Integral Representations for Scattering Amplitudes in Perturbation Theory. II

Abstract Theories with both electric and magnetic charges (“mutually non-local” theories) have several major obstacles to calculating scattering amplitudes. Even when the interaction arises through the kinetic mixing of two, otherwise independent, U(1)’s, so that all low-energy interactions are perturbative, difficulties remain: using a self-dual, local formalism leads to spurious poles at any finite order in perturbation theory. Correct calculations must show how the spurious poles cancel in observable scattering amplitudes. Consistency requires that one type of charge is confined as a result of one of the U(1)’s being broken. Here we show how the constraints of confinement and parity conservation on observable processes manages to cancel the spurious poles in scattering and pair production amplitudes, paving the way for systematic studies of the experimental signatures of “dark” electric-magnetic processes. Along the way we demonstrate some novel effects in electric-magnetic interactions, including that the amplitude for single photon production of magnetic particles by electric particles vanishes.

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Perturbation Theory of Scattering Amplitudes at High Energies

Physical Review ◽

10.1103/physrev.130.2566 ◽

1963 ◽

Vol 130 (6) ◽

pp. 2566-2572 ◽

Cited By ~ 84

Author(s):

James D. Bjorken ◽

Tai Tsun Wu

Keyword(s):

Perturbation Theory ◽

Scattering Amplitudes ◽

High Energies

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Hidden non-locality and self-superrenormalization of quantum gravity

Modern Physics Letters A ◽

10.1142/s0217732320502880 ◽

2020 ◽

Vol 35 (35) ◽

pp. 2050288

Author(s):

Andrea Addazi

Keyword(s):

Black Holes ◽

Perturbation Theory ◽

Scattering Amplitudes ◽

Quantum Gravity ◽

Uncertainty Principle ◽

Quantum Effects ◽

Perturbative Quantum ◽

Heisenberg's Uncertainty Principle ◽

Non Locality

We show that the formation/evaporation of Black Holes (BH) unitarizes quantum gravity at all the orders of the perturbation theory. Non-perturbative quantum effects save the scattering amplitudes from any polynomial divergences. Such a phenomena is intimately related to the dynamical emergence of an effective non-locality as well as emergent modifications of the Heisenberg’s uncertainty principle. The BH production delocalizes quantum gravity vertices and propagators as a consequence of its holographically stored entropy. In this sense, quantum gravity is a superrenormalizable theory, although non-locality is hidden in its action.

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GLUON SCATTERING AMPLITUDES FROM GAUGE/STRING DUALITY AND INTEGRABILITY

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194513009379 ◽

2013 ◽

Vol 21 ◽

pp. 1-21

Author(s):

YUJI SATOH

Keyword(s):

Perturbation Theory ◽

Scattering Amplitudes ◽

String Duality ◽

Bethe Ansatz ◽

Strong Coupling ◽

Minimal Surfaces ◽

Wilson Loops ◽

Thermodynamic Bethe Ansatz ◽

Yang Mills ◽

Sine Gordon Model

We discuss gluon scattering amplitudes/null-polygonal Wilson loops of [Formula: see text] super Yang-Mills theory at strong coupling based on the gauge/string duality and its underlying integrability. We focus on the amplitudes/Wilson loops corresponding to the minimal surfaces in AdS3, which are described by the thermodynamic Bethe ansatz equations of the homogeneous sine-Gordon model. Using conformal perturbation theory and an interesting relation between the g-function (boundary entropy) and the T-function, we derive analytic expansions around the limit where the Wilson loops become regular-polygonal. We also compare our analytic results with those at two loops, to find that the rescaled remainder functions are close to each other for all multi-point amplitudes.

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THE SU(2) NONLINEAR σ MODEL IN 2+1 DIMENSIONS: PERTURBATION THEORY IN A POLYNOMIAL FORMULATION

International Journal of Modern Physics A ◽

10.1142/s0217751x95000796 ◽

1995 ◽

Vol 10 (11) ◽

pp. 1655-1670 ◽

Cited By ~ 1

Author(s):

C.D. FOSCO ◽

T. MATSUYAMA

Keyword(s):

Perturbation Theory ◽

Vector Field ◽

Scattering Amplitudes ◽

Loop Order ◽

Normal Ordering ◽

First Order ◽

Feynman Rules ◽

Field L ◽

Polynomial Formulation ◽

Full Propagator

We construct a perturbation theory for the SU(2) nonlinear σ model in 2+1 dimensions using a polynomial, first-order formulation, where the variables are a non-Abelian vector field Lμ [the left SU(2) current], and a non-Abelian pseudovector field θμ, which imposes the condition Fμv(L)=0. The coordinates on the group do not appear in the Feynman rules, but their scattering amplitudes are easily related to those of the currents. We show that all the infinities affecting physical amplitudes at one-loop order can be cured by normal-ordering, presenting the calculation of the full propagator as an example of an application.

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