On euclidean systems of covariance for massless particles

1981 ◽  
Vol 5 (4) ◽  
pp. 303-309 ◽  
Author(s):  
D. P. L. Castrigiano
Keyword(s):  
Massless Particles ◽  
Systems Of Covariance

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 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.

Massless Particles

1986 ◽  
pp. 159-188
Author(s):  
Y. S. Kim ◽  
Marilyn E. Noz
Keyword(s):  
Massless Particles
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