scholarly journals Perturbative Yang–Mills theory without Faddeev–Popov ghost fields

2018 ◽  
Vol 780 ◽  
pp. 418-421 ◽  
Author(s):  
Helmuth Huffel ◽  
Danijel Markovic
Keyword(s):  
Yang Mills ◽  
Popov Ghost

Construction of a translation-invariant U(N) damped noncommutative gauge model

2020 ◽  
Vol 35 (22) ◽  
pp. 2050118
Author(s):  
Ouahiba Toumi ◽  
Smain Kouadik
Keyword(s):  
Covariant Derivative ◽  
Torsion Tensor ◽  
Tree Level ◽  
Dirac Field ◽  
Translation Invariance ◽  
Group Model ◽  
Translation Invariant ◽  
Yang Mills ◽  
Interaction Term ◽  
Popov Ghost

We have built a noncommutative unitary gauge group model preserving translation invariance. It describes the interaction of the Dirac field with the gauge field. The interaction term is expanded as a power series resulting from the introduction of the inverse covariant derivative. The consistency of the model is sustained by the fact that the Ward identity holds at tree level. The pure Yang–Mills action, including the fixing term and the Faddeev–Popov ghost term were constructed. It is striking that the commutator of our covariant derivative contained the torsion tensor, in addition to the field strength from which the Yang–Mills action was built.

Gauge Interactions

2021 ◽  
pp. 273-286
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Quantum Electrodynamics ◽  
Integral Method ◽  
Equations Of Motion ◽  
Internal Symmetry ◽  
Symmetry Groups ◽  
Yang Mills ◽  
Path Integral Method ◽  
Popov Ghost ◽  
Mills Field ◽  
Matter Fields

The principle of gauge symmetry is introduced as a consequence of the invariance of the equations of motion under local transformations. We apply it to Abelian, as well as non-Abelian, internal symmetry groups. We derive in this way the Lagrangian of quantum electrodynamics and that of Yang–Mills theories. We quantise the latter using the path integral method and show the need for unphysical Faddeev–Popov ghost fields. We exhibit the geometric properties of the theory by formulating it on a discrete space-time lattice. We show that matter fields live on lattice sites and gauge fields on oriented lattice links. The Yang–Mills field strength is related to the curvature in field space.

scholarly journals THE MOST GENERAL AND RENORMALIZABLE MAXIMAL ABELIAN GAUGE

2003 ◽  
Vol 18 (31) ◽  
pp. 5733-5756 ◽  
Author(s):  
TORU SHINOHARA ◽  
TAKAHITO IMAI ◽  
KEI-ICHI KONDO
Keyword(s):  
Beta Function ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Diagonal Part ◽  
Gauge Term ◽  
Gauge Fixing ◽  
Popov Ghost ◽  
Independent Parameters ◽  
Energy Physics

We construct the most general gauge fixing and the associated Faddeev–Popov ghost term for the SU(2) Yang–Mills theory, which leaves the global U(1) gauge symmetry intact (i.e. the most general Maximal Abelian gauge). We show that the most general form involves eleven independent gauge parameters. Then we require various symmetries which help to reduce the number of independent parameters for obtaining the simpler form. In the simplest case, the off-diagonal part of the gauge fixing term obtained in this way is identical to the modified maximal Abelian gauge term with two gauge parameters which was proposed in the previous paper from the viewpoint of renormalizability. In this case, moreover, we calculate the beta function, anomalous dimensions of all fields and renormalization group functions of all gauge parameters in perturbation theory to one-loop order. We also discuss the implication of these results to obtain information on low-energy physics of QCD.

scholarly journals Faddeev-Popov Ghost and BRST Symmetry in Yang-Mills Theory

2020 ◽  
Vol 31 (1) ◽  
pp. 30-34
Author(s):  
Edyharto Yanuwar ◽  
Jusak Sali Kosasih
Keyword(s):  
Gauge Field ◽  
Gauge Transformation ◽  
Brst Symmetry ◽  
Brst Transformation ◽  
Least Action Principle ◽  
Yang Mills ◽  
Least Action ◽  
Gauge Fixing ◽  
Popov Ghost ◽  
Ghost Field

Ghost fields arise from the quantization of the gauge field with constraints (gauge fixing) through the path integral method. By substituting a form of identity, an effective propagator will be obtained from the gauge field with constraints and this is called the Faddeev-Popov method. The Grassmann odd properties of the ghost field cause the gauge transformation parameter to be Grassmann odd, so a BRST transformation is defined. Ghost field emergence with Grassmann odd properties can also be obtained through the least action principle with gauge transformation, and thus the relations between the BRST transformation parameters and the ghost field is obtained.

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