ONE-LOOP RENORMALIZATION OF NON-ABELIAN GAUGE THEORY AND β FUNCTION BASED ON LOOP REGULARIZATION METHOD

All one-loop renormalization constants for non-Abelian gauge theory are computed in detail by using the symmetry-preserving loop regularization method proposed in Refs. 1 and 2. The resulting renormalization constants are manifestly shown to satisfy Ward–Takahaski–Slavnov–Taylor identities, and lead to the well-known one loop β function for non-Abelian gauge theory of QCD.3-5 The loop regularization method is realized in the dimension of original field theories, it maintains not only symmetries but also divergent behaviors of original field theories with the introduction of two energy scales. Such two scales play the roles of characterizing and sliding energy scales as well as ultraviolet and infrared cutoff energy scales. An explicit check of those identities provides a clear demonstration how the symmetry-preserving loop regularization method can consistently be applied to non-Abelian gauge theories.

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NON-ABELIAN GAUGE THEORIES AS A CONSEQUENCE OF PERTURBATIVE QUANTUM GAUGE INVARIANCE

International Journal of Modern Physics A ◽

10.1142/s0217751x99001573 ◽

1999 ◽

Vol 14 (21) ◽

pp. 3421-3432 ◽

Cited By ~ 10

Author(s):

A. ASTE ◽

G. SCHARF

Keyword(s):

Gauge Theory ◽

Gauge Invariance ◽

Gauge Theories ◽

Fundamental Concept ◽

Abelian Gauge ◽

Abelian Gauge Theory ◽

Yang Mills ◽

Vector Bosons ◽

Perturbative Quantum

We show for the case of interacting massless vector bosons, how the structure of Yang–Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-Abelian gauge theory is necessarily of Yang–Mills type plus divergence- and coboundary-couplings. The extension of the method to massive gauge theories is briefly discussed.

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GEOMETRIC QUANTIZATION AND FIELD THEORIES — THE CHIRAL ANOMALY EXAMPLE

Modern Physics Letters A ◽

10.1142/s0217732389000587 ◽

1989 ◽

Vol 04 (05) ◽

pp. 483-490 ◽

Cited By ~ 2

Author(s):

P. SCHALLER ◽

G. SCHWARZ

Keyword(s):

Gauge Theory ◽

Geometric Quantization ◽

Field Theories ◽

Chiral Anomaly ◽

Abelian Gauge ◽

Abelian Gauge Theory ◽

Quantum Operator

In the framework of geometric quantization, the chiral U(1) symmetry of a non-abelian gauge theory is considered. The chiral anomaly is computed from half form contribution of the quantum operator.

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SOME PROPERTIES OF RENORMALONS IN GAUGE THEORIES

International Journal of Modern Physics A ◽

10.1142/s0217751x95000693 ◽

1995 ◽

Vol 10 (10) ◽

pp. 1449-1463 ◽

Cited By ~ 6

Author(s):

G. DI CECIO ◽

G. PAFFUTI

Keyword(s):

Gauge Theory ◽

Gauge Theories ◽

Perturbative Expansion ◽

Abelian Gauge ◽

Nonlocal Operators ◽

Abelian Gauge Theory ◽

Effective Lagrangian ◽

Local Operators

We find the explicit operatorial form of renormalon type singularities in Abelian gauge theory. Local operators of dimension six take care of the first UV renormalon; nonlocal operators are needed for IR singularities. In the effective Lagrangian constructed with these operators nonlocal imaginary parts appearing in the usual perturbative expansion at large orders are canceled.

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Solitary Waves and Vortices in Non-Abelian Gauge Theories with Matter

Advanced Nonlinear Studies ◽

10.1515/ans-2012-0404 ◽

2012 ◽

Vol 12 (4) ◽

Cited By ~ 5

Author(s):

Vieri Benci ◽

Claudio Bonanno

Keyword(s):

Gauge Theory ◽

Solitary Waves ◽

Gauge Theories ◽

Abelian Gauge ◽

Abelian Gauge Theory

AbstractWe consider a non-Abelian gauge theory in ℝ

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Gravitational vector Dark Matter

Journal of High Energy Physics ◽

10.1007/jhep03(2021)174 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Christian Gross ◽

Sotirios Karamitsos ◽

Giacomo Landini ◽

Alessandro Strumia

Keyword(s):

Dark Matter ◽

Gauge Theory ◽

Bound States ◽

Gauge Theories ◽

Dark Sector ◽

Abelian Gauge ◽

Abelian Gauge Theory ◽

Gravitational Vector ◽

Relic Abundance

Abstract A new dark sector consisting of a pure non-abelian gauge theory has no renormalizable interaction with SM particles, and can thereby realise gravitational Dark Matter (DM). Gauge interactions confine at a scale ΛDM giving bound states with typical lifetimes $$ \tau \sim {M}_{\mathrm{P}1}^4/{\Lambda}_{\mathrm{DM}}^5 $$ τ ∼ M P 1 4 / Λ DM 5 that can be DM candidates if ΛDM is below 100 TeV. Furthermore, accidental symmetries of group-theoretical nature produce special gravitationally stable bound states. In the presence of generic Planck-suppressed operators such states become long-lived: SU(N) gauge theories contain bound states with $$ \tau \sim {M}_{\mathrm{P}1}^8/{\Lambda}_{\mathrm{DM}}^9 $$ τ ∼ M P 1 8 / Λ DM 9 ; even longer lifetimes τ = (MPl/ΛDM)2N−4/ΛDM arise from SO(N) theories with N ≥ 8, and possibly from F4 or E8. We compute their relic abundance generated by gravitational freeze-in and by inflationary fluctuations, finding that they can be viable DM candidates for ΛDM ≳ 1010 GeV.

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SOLITONIC ASPECTS OF q-FIELD THEORIES

International Journal of Modern Physics A ◽

10.1142/s0217751x03013880 ◽

2003 ◽

Vol 18 (04) ◽

pp. 627-650 ◽

Cited By ~ 1

Author(s):

R. J. FINKELSTEIN

Keyword(s):

Gauge Theory ◽

Lie Algebra ◽

Lie Group ◽

Degrees Of Freedom ◽

Field Theories ◽

Standard Theory ◽

Abelian Gauge ◽

Abelian Gauge Theory ◽

Point Particles ◽

Non Locality

We have examined the deformation of a generic non-Abelian gauge theory obtained by replacing its Lie group by the corresponding quantum group. This deformed gauge theory has more degrees of freedom than the theory from which it is derived. By going over from point particles in the standard theory to solitonic particles in the deformed theory, it is proposed that we interpret the new degrees of freedom as being descriptive of the non-locality of the deformed theory. It also turns out that the original Lie algebra gets replaced by two dual algebras, one of which lies close to and approaches the original Lie algebra in a correspondence limit, while the second algebra is new and disappears in this same correspondence limit. The exotic field particles associated with the second algebra can be interpreted as quark-like constituents of the solitons, which are themselves described as point particles in the first algebra. These ideas are explored for q-deformed SU(2) and GL q(3).

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Gauge theories

10.1093/oso/9780198802877.003.0010 ◽

2018 ◽

Author(s):

Michael Kachelriess

Keyword(s):

Gauge Theory ◽

Field Strength ◽

Gauge Theories ◽

Local Symmetry ◽

Abelian Gauge ◽

Abelian Gauge Theory ◽

Abelian Field ◽

Feynman Rules ◽

Popov Method ◽

Special Case

After reviewing electrodynamics as the special case of an abelian gauge theory, this local symmetry is generalised to non-abelian gauge theories. The curvature of space-time is introduced as analogue of the non-abelian field-strength. Non-abelian gauge theories are quantised using the Fadeev–Popov method and the resulting Feynman rules are derived.

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HOW TO SOLVE QUANTUM NONLINEAR ABELIAN GAUGE THEORY IN TWO DIMENSIONS IN THE HEISENBERG PICTURE

International Journal of Modern Physics A ◽

10.1142/s0217751x98001621 ◽

1998 ◽

Vol 13 (19) ◽

pp. 3245-3254 ◽

Cited By ~ 2

Author(s):

NORIAKI IKEDA

Keyword(s):

Gauge Theory ◽

Canonical Quantization ◽

Gravitational Theory ◽

Two Dimensions ◽

Field Theories ◽

Quantum Field Theories ◽

Operator Formalism ◽

Abelian Gauge ◽

Abelian Gauge Theory ◽

Heisenberg Picture

The new method based on the operator formalism proposed by Abe and Nakanishi is applied to the quantum nonlinear Abelian gauge theory in two dimensions. The soluble models in this method are extended to a wider class of quantum field theories. We obtain the exact solution in the canonical-quantization operator formalism in the Heisenberg picture, so this analysis might shed some light on the analysis of gravitational theory and nonpolynomial field theories.

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