kaluza-Klein Model with Spontaneous Symmetry Breaking: Light-Particle Effective Action and its Compactification Scale Dependence
Additionally, one-loop corrections have generated a divergent A4 5 term that also needs to be subtracted by a new counter term that does not respect 5-d gauge invariance.
A Kaluza-Klein Model with Spontaneous Symmetry Breaking: Light-Particle Effective Action and its Compactification Scale Dependence
Feynman diagrams, divergences, (dimensional) regularization, counter-terms and the Feynman gauge appeared.
Analytic approximations, perturbation methods, and their applications
Following FS’technic (see next section) however, one can introduce the local counter term Λ(R, L; g ), (g (z , ¯z) ∈ G) so that the gauge variation of Λ cancels the non invariance of WR (R).
The Quantization of Anomalous Gauge Field Theory and BRST-invariant Models of Two Dimensional Quantum Gravity
A and c are the classical counter parts of the gauge ﬁelds A and ghost c, while {Φi} are the classical ﬁelds for the matter X and newly introduced ﬁeld g ; K, Ki and L are the usual external sources for the gauge variations ˆδA, ˆδΦi and δc respectively).
The Quantization of Anomalous Gauge Field Theory and BRST-invariant Models of Two Dimensional Quantum Gravity
A0 and F0 are the two dimensional counter part of the generalized classical gauge ﬁeld and curvature.
Non-String Pursuit towards Unified Model on the Lattice
It should be noted that the counter terms of the gluon self-interaction vertices and the ghost-sector are ﬁxed by Z1 , Z2 and Z3 through gauge invariance.
Automated Evaluation of One-Loop Six-Point Processes for the LHC
These boundary counter-terms are absent in fewer than three dimensions, as they are for Yang-Mills theory in four dimensions due to gauge invariance.
Finite VEVs from a Large Distance Vacuum Wave Functional
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