scholarly journals Multiplicative renormalizability of gluon and ghost propagators in QCD

2001 ◽  
Vol 64 (11) ◽  
Author(s):  
J. C. R. Bloch
Keyword(s):  
Multiplicative Renormalizability

scholarly journals Renormalizable Abelian-Projected Effective Gauge Theory Derived from Quantum Chromodynamics II

2003 ◽  
Vol 18 (20) ◽  
pp. 1403-1412 ◽  
Author(s):  
Toru Shinohara
Keyword(s):  
Gauge Theory ◽  
Tensor Field ◽  
Anomalous Dimension ◽  
Low Energy ◽  
Effective Theory ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Antisymmetric Tensor Field ◽  
Group Functions ◽  
Multiplicative Renormalizability

In the previous paper,1 we derived the Abelian projected effective gauge theory as a low energy effective theory of the SU (N) Yang–Mills theory by adopting the maximal Abelian gauge. At that time, we have demonstrated the multiplicative renormalizability of the propagators for the diagonal gluon and the dual Abelian antisymmetric tensor field. In this paper, we show the multiplicative renormalizability of the Green's functions also for the off-diagonal gluon. Moreover, we complement the previous results by calculating the anomalous dimension and the renormalization group functions which are undetermined in the previous paper.

MULTIPLICATIVE RENORMALIZABILITY AND SELF-CONSISTENT TREATMENTS OF THE SCHWINGER-DYSON EQUATIONS

1991 ◽  
Vol 06 (04) ◽  
pp. 317-324 ◽  
Author(s):  
N. BROWN ◽  
N. DOREY
Keyword(s):  
The Self ◽  
Fermion Propagator ◽  
Self Consistent ◽  
Renormalization Constants ◽  
Multiplicative Renormalizability ◽  
Self Consistency ◽  
Important Test

Many approximations to the Schwinger-Dyson equations place constraints on the renormalization constants of a theory. The requirement that the solutions to the equations be multiplicatively renormalizable also places constraints on these constants. Demanding that these two sets of constraints be compatible is an important test of the self-consistency of the approximations made. We illustrate this idea by considering the equation for the fermion propagator in massless quenched QED, checking the consistency of various approximations.

MULTIPLICATIVE RENORMALIZABILITY AND THE LAPLACE-BELTRAMI OPERATOR

1991 ◽  
Vol 06 (06) ◽  
pp. 955-976
Author(s):  
D. OLIVIER ◽  
G. VALENT
Keyword(s):  
Irreducible Representation ◽  
Isometry Group ◽  
Zero Mode ◽  
Beltrami Operator ◽  
Sufficient Condition ◽  
Representation Space ◽  
Necessary And Sufficient Condition ◽  
Infinite Dimensional ◽  
Necessary And Sufficient ◽  
Multiplicative Renormalizability

For some rank 1 non-linear σ models we prove that a necessary and sufficient condition of multiplicative renormalizability for composite fields is that they should be eigenfunctions of the coset Laplace-Beltrami operator. These eigenfunctions span the irreducible representation space of the isometry group and may be finite- or infinite-dimensional. The zero mode of the Laplace-Beltrami operator plays a particular role since it is not renormalized at all.

scholarly journals Renormalizability of pure 𝒩 = 1 super-Yang–Mills in the Wess–Zumino gauge in the presence of the local composite operators A2 and λ̄λ

2018 ◽  
Vol 33 (28) ◽  
pp. 1850161 ◽  
Author(s):  
M. A. L. Capri ◽  
S. P. Sorella ◽  
R. C. Terin ◽  
H. C. Toledo
Keyword(s):  
Gauge Field ◽  
Landau Gauge ◽  
Composite Operator ◽  
Nonlinear Realization ◽  
Yang Mills ◽  
Invariant Action ◽  
Renormalization Factor ◽  
Gauge Fixing ◽  
Multiplicative Renormalizability ◽  
Supersymmetric Structure

The [Formula: see text] super-Yang–Mills theory in the presence of the local composite operator [Formula: see text] is analyzed in the Wess–Zumino gauge by employing the Landau gauge fixing condition. Due to the supersymmetric structure of the theory, two more composite operators, [Formula: see text] and [Formula: see text], related to the SUSY variations of [Formula: see text] are also introduced. A BRST invariant action containing all these operators is obtained. An all-order proof of the multiplicative renormalizability of the resulting theory is then provided by means of the algebraic renormalization setup. Though, due to the nonlinear realization of the supersymmetry in the Wess–Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino.

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