scholarly journals Feynman Gauge on the Lattice: New Results and Perspectives

2011 ◽  
Author(s):  
Attilio Cucchieri ◽  
Tereza Mendes ◽  
Gilberto M. Nakamura ◽  
Elton M. S. Santos
Keyword(s):  
Feynman Gauge

Two-loop renormalization of Feynman gauge QED

2001 ◽  
Vol 63 (12) ◽  
Author(s):  
Gregory S. Adkins ◽  
Richard N. Fell ◽  
J. Sapirstein
Keyword(s):  
Feynman Gauge

scholarly journals Mass spectra of heavy pseudoscalars using instantaneous Bethe–Salpeter equation with different kernels

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Wei Li ◽  
Ying-Long Wang ◽  
Tai-Fu Feng ◽  
Guo-Li Wang
Keyword(s):  
Mass Spectra ◽  
Scalar Potential ◽  
Landau Gauge ◽  
Mass Splitting ◽  
Coulomb Gauge ◽  
Exchange Vector ◽  
Feynman Gauge ◽  
Vector Potentials ◽  
Time Component ◽  
Linear Scalar

Abstract We solved the instantaneous Bethe–Salpeter equation for heavy pseudoscalars in different kernels, where the kernels are obtained using linear scalar potential plus one gluon exchange vector potentials in Feynman gauge, Landau gauge, Coulomb gauge and time-component Coulomb gauge. Since we cannot give a complete QCD-based calculation, the results are gauge dependent. We compared the obtained mass spectra of heavy pseudoscalars between different kernels, found that using the same parameters we obtain the smallest mass splitting in time-component Coulomb gauge, the similar largest mass splitting in Feynman and Coulomb gauges, middle size splitting in Landau gauge.

scholarly journals Electroweak fermion triangle loop contributions to the muon anomalous magnetic moment revisited

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Ken Sasaki
Keyword(s):  
Magnetic Moment ◽  
Top Quark ◽  
Anomalous Magnetic Moment ◽  
Ward Identity ◽  
Axial Vector ◽  
Goldstone Boson ◽  
Muon Anomalous Magnetic Moment ◽  
Feynman Gauge ◽  
Unitary Gauge ◽  
The One

Abstract The contribution to the muon anomalous magnetic moment from the fermion triangle loop diagrams connected to the muon line by a photon and a $Z$ boson is re-analyzed in both the unitary gauge and the ’t Hooft–Feynman gauge. With use of the anomalous axial-vector Ward identity, it is shown that the calculation in the unitary gauge exactly coincides with the one in the ’t Hooft–Feynman gauge. The part which arises from the ordinary axial-vector Ward identity corresponds to the contribution of the neutral Goldstone boson. For the top-quark contribution, the one-parameter integral form is obtained up to the order of $m_\mu^2/m_Z^2$. The results are compared with those obtained by the asymptotic expansion method.

Bound state QED effects from the Schrödinger equation

1992 ◽  
Vol 70 (8) ◽  
pp. 670-682 ◽  
Author(s):  
Tao Zhang ◽  
Lixin Xiao ◽  
Roman Koniuk
Keyword(s):  
Integral Equation ◽  
Scattering Amplitudes ◽  
Principal Quantum Number ◽  
Bound State ◽  
Renormalization Scheme ◽  
Dirac Particles ◽  
Feynman Gauge ◽  
The One ◽  
Qed Effects ◽  
Bound State Qed

We present a new relativistic bound-state formalism for two interacting Fermi–Dirac particles. The kernel of the integral equation for the bound-state system is generated by summing Feynman scattering amplitudes and multiplying by a bound-state amplitude. The method is illustrated through calculations of the hyperfine and fine splittings of positronium up to order α5. Our calculations of the one-loop contributions are carried out in the explicitly covariant Feynman gauge. We also present new results for the hyperfine and fine splittings in positronium to order α5 for arbitrary principal quantum number n, which are easily obtained owing to the virtue of conceptual and calculational simplicity of our formalism. In addition, we present the one-loop renormalization scheme in our formalism.

Boundary conditions, gauge fixing ambiguities and exact expectation values in U(1) lattice gauge theory

2016 ◽  
Vol 31 (08) ◽  
pp. 1650035
Author(s):  
Carlos Pinto
Keyword(s):  
Gauge Theory ◽  
Boundary Conditions ◽  
Weak Coupling ◽  
Lattice Gauge Theory ◽  
Exact Results ◽  
Feynman Gauge ◽  
Lattice Gauge ◽  
Coupling Approximation ◽  
Gauge Fixing ◽  
Weak Coupling Approximation

We analyze the interplay between gauge fixing and boundary conditions in two-dimensional U(1) lattice gauge theory. We show on the basis of a general argument that periodic boundary conditions result in an ill-defined weak coupling approximation but that the approximation can be made well-defined if the boundaries are fixed to zero. We confirm this result in the particular case of the Feynman gauge. We show that the zero momentum mode divergence in the propagator that appears in the Feynman gauge vanishes when the weak coupling approximation is well-defined. In addition we obtain exact results (for arbitrary coupling), including finite size corrections, for the partition function and for general one-point and two-point functions in the axial gauge under both periodic and zero boundary conditions and confirm these results numerically. The dependence of these objects on both lattice size and coupling constant is investigated using specific examples. These exact results may provide insight into similar gauge fixing issues in more complex models.

Inclusive hadron-hadron scattering in the Feynman gauge

1985 ◽  
Vol 254 ◽  
pp. 425-440 ◽  
Author(s):  
J.M.F. Labastida ◽  
George Sterman
Keyword(s):  
Feynman Gauge

scholarly journals 1+1 Dimensional Yang-Mills Theories in Light-Cone Gauge

1997 ◽  
Vol 12 (06) ◽  
pp. 1075-1090 ◽  
Author(s):  
A. Bassetto ◽  
G. Nardelli
Keyword(s):  
Integral Equation ◽  
Light Cone ◽  
Wilson Loop ◽  
Bound State ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Feynman Gauge ◽  
Large N

In 1+1 dimensions two different formulations exist of SU(N) Yang Mills theories in light-cone gauge; only one of them gives results which comply with the ones obtained in Feynman gauge. Moreover the theory, when considered 1+(D-1) dimensions, looks discontinuous in the limit D = 2. All those features are proven in Wilson loop calculations as well as in the study of the [Formula: see text] bound state integral equation in the large N limit.

scholarly journals Using Covariant Polarisation Sums in QCD

2022 ◽  
Vol 137 (1) ◽  
Author(s):  
M. Kachelrieß ◽  
M. N. Malmquist
Keyword(s):  
Gauge Boson ◽  
Ward Identity ◽  
Gauge Theories ◽  
Feynman Rule ◽  
Optical Theorem ◽  
Gauge Bosons ◽  
Abelian Gauge ◽  
Feynman Gauge ◽  
Cross Terms ◽  
External Gauge

AbstractCovariant gauges lead to spurious, non-physical polarisation states of gauge bosons. In QED, the use of the Feynman gauge, $$\sum _{\lambda } \varepsilon _\mu ^{(\lambda )}\varepsilon _\nu ^{(\lambda )*} = -\eta _{\mu \nu }$$ ∑ λ ε μ ( λ ) ε ν ( λ ) ∗ = - η μ ν , is justified by the Ward identity which ensures that the contributions of non-physical polarisation states cancel in physical observables. In contrast, the same replacement can be applied only to a single external gauge boson in squared amplitudes of non-abelian gauge theories like QCD. In general, the use of this replacement requires to include external Faddeev–Popov ghosts. We present a pedagogical derivation of these ghost contributions applying the optical theorem and the Cutkosky cutting rules. We find that the resulting cross terms $$\mathcal {A}(c_1,\bar{c}_1;\ldots )\mathcal {A}(\bar{c}_1,c_1;\ldots )^*$$ A ( c 1 , c ¯ 1 ; … ) A ( c ¯ 1 , c 1 ; … ) ∗ between ghost amplitudes cannot be transformed into $$(-1)^{n/2}|\mathcal {A}(c_1,\bar{c}_1;\ldots )|^2$$ ( - 1 ) n / 2 | A ( c 1 , c ¯ 1 ; … ) | 2 in the case of more than two ghosts. Thus the Feynman rule stated in the literature holds only for two external ghosts, while it is in general incorrect.

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