Dynamical equations for a Regge theory with crossing symmetry and unitarity. III. Crossing-symmetric representation with explicit Regge-pole terms

1977 ◽  
Vol 16 (2) ◽  
pp. 482-493 ◽  
Author(s):  
Porter W. Johnson ◽  
Robert L. Warnock ◽  
M. Kaekebeke
Keyword(s):  
Regge Pole ◽  
Dynamical Equations ◽  
Symmetric Representation ◽  
Regge Theory ◽  
Crossing Symmetry

Rigid Body Dynamical Equations With Lie Algebra

2000 ◽  
Author(s):  
Krishna C. Gupta
Keyword(s):  
Lie Algebra ◽  
Center Of Mass ◽  
Interesting Property ◽  
Rate Of Change ◽  
The Body ◽  
Base System ◽  
Dynamical Equations ◽  
Symmetric Representation ◽  
Direct Derivation ◽  
Similar Appearance

Abstract A direct derivation is presented for the Generalized Euler’s equation in the translated base system that is located at the center of mass of the body. The use of Lie algebra reveals an interesting property of the time-variant inertia matrix I(t) — its rate of change is the Lie product [Ω, I], where [Ω] is the skew-symmetric representation of the angular velocity ω. This observation also simplifies the derivation. The standard body system form and the ZRP-form are then deduced. With differing meanings of terms, all three forms have a similar appearance: MG = [I] α + [Ω] [I] ω.

scholarly journals ANALYTIC MULTI-REGGE THEORY AND THE POMERON IN QCD II: GAUGE-THEORY ANALYSIS

1993 ◽  
Vol 08 (27) ◽  
pp. 4755-4895 ◽  
Author(s):  
ALAN R. WHITE
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Transverse Momentum ◽  
Symmetry Breaking ◽  
Gauge Theories ◽  
Regge Pole ◽  
High Energy ◽  
Asymptotic Freedom ◽  
Regge Theory ◽  
Regge Behavior

The high-energy Regge behavior of gauge theories is studied via the formalism of analytic multi-Regge theory. Perturbative results for spontaneously broken theories are first organized into Reggeon diagrams. Unbroken gauge theories are studied via a Reggeon-diagram infrared analysis of symmetry restoration. Massless fermions play a crucial role and the case of QCD involves the supercritical Pomeron as an essential intermediate stage. An introductory review of the buildup of transverse-momentum diagrams and Reggeon diagrams from leading-log calculations in gauge theories is presented first. It is then shown that the results closely reproduce the general structure for multi-Regge amplitudes derived in Part I of the article, allowing the construction of general Reggeon diagrams for spontaneously broken theories. Next it is argued that, with a transverse-momentum cutoff, unbroken gauge theories can be reached through an infrared limiting process which successively decouples fundamental-representation Higgs fields. The first infrared limit studied is the restoration of SU(2) gauge symmetry. The analysis is dominated by the exponentiation of divergences imposed by Reggeon unitarity and the contribution of massless quarks to Reggeon interactions. Massless quarks also produce “triangle anomaly” transverse-momentum divergences which do not exponentiate but instead are absorbed into a Reggeon condensate — which can be viewed as a “generalized winding-number condensate.” The result is a Reggeon spectrum consistent with confinement and chiral-symmetry breaking, but there is no Pomeron. The analysis is valid when the gauge coupling does not grow in the infrared region, i.e. when a sufficient number of massless quarks is present. An analogy is drawn between the confinement produced by the Reggeon condensate and that produced by regularization of the fermion sea, in the presence of the anomaly, in the two-dimensional Schwinger model. When the analysis is extended to the case of QCD with the gauge symmetry restored to SU(2), the Reggeon condensate can be identified with the Pomeron condensate of supercritical Pomeron theory. In this case, the condensate converts an SU(2) singlet Reggeized gluon to a Pomeron Regge pole — which becomes an SU(3) singlet when the full gauge symmetry is restored, The condensate disappears as SU(3) symmetry is recovered, and in general this limit gives the critical Pomeron at a particular value of the transverse cutoff. If the maximal number of fermions consistent with asymptotic freedom is present, no transverse-momentum cutoff is required. For SU (N) gauge theory it is argued that, when the theory contains many fermions, there are N–2 Pomeron Regge poles of alternating signature. This spectrum of Pomeron trajectories is in direct correspondence with the topological properties of transverse flux tubes characterized by the center ZN of the gauge group. The corresponding Reggeon-field-theory solution of s-channel unitarity should include a representation of ZN in the cutting rules. Finally, the implications of the results for the phenomenological study of the Pomeron as well as for the construction of QCD with a small number of flavors are discussed. Also discussed is the attractive possibility that a flavor doublet of color-sextet quarks could both produce the critical Pomeron in QCD and be responsible for electroweak dynamical-symmetry breaking.

Sign in / Sign up

Export Citation Format

Share Document