scholarly journals On Parametric and Dispersive Integrals

1993 ◽  
Vol 46 (6) ◽  
pp. 729
Author(s):  
R Delbourgo
Keyword(s):  
Gauge Theories ◽  
Parametric Form ◽  
Arbitrary Mass ◽  
Self Energy ◽  
Energy Integrals

Parametric and dispersive representations of self-energy integrals for particles of arbitrary mass in any dimension look very different. We establish their equivalence explicitly and suggest ways in which the parametric form might prove suitable for tackling Schwinger-Dyson equations in gauge theories.

scholarly journals Closed expressions for specific massive multiloop self-energy integrals

1994 ◽  
Vol 63 (2) ◽  
pp. 227-234 ◽  
Author(s):  
F. A. Berends ◽  
M. B�hm ◽  
M. Buza ◽  
R. Scharf
Keyword(s):  
Self Energy ◽  
Energy Integrals

scholarly journals Tensor Two-loop Self-energy Integrals

2010 ◽  
Vol 20 (2) ◽  
Author(s):  
Phan Hong Khiem ◽  
Do Hoang Son
Keyword(s):  
Self Energy ◽  
Energy Integrals

scholarly journals TSIL: a program for the calculation of two-loop self-energy integrals

2006 ◽  
Vol 174 (2) ◽  
pp. 133-151 ◽  
Author(s):  
Stephen P. Martin ◽  
David G. Robertson
Keyword(s):  
Self Energy ◽  
Energy Integrals

QUANTUM GRAVITY AT FINITE TEMPERATURE

1988 ◽  
Vol 03 (07) ◽  
pp. 667-672
Author(s):  
A.E.I. JOHANSSON ◽  
G. PERESSUTTI ◽  
B.-S. SKAGERSTAM
Keyword(s):  
Effective Mass ◽  
Effective Temperature ◽  
Gauge Invariance ◽  
Finite Temperature ◽  
Gauge Theories ◽  
Temperature Dependent ◽  
Self Energy ◽  
The One ◽  
Dependent Mass ◽  
Increasing Function

Self-energy corrections induced by the presence of thermal gravitons are computed at the one-loop level. It is found that thermal gravitons lead to a decreasing, effective temperature-dependent mass contrary to the situation in ordinary gauge theories where the effective mass is an increasing function of the temperature. It is argued that for 4πT2 larger then [Formula: see text], massive modes in the system are damped out in time or they cause instabilities. We also verify that the temperature-dependent effective mass satisfies Weinberg’s on-shell gauge invariance.

scholarly journals DAMPING AND REACTION RATES AND WAVE FUNCTION RENORMALIZATION OF FERMIONS IN HOT GAUGE THEORIES

2000 ◽  
Vol 15 (19) ◽  
pp. 2953-2969
Author(s):  
ALEJANDRO AYALA ◽  
JUAN CARLOS D'OLIVO ◽  
AXEL WEBER
Keyword(s):  
Wave Function ◽  
Production Rate ◽  
Reaction Rate ◽  
Gauge Theories ◽  
Reaction Rates ◽  
Chiral Fermion ◽  
Wave Function Renormalization ◽  
Self Energy ◽  
Hot Plasma ◽  
Damping Rate

We examine the relation between the damping rate of a chiral fermion mode propagating in a hot plasma and the rate at which the mode approaches equilibrium. We show how these two quantities, obtained from the imaginary part of the fermion self-energy, are equal when the reaction rate is defined using the appropriate wave function of the mode in the medium. As an application, we compute the production rate of hard axions by Compton-like scattering processes in a hot QED plasma starting from both, the axion self-energy and the electron self-energy. We show that the latter rate coincides with the former only when this is computed using the corresponding medium spinor modes.

scholarly journals Dyson’s Equations for Quantum Gravity in the Hartree–Fock Approximation

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 120
Author(s):  
Herbert W. Hamber ◽  
Lu Heng Sunny Yu
Keyword(s):  
Quantum Gravity ◽  
Integral Equations ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Gauge Field Theories ◽  
Closed Set ◽  
Four Dimensions ◽  
Hartree Fock ◽  
Self Energy ◽  
Starting Point

Unlike scalar and gauge field theories in four dimensions, gravity is not perturbatively renormalizable and as a result perturbation theory is badly divergent. Often the method of choice for investigating nonperturbative effects has been the lattice formulation, and in the case of gravity the Regge–Wheeler lattice path integral lends itself well for that purpose. Nevertheless, lattice methods ultimately rely on extensive numerical calculations, leaving a desire for alternate methods that can be pursued analytically. In this work, we outline the Hartree–Fock approximation to quantum gravity, along lines which are analogous to what is done for scalar fields and gauge theories. The starting point is Dyson’s equations, a closed set of integral equations which relate various physical amplitudes involving graviton propagators, vertex functions, and proper self-energies. Such equations are in general difficult to solve, and as a result they are not very useful in practice, but nevertheless provide a basis for subsequent approximations. This is where the Hartree–Fock approximation comes in, whereby lowest order diagrams get partially dressed by the use of fully interacting Green’s function and self-energies, which then lead to a set of self-consistent integral equations. The resulting nonlinear equations for the graviton self-energy show some remarkable features that clearly distinguish it from the scalar and gauge theory cases. Specifically, for quantum gravity one finds a nontrivial ultraviolet fixed point in Newton’s constant G for spacetime dimensions greater than two, and nontrivial scaling dimensions between d=2 and d=4, above which one obtains Gaussian exponents. In addition, the Hartree–Fock approximation gives an explicit analytic expression for the renormalization group running of Newton’s constant, suggesting gravitational antiscreening with Newton’s constant slowly increasing on cosmological scales.

scholarly journals TVID 2: evaluation of planar-type three-loop self-energy integrals with arbitrary masses

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Stefan Bauberger ◽  
Ayres Freitas ◽  
Daniel Wiegand
Keyword(s):  
Self Energy ◽  
Energy Integrals
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