Infrared Effects

2021 ◽  
pp. 334-348
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Long Range ◽  
Perturbation Expansion ◽  
Coulomb Scattering ◽  
Physical Origin ◽  
Zero Mass ◽  
Loop Level ◽  
S Matrix ◽  
Infrared Divergences ◽  
Double Logarithm

It is shown that the presence of zero mass particles makes the elements of the S-matrix divergent. We explain the physical origin of such divergences. We argue that they are due to the long range of the interactions which violate the assumptions we made when we derived the asymptotic conditions for scattering. We study these divergences in the particular case of QED at tree, as well as one-loop level and present the Bloch–Nordsieck solution. We show that the cancellation of infrared divergences among virtual exchanged and real emitted soft photons is true to all orders in the perturbation expansion and we obtain the Sudakov double logarithm formula for Coulomb scattering.

KINETIC EQUATION FOR A GAS WITH LONG-RANGE ATTRACTION

1967 ◽  
Vol 45 (11) ◽  
pp. 3555-3567 ◽  
Author(s):  
R. A. Elliott ◽  
Luis de Sobrino
Keyword(s):  
Kinetic Equation ◽  
Long Range ◽  
Short Range ◽  
Kinetic Equations ◽  
Perturbation Expansion ◽  
Interparticle Distance ◽  
Range Interaction ◽  
Short Range Repulsion ◽  
Self Consistent Field ◽  
Range Force

A classical gas whose particles interact through a weak long-range attraction and a strong short-range repulsion is studied. The Liouville equation is solved as an infinite-order perturbation expansion. The terms in this series are classified by Prigogine-type diagrams according to their order in the ratio of the range of the interaction to the average interparticle distance. It is shown that, provided the range of the short-range force is much less than the average interparticle distance which, in turn, is much less than the range of the long-range force, the terms can be grouped into two classes. The one class, represented by chain diagrams, constitutes the significant contributions of the short-range interaction; the other, represented by ring diagrams, makes up, apart from a self-consistent field term, the significant contributions from the long-range force. These contributions are summed to yield a kinetic equation. The orders of magnitude of the terms in this equation are compared for various ranges of the parameters of the system. Retaining only the dominant terms then produces a set of eight kinetic equations, each of which is valid for a definite range of the parameters of the system.

Coexistence of 1 : 2 and 1 : 1 long-range ordering types in La-modified Ba(Mg0.33Ta0.67)O3 ceramics

1997 ◽  
Vol 12 (3) ◽  
pp. 589-592 ◽  
Author(s):  
Hyuk-Joon Youn ◽  
Kug Sun Hong ◽  
Hwan Kim
Keyword(s):  
Solid Solution ◽  
Dielectric Properties ◽  
Long Range ◽  
Phase Coexistence ◽  
Microwave Measurements ◽  
X Ray Diffraction ◽  
Physical Origin ◽  
X Ray ◽  
Wide Range ◽  
Long Range Ordering

The ordering structure of lanthanum-substituted Ba(Mg0.33Ta0.67)O3 was investigated using x-ray diffraction. It was observed that the ordering type of this solid solution transformed from 1: 2 to 1: 1 with 10 mol% substitution of La(Mg0.67Ta0.33)O3. These two types of ordering coexist over a wide range of composition. This coexistence of ordering types was considered as phase coexistence and its physical origin was investigated using microwave measurements. Based on the intensity of superlattice reflections and the discontinuity in dielectric properties, it was suggested that the coexistence of two ordering types originates from the overlap of the two stability regions.

scholarly journals Closed superstring field theory and its applications

2017 ◽  
Vol 32 (28n29) ◽  
pp. 1730021 ◽  
Author(s):  
Corinne de Lacroix ◽  
Harold Erbin ◽  
Sitender Pratap Kashyap ◽  
Ashoke Sen ◽  
Mritunjay Verma
Keyword(s):  
Field Theory ◽  
Vacuum Expectation ◽  
Space Time ◽  
Field Theories ◽  
Quantum Corrections ◽  
Type Ii ◽  
Expectation Values ◽  
S Matrix ◽  
Recent Developments ◽  
Infrared Divergences

We review recent developments in the construction of heterotic and type II string field theories and their various applications. These include systematic procedures for determining the shifts in the vacuum expectation values of fields under quantum corrections, computing renormalized masses and S-matrix of the theory around the shifted vacuum and a proof of unitarity of the S-matrix. The S-matrix computed this way is free from all divergences when there are more than 4 noncompact space–time dimensions, but suffers from the usual infrared divergences when the number of noncompact space–time dimensions is 4 or less.

A Problem of Mass

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Long Range ◽  
Gauge Invariance ◽  
Weak Interactions ◽  
Elementary Particles ◽  
Gauge Invariant ◽  
Zero Mass ◽  
Gauge Symmetries ◽  
Symmetry Properties ◽  
Long Range Interactions ◽  
The Masses

This chapter examines the constraints coming from the symmetry properties of the fundamental interactions on the possible values of the masses of elementary particles. We first establish a relation between the range of an interaction and the mass of the particle which mediates it. This relation implies, in particular, that long-range interactions are mediated by massless particles. Then we argue that gauge invariant interactions are long ranged and, therefore, the associated gauge particles must have zero mass. Second, we look at the properties of the constituents of matter, the quarks and the leptons. We introduce the notion of chirality and we show that the known properties of weak interactions, combined with the requirement of gauge invariance, force these particles also to be massless. The conclusion is that gauge symmetries appear to be incompatible with massive elementary particles, in obvious contradiction with experiment. This is the problem of mass.

On the Poles of the S Matrix for Long‐Range Potentials

1966 ◽  
Vol 7 (7) ◽  
pp. 1207-1217 ◽  
Author(s):  
Erasmo M. Ferreira ◽  
Antonio F. F. Teixeira
Keyword(s):  
Long Range ◽  
S Matrix

scholarly journals Gluon fragmentation into 3$$ {P}_J^{\left[1,8\right]} $$ quark pair and test of NRQCD factorization at two-loop level

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Peng Zhang ◽  
Ce Meng ◽  
Yan-Qing Ma ◽  
Kuang-Ta Chao
Keyword(s):  
Short Distance ◽  
Distance Matrix ◽  
Matrix Elements ◽  
Leading Order ◽  
Long Distance ◽  
Loop Level ◽  
Matching Procedure ◽  
Fragmentation Functions ◽  
Infrared Divergences ◽  
Gluon Fragmentation

Abstract The next-to-leading order (NLO) ($$ \mathcal{O} $$ O ($$ {\alpha}_s^3 $$ α s 3 )) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in 3$$ {P}_J^{\left[1,8\right]} $$ P J 1 8 states are calculated within the NRQCD factorization. We use the integration-by-parts reduction and differential equations to semi-analytically calculate the fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergences. Through the matching procedure, infrared-safe short distance coefficients and $$ \mathcal{O} $$ O ($$ {\alpha}_s^2 $$ α s 2 ) perturbative NRQCD matrix elements ⟨$$ {\mathcal{O}}^3{P}_J^{\left[1,8\right]} $$ O 3 P J 1 8 (3$$ {S}_1^{\left[8\right]} $$ S 1 8 )⟩ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones.

scholarly journals Infrared-safe scattering without photon vacuum transitions and time-dependent decoherence

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Dominik Neuenfeld
Keyword(s):  
Low Energy ◽  
Time Dependent ◽  
Matrix Elements ◽  
Scattering Process ◽  
Zero Energy ◽  
Ir Radiation ◽  
S Matrix ◽  
Inequivalent Representations ◽  
Infrared Divergences ◽  
Over Time

Abstract Scattering in 3 + 1-dimensional QED is believed to give rise to transitions between different photon vacua. We show that these transitions can be removed by taking into account off-shell modes which correspond to Liénard-Wiechert fields of asymptotic states. This makes it possible to formulate scattering in 3 + 1-dimensional QED on a Hilbert space which furnishes a single representation of the canonical commutation relations (CCR). Different QED selection sectors correspond to inequivalent representations of the photon CCR and are stable under the action of an IR finite, unitary S-matrix. Infrared divergences are cancelled by IR radiation. Using this formalism, we discuss the time-dependence of decoherence and phases of out-going density matrix elements in the presence of classical currents. The results demonstrate that although no information about a scattering process is stored in strictly zero-energy modes of the photon field, entanglement between charged matter and low energy modes increases over time.

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