scholarly journals PLANCKIAN SCATTERING OF NON-ABELIAN GAUGE PARTICLES

1995 ◽  
Vol 10 (19) ◽  
pp. 2733-2745 ◽  
Author(s):  
SUPRIYA KAR ◽  
JNANADEVA MAHARANA
Keyword(s):  
Shock Wave ◽  
Systematic Study ◽  
Vertex Operator ◽  
Gauge Invariance ◽  
High Energy ◽  
Einstein Gravity ◽  
Effective Theory ◽  
Abelian Gauge ◽  
Yang Mills ◽  
High Energy Scattering

We present a systematic study of high energy scattering of non-Abelian gauge particles in (3+1)-dimensional Einstein gravity using semiclassical techniques of Verlinde and Verlinde. It is shown that the BRST gauge invariance of the Yang-Mills action in the presence of quantum gravity in the Planckian energy regime is maintained and the vertex operator is invariant under BRST transformations. The presence of gravitational shock wave describing the gauge particles is discussed in the resulting (3+1)-dimensional effective theory of Yang-Mills gravity.

scholarly journals High energy scattering in Einstein–Cartan gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
S. Bondarenko ◽  
S. Pozdnyakov ◽  
M. A. Zubkov
Keyword(s):  
High Energy ◽  
Einstein Gravity ◽  
Nucl Phys ◽  
Effective Theory ◽  
Spin Connection ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Energy Scattering ◽  
High Energy Scattering ◽  
Reggeon Field Theory

AbstractWe consider Riemann–Cartan gravity with minimal Palatini action, which is classically equivalent to Einstein gravity. Following the ideas of Lipatov (Nucl Phys B 365:614–632, 1991, Phys Part Nucl 44:391–413, 2013, Subnucl Ser 49:131, 2013, Subnucl Ser 50:213–225, 2014, Int J Mod Phys A 31(28/29):1645011, 2016, EPJ Web Conf 125:01010, 2016) and Bartels et al. (JHEP 07:056, 2014) we propose the effective action for this theory aimed at the description of the high-energy scattering of gravitating particles in the multi-Regge kinematics. We add to the Palatini action the new terms. These terms are responsible for the interaction of gravitational quanta with gravitational reggeons. The latter replace exchange by multiple gravitational excitations. We propose the heuristic explanation of its particular form based on an analogy to the reggeon field theory of QCD. We argue that Regge kinematics assumes the appearance of an effective two-dimensional model describing the high-energy scattering similar to that of QCD. Such a model may be formulated in a way leading to our final effective theory. It contains interaction between the ordinary quanta of spin connection and vielbein with the gravitational reggeons.

Diagrammatic derivation of the eikonal formula for high-energy scattering in Yang-Mills theory

1981 ◽  
Vol 23 (2) ◽  
pp. 534-552 ◽  
Author(s):  
Hung Cheng ◽  
John A. Dickinson ◽  
Kaare Olaussen
Keyword(s):  
High Energy ◽  
Yang Mills ◽  
Energy Scattering ◽  
High Energy Scattering

scholarly journals LOOP VARIABLES WITH CHAN–PATON FACTORS

2004 ◽  
Vol 19 (01) ◽  
pp. 59-70 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Continuum Limit ◽  
Open String ◽  
Equation Of Motion ◽  
Low Energy ◽  
Scale Transformation ◽  
Abelian Gauge ◽  
Rotation Symmetry ◽  
Yang Mills ◽  
Massless Fields

The loop variable method that has been developed for the U(1) bosonic open string is generalized to include non-Abelian gauge invariance by incorporating "Chan–Paton" gauge group indices. The scale transformation symmetry k(s)→λ(s)k(s) that was responsible for gauge invariance in the U(1) case continues to be a symmetry. In addition there is a non-Abelian "rotation" symmetry. Both symmetries crucially involve the massive modes. However, it is plausible that only a linear combination, which is the usual Yang–Mills transformation on massless fields, has a smooth (worldsheet) continuum limit. We also illustrate how an infinite number of terms in the equation of motion in the cutoff theory add up to give a term that has a smooth continuum limit, and thus contributes to the low energy Yang–Mills equation of motion.

scholarly journals Effective theory calculation of resonant high-energy scattering

2004 ◽  
Vol 686 (1-2) ◽  
pp. 205-247 ◽  
Author(s):  
M. Beneke ◽  
A.P. Chapovsky ◽  
A. Signer ◽  
G. Zanderighi
Keyword(s):  
High Energy ◽  
Effective Theory ◽  
Energy Scattering ◽  
High Energy Scattering ◽  
Theory Calculation

scholarly journals Gauge Invariance and Mass Gap in (2+1)-Dimensional Yang–Mills Theory

1997 ◽  
Vol 12 (06) ◽  
pp. 1161-1171 ◽  
Author(s):  
Dimitra Karabali ◽  
V. P. Nair
Keyword(s):  
Gauge Invariance ◽  
Gauge Theories ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Mass Gap ◽  
Spatial Dimensions

In terms of a gauge-invariant matrix parametrization of the fields, we give an analysis of how the mass gap could arise in non-Abelian gauge theories in two spatial dimensions.

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

1999 ◽  
Vol 14 (21) ◽  
pp. 3421-3432 ◽  
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.

scholarly journals THE BV MASTER EQUATION FOR THE WILSON ACTION IN GENERAL YANG-MILLS GAUGE THEORY

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2255-2256
Author(s):  
TAKESHI HIGASHI ◽  
ETSUKO ITOU ◽  
TAICHIRO KUGO
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Master Equation ◽  
Effective Action ◽  
Gauge Invariance ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Yang Mills ◽  
Usual Form

We study the four dimensional gauge theory within Wilsonian Renormalization Group (WRG) method. The Wilson effective action for general Yang-Mills gauge theory is shown to satisfy the usual form of Batalin-Vilkovisky (BV) master equation, despite that a momentum cutoff apparently breaks the gauge invariance. In the case of Abelian gauge theory, in particular, it actually deduces the Ward-Takahashi identity for Wilson action recently derived by Sonoda. We elucidated the relation of our Wilson master action with that derived by Ref. 2 and, in particular, showed that our BV Master equation really reproduced the Sonoda's WT identity for the Wilson action in QED. (This is a proceeding to the conference based on the poster given by E.I.).

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.

scholarly journals Non-Abelian Gauge Symmetry in the Causal Epstein–Glaser Approach

1997 ◽  
Vol 12 (24) ◽  
pp. 4461-4476 ◽  
Author(s):  
Tobias Hurth
Keyword(s):  
Perturbation Theory ◽  
Gauge Symmetry ◽  
Gauge Invariance ◽  
Fock Space ◽  
Dimensional Space ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Tree Graphs ◽  
Adiabatic Switching ◽  
Dimensional Space Time

Non-Abelian gauge symmetry in (3 + 1)-dimensional space–time is analyzed in the causal Epstein–Glaser framework. In this formalism, the technical details concerning the well-known UV and IR problem in quantum field theory are separated and reduced to well-defined problems, namely the causal splitting and the adiabatic switching of operator-valued distributions. Non-Abelian gauge invariance in perturbation theory is completely discussed in the well-defined Fock space of free asymptotic fields. The LSZ formalism is not used in this construction. The linear operator condition of asymptotic gauge invariance is sufficient for the unitarity of the S matrix in the physical subspace and the usual Slavnov–Taylor identities. We explicitly derive the most general specific coupling compatible with this condition. By analyzing only tree graphs in the second order of perturbation theory we show that the well-known Yang–Mills couplings with anticommuting ghosts are the only ones which are compatible with asymptotic gauge invariance. The required generalizations for linear gauges are given.

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