scholarly journals Gravitational dyonic amplitude at one-loop and its inconsistency with the classical impulse

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Jung-Wook Kim ◽  
Myungbo Shim
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
Resonance Excitation ◽  
Quantum Field ◽  
Geodesic Motion ◽  
Loop Order ◽  
Recent Proposal ◽  
Order Analysis ◽  
Excitation Parameters ◽  
Static Background

Abstract The recent proposal [1, 2] of implementing electric-magnetic duality rotation at the level of perturbative scattering amplitudes and its generalisation to gravitational context where usual gravitational mass is rotated to the NUT parameter of the Taub-NUT spacetime opens up an interesting avenue for studying NUT-charged objects as dynamical entities, in contrast to the usual approach where NUT-charged objects are considered as a static background. We extend the tree-order analysis to one-loop order, and find a disagreement between geodesic motion on Taub-NUT background and impulse computation of scattering amplitudes. As a by-product of our analysis, we find a relation between tidal response parameters and resonance excitation parameters in the language of quantum field theory scattering amplitudes.

scholarly journals A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 956
Author(s):  
Dafne Carolina Arias-Perdomo ◽  
Adriano Cherchiglia ◽  
Brigitte Hiller ◽  
Marcos Sampaio
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Symmetry ◽  
Particle Physics ◽  
Analytic Extension ◽  
Quantum Field ◽  
Loop Order ◽  
Time Dimension ◽  
The Core ◽  
Striking Success

Quantum Field Theory, as the keystone of particle physics, has offered great insights into deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of divergent quantities in intermediary steps of the calculation, which encompasses the need for some regularization/renormalization prescription. As an alternative to traditional methods, based on the analytic extension of space–time dimension, frameworks that stay in the physical dimension have emerged; Implicit Regularization is one among them. We briefly review the method, aiming to illustrate how Implicit Regularization complies with the BPHZ theorem, which implies that it respects unitarity and locality to arbitrary loop order. We also pedagogically discuss how the method complies with gauge symmetry using one- and two-loop examples in QED and QCD.

Evaluation of loop diagrams using quantum mechanics

1992 ◽  
Vol 70 (8) ◽  
pp. 652-655 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Matrix Element ◽  
Proper Time ◽  
Quantum Field ◽  
Loop Momentum ◽  
Loop Order ◽  
Point Function ◽  
Integral Formalism ◽  
Time Formalism

In using the proper time formalism, Schwinger demonstrated that one-loop processes in quantum field theory can be expressed in terms of a matrix element whose form is encountered in quantum mechanics, and which can be evaluated using the Heisenberg formalism. We demonstrate how instead this matrix element can be computed using standard results in the path-integral formalism. The technique of operator regularization allows one to extend this approach to arbitrary loop order. No loop-momentum integrals are ever encountered. This technique is illustrated by computing the two-point function in [Formula: see text] theory to one-loop order.

scholarly journals DUALITY OF STRING AMPLITUDES IN A CURVED BACKGROUND

1993 ◽  
Vol 08 (30) ◽  
pp. 5409-5440
Author(s):  
MÅNS HENNINGSON
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitudes ◽  
String Theory ◽  
Target Space ◽  
Quantum Field ◽  
Group Manifold ◽  
String Amplitudes ◽  
Theory Calculation ◽  
The Relationship

We initiate a program to study the relationship between the target space, the spectrum and the scattering amplitudes in string theory. We consider scattering amplitudes following from string theory and quantum field theory on a curved target space, which is taken to be the SU(2) group manifold, with special attention given to the duality between contributions from different channels. We give a simple example of the equivalence between amplitudes coming from string theory and quantum field theory, and compute the general form of a four-scalar field-theoretical amplitude. The corresponding string theory calculation is performed for a special case, and we discuss how more general string theory amplitudes could be evaluated.

scholarly journals Optical theorem and indefinite metric in λϕ4 delta-theory

2020 ◽  
Vol 35 (33) ◽  
pp. 2050214
Author(s):  
Ricardo Avila ◽  
Carlos M. Reyes
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Coupling Parameter ◽  
Effective Field ◽  
Optical Theorem ◽  
Indefinite Metric ◽  
Quantum Field ◽  
Scalar Model ◽  
Loop Order ◽  
Interaction Term

A class of effective field theory called delta-theory, which improves ultraviolet divergences in quantum field theory, is considered. We focus on a scalar model with a quartic self-interaction term and construct the delta theory by applying the so-called delta prescription. We quantize the theory using field variables that diagonalize the Lagrangian, which include a standard scalar field and a ghost or negative norm state. As well known, the indefinite metric may lead to the loss of unitary of the [Formula: see text]-matrix. We study the optical theorem and check the validity of the cutting equations for three processes at one-loop order, and found suppressed violations of unitarity in the delta coupling parameter of the order of [Formula: see text].

scholarly journals Analytic computing methods for precision calculations in quantum field theory

2018 ◽  
Vol 33 (17) ◽  
pp. 1830015 ◽  
Author(s):  
Johannes Blümlein ◽  
Carsten Schneider
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Computing Methods ◽  
Current Status ◽  
Quantum Field ◽  
Loop Order ◽  
Single Scale ◽  
Double Mass ◽  
Mathematical Computation ◽  
And Function

An overview is presented on the current status of main mathematical computation methods for the multiloop corrections to single-scale observables in quantum field theory and the associated mathematical number and function spaces and algebras. At present, massless single-scale quantities can be calculated analytically in QCD to 4-loop order and single mass and double mass quantities to 3-loop order, while zero-scale quantities have been calculated to 5-loop order. The precision requirements of the planned measurements, particularly at the FCC-ee, form important challenges to theory, and will need important extensions of the presently known methods.

Introduction to scattering amplitudes

2019 ◽  
pp. 183-204
Author(s):  
David A. Kosower
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitudes ◽  
Traditional Approach ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
The Past

This chapter covers the new on-shell methods that have been developed over the past twenty years for computing scattering amplitudes in quantum field theory. These methods break free from the traditional approach of Feynman diagrams. The chapter covers a subset of topics, setting up the basic kinematics, spinor helicities, spinor products, and the calculation of tree amplitudes.

scholarly journals On the singular behaviour of scattering amplitudes in quantum field theory

2014 ◽  
Vol 2014 (11) ◽  
Author(s):  
Sebastian Buchta ◽  
Grigorios Chachamis ◽  
Petros Draggiotis ◽  
Ioannis Malamos ◽  
Germán Rodrigo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitudes ◽  
Quantum Field ◽  
Singular Behaviour

Renormalization scheme ambiguities in the models with more than one coupling

2020 ◽  
Vol 98 (1) ◽  
pp. 76-80
Author(s):  
D.G.C. McKeon ◽  
Chenguang Zhao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Physical Process ◽  
Renormalization Scheme ◽  
Quantum Field ◽  
Loop Order ◽  
Massless Limit ◽  
The Standard Model

The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making such finite renormalizations have been examined in the case of there being one or two couplings. In this paper, we consider how finite renormalizations can affect more general models in which there are more than two couplings. In particular, we consider the massless limit of the Standard Model in which there are essentially five couplings. We show that in this model (when neglecting all mass parameters) if we use mass independent renormalization, then the renormalization group β-functions are not unique beyond one-loop order, that it is not in general possible to eliminate all terms beyond certain order for all these β-functions, but that for a physical process, all contributions beyond one-loop order can be subsumed into the β-functions.

scholarly journals SYSTEMATIC IMPLEMENTATION OF IMPLICIT REGULARIZATION FOR MULTILOOP FEYNMAN DIAGRAMS

2011 ◽  
Vol 26 (15) ◽  
pp. 2591-2635 ◽  
Author(s):  
A. L. CHERCHIGLIA ◽  
MARCOS SAMPAIO ◽  
M. C. NEMES
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Feynman Diagram ◽  
Lorentz Invariance ◽  
Recursion Formula ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
Loop Momentum ◽  
Loop Order ◽  
Fundamental Symmetry

Implicit Regularization (IReg) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IReg program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multiloop amplitude in a well-defined set of basic divergent integrals in one-loop momentum only which is the essence of IReg. Moreover, we conjecture that momentum routing invariance in the loops, which has been shown to be connected with gauge symmetry, is a fundamental symmetry of any Feynman diagram in a renormalizable quantum field theory.

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