Infrared Singularities in Theories with Scalar Massless Particles

1973 ◽  
pp. 199-240
Author(s):  
K. Symanzik
Keyword(s):  
Massless Particles ◽  
Infrared Singularities

NONPERTURBATIVE BEHAVIOR IN THREE-DIMENSIONAL QED

1992 ◽  
Vol 07 (27) ◽  
pp. 6857-6872 ◽  
Author(s):  
A.B. WAITES ◽  
R. DELBOURGO
Keyword(s):  
Three Dimensional ◽  
Green Functions ◽  
Asymptotic Results ◽  
Massless Particles ◽  
Infrared Singularities

Infrared singularities in QED3 can be avoided by including at least one massless source which couples to the photon. Once that is arranged it is possible to obtain nonzeromass solutions for the source Green functions in scalar and (doubled) spinor electrodynamics, by using the gauge technique. We find that the asymptotic results for the source spectral ρ functions are typically ρ(p)≃(p2−m2)−1−e2/cπ2 as p→m, and ρ(p)≃p−2 exp (c′e2/πp) as p→∞. The constants c and c′ are respectively related to the number of charged massless particles and their “spin” character.

Energy and Momentum

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Time Dilation ◽  
Speed Of Light ◽  
Massless Particles ◽  
The Everyday ◽  
Low Speeds ◽  
Energy And Momentum ◽  
Deep Relationship ◽  
Insight Into ◽  
Momentum Relation

Tis chapter explains the famous equation E = mc2 as part of a wider relationship between energy, mass, and momentum. We start by defning energy and momentum in the everyday sense. We then build on the stretching‐triangle picture of spacetime vectors developed in Chapter 11 to see how energy, mass, and momentum have a deep relationship that is not obvious at everyday low speeds. When momentum is zero (a mass is at rest) this energy‐momentum relation simplifes to E = mc2, which implies that mass at rest quietly stores tremendous amounts of energy. Te energymomentum relation also implies that traveling near the speed of light (e.g., to take advantage of time dilation for interstellar journeys) will require tremendous amounts of energy. Finally, we look at the simplifed form of the energy‐momentum relation when the mass is zero. Tis gives us insight into the behavior of massless particles such as the photon.

scholarly journals Exploration of the tree-level S-matrix of massless particles

2012 ◽  
Vol 60 (7-8) ◽  
pp. 889-895
Author(s):  
P. Benincasa
Keyword(s):  
Tree Level ◽  
Massless Particles ◽  
S Matrix

scholarly journals Localizability, gauge symmetry and Newton–Wigner operator for massless particles

2018 ◽  
Vol 398 ◽  
pp. 203-213
Author(s):  
P. Kosiński ◽  
P. Maślanka
Keyword(s):  
Gauge Symmetry ◽  
Massless Particles ◽  
Wigner Operator

scholarly journals A prescription for projectors to compute helicity amplitudes in D dimensions

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Long Chen
Keyword(s):  
Dimensional Regularization ◽  
Tensor Decomposition ◽  
Regularization Scheme ◽  
Lorentz Index ◽  
Dimensional Splitting ◽  
Lorentz Tensor ◽  
Helicity Amplitudes ◽  
Amplitude Level ◽  
Infrared Singularities

AbstractThis article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor decomposition and avoids also dimensional splitting. Because of the latter, commutation between Lorentz index contraction and loop integration is preserved within this prescription, which entails certain technical advantages. The usage of these D-dimensional polarized amplitude projectors results in helicity amplitudes that can be expressed solely in terms of external momenta, but different from those defined in the existing dimensional regularization schemes. Furthermore, we argue that despite being different from the conventional dimensional regularization scheme (CDR), owing to the amplitude-level factorization of ultraviolet and infrared singularities, our prescription can be used, within an infrared subtraction framework, in a hybrid way without re-calculating the (process-independent) integrated subtraction coefficients, many of which are available in CDR. This hybrid CDR-compatible prescription is shown to be unitary. We include two examples to demonstrate this explicitly and also to illustrate its usage in practice.

scholarly journals Microlocal Analysis of Infrared Singularities

1988 ◽  
pp. 309-330 ◽  
Author(s):  
Takahiro Kawai ◽  
Henry P. Stapp
Keyword(s):  
Microlocal Analysis ◽  
Infrared Singularities

scholarly journals Celestial diamonds: conformal multiplets in celestial CFT

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Sabrina Pasterski ◽  
Andrea Puhm ◽  
Emilio Trevisani
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitudes ◽  
Explicit Construction ◽  
Conformal Dimension ◽  
Massless Particles ◽  
Special Values ◽  
Left And Right ◽  
Opposite Helicity ◽  
Asymptotic Symmetries

Abstract We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin s = $$ \left\{0,\frac{1}{2},1,\frac{3}{2},2\right\} $$ 0 1 2 1 3 2 2 we classify and construct all SL(2,ℂ) primary descendants which are organized into ‘celestial diamonds’. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with SL(2,ℂ) conformal dimension ∆ and spin J. Radiative conformal primary wavefunctions have J = ±s and give rise to conformally soft theorems for special values of ∆ ∈ $$ \frac{1}{2}\mathbb{Z} $$ 1 2 ℤ . They are located either at the top of celestial diamonds, where they descend to trivial null primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have |J| ≤ s. Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D shadow transform relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.

scholarly journals Classical soft graviton theorem rewritten

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Biswajit Sahoo ◽  
Ashoke Sen
Keyword(s):  
Low Frequency ◽  
Constant Term ◽  
Wave Form ◽  
Null Infinity ◽  
Final State ◽  
Massless Particles ◽  
Retarded Time ◽  
Hard Particles ◽  
State Radiation ◽  
Large Impact Parameter

Abstract Classical soft graviton theorem gives the gravitational wave-form at future null infinity at late retarded time u for a general classical scattering. The large u expansion has three known universal terms: the constant term, the term proportional to 1/u and the term proportional to ln u/u2, whose coefficients are determined solely in terms of the momenta of incoming and the outgoing hard particles, including the momenta carried by outgoing gravitational and electromagnetic radiation produced during scattering. For the constant term, also known as the memory effect, the dependence on the momenta carried away by the final state radiation / massless particles is known as non-linear memory or null memory. It was shown earlier that for the coefficient of the 1/u term the dependence on the momenta of the final state massless particles / radiation cancels and the result can be written solely in terms of the momenta of the incoming particles / radiation and the final state massive particles. In this note we show that the same result holds for the coefficient of the ln u/u2 term. Our result implies that for scattering of massless particles the coefficients of the 1/u and ln u/u2 terms are determined solely by the incoming momenta, even if the particles coalesce to form a black hole and massless radiation. We use our result to compute the low frequency flux of gravitational radiation from the collision of massless particles at large impact parameter.

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