Regge trajectories and the renormalization group

The asymptotic high momentum behavior of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x 1. Particular emphasis is paid to theories with interactions involving more than one field where it is found that a matrix renormalization is necessary. Asymptotic scaling forms, in agreement with Regge theory, are derived for the elastic two-particle scattering amplitude and verified in one-loop renormalization group improved perturbation theory, corresponding to the summation of leading logs to all orders. We give explicit forms for the Regge trajectories of different scalar theories in this approximation and determine the signatures.

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“…10). In particular we will treat quite generally "cubic" field theories, wherein the asymmetric Regge limit is a particularly interesting one.…”

Section: Introductionmentioning

confidence: 93%

QUANTUM FIELD THEORY IN THE LIMIT x≪1

Stephens

Weber

Vieyra

et al. 2000

Int. J. Mod. Phys. A

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“…Work by Mexican researchers has shown how RG techniques can be adapted to deal with such kinematic dimensional reductions [23,24,25]. I will briefly illustrate the phenomenon within the context of a cubic scalar field theory.…”

Section: More Than One Singularity Per Greens Functionmentioning

confidence: 99%

“…For the pure cubic scalar theory in four dimensions with coupling g and mass m, to one loop the only UV divergence is a logarithmically divergent correction to m. This UV divergence can be removed in the standard fashion. After this renormalization, although UV finite the theory is not perturbatively reliable in the extreme, asymmetric scaling limits as can be illustrated using the two-particle scattering amplitude in the asymmetric limit t → ∞ for fixed s. The one-loop diagrams of the on-shell amplitude can be classified according to whether they contain a factor of lnt, a factor of ln(−t), or are "finite", a separation which can in principle be carried out to all orders leading to the following decomposition forΓ i jkl B [23]:…”

Section: More Than One Singularity Per Greens Functionmentioning

confidence: 99%

“…In some simple cases these logarithms can be summed by hand. However, Mexican researchers have shown how this can be done systematically using the RG [23,24]. In distinction to the standard case, as there are two sets of large logarithms, one associated with B B,t and another set with B B,u , an overall multiplicative renormalization of the connected four-point function will not be sufficient.…”

Section: More Than One Singularity Per Greens Functionmentioning

confidence: 99%

“…Naturally, in the different asymptotic limits the diagrams that contribute to the renormalization are different. An explicit one-loop calculation (5) yields [23,24]…”

Section: More Than One Singularity Per Greens Functionmentioning

confidence: 99%

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Renormalization Group Theory

Stephens¹

2006

AIP Conference Proceedings

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In this article I give a brief account of the development of research in the Renormalization Group in Mexico, paying particular attention to novel conceptual and technical developments associated with the tool itself, rather than applications of standard Renormalization Group techniques. Some highlights include the development of new methods for understanding and analysing two extreme regimes of great interest in quantum field theory-the "high temperature" regime and the Regge regime.

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Bound States From Regge Trajectories in a Scalar Model

Weber

Vieyra

Stephens

et al. 2001

Int. J. Mod. Phys. A

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The calculation of bound state properties using renormalization group techniques to compute the corresponding Regge trajectories is presented. In particular, we investigate the bound states in different charge sectors of a scalar theory with interaction φ † φχ. The resulting bound state spectrum is surprisingly rich. Where possible we compare and contrast with known results of the Bethe-Salpeter equation in the ladder approximation and, in the non-relativistic limit, with the corresponding Schrödinger equation.

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Regge trajectories and the renormalization group

Cited by 3 publications

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QUANTUM FIELD THEORY IN THE LIMIT x≪1

QUANTUM FIELD THEORY IN THE LIMIT x≪1

Renormalization Group Theory

Bound States From Regge Trajectories in a Scalar Model

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