scholarly journals Integrands and loop momentum in string and field theory

2020 ◽  
Vol 102 (2) ◽  
Author(s):  
Piotr Tourkine
Keyword(s):  
Field Theory ◽  
Loop Momentum

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.

RADIATIVE EFFECTS IN A CONSTANT MAGNETIC FIELD USING THE QUANTUM MECHANICAL PATH-INTEGRAL

1994 ◽  
Vol 09 (23) ◽  
pp. 2167-2178 ◽  
Author(s):  
D.G.C. MCKEON ◽  
T.N. SHERRY
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Quantum Field Theory ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Quantum Mechanical ◽  
Quantum Field ◽  
Matrix Elements ◽  
Loop Momentum ◽  
Background Magnetic Field

It has been shown how evaluation of matrix elements of the form <x| exp −iHt|y> using the quantum mechanical path-integral allows one to determine radiative corrections in quantum field theory without encountering loop momentum integrals. In this paper we show how this technique can be applied when there is a constant background magnetic field contributing to the “Hamiltonian” H.

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.

scholarly journals Loop amplitudes monodromy relations and color-kinematics duality

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Eduardo Casali ◽  
Sebastian Mizera ◽  
Piotr Tourkine
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Gauge Theory ◽  
Tree Level ◽  
First Principle ◽  
Loop Momentum ◽  
New Developments ◽  
Feynman Graphs ◽  
Definition Of ◽  
Double Copy

Abstract Color-kinematics duality is a remarkable conjectured property of gauge theory which, together with double copy, is at the heart of a wealth of new developments in scattering amplitudes. So far, its validity has been verified in most cases only empirically, with limited ab initio understanding beyond tree-level. In this paper we provide initial steps in a first-principle understanding of color-kinematics duality and double-copy at loop level, through a detailed analysis of the field-theory limit of the monodromy relations of string theory at one loop. In this limit, we dissect the type of Feynman graphs generated and the relations they obey. We find that graphs with contact-terms are unavoidable and are generated in the field theory limit of “bulk” contours which do not have a standard physical interpretation in string perturbation theory. We show how they are related to ambiguities in the definition of the loop momentum and that their role is precisely to cancel those ambiguities.

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