Energy and momentum spectral function of coherent bremsstrahlung radiation

Journal Article · Mon Oct 15 00:00:00 EDT 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.20.2011· OSTI ID:6002068

Zwanziger, D

We calculate nonperturbatively and for small Q the cross section sigma (Q) for a scattering process to occur with loss of four-momentum Q to unobserved photons, a quantity which may be measured by observing the net recoil to all other particles. The calculation proceeds by means of a threshold theorem which asserts that for small Q, sigma (Q) approx. sigma/sub 0/P (Q), where sigma/sub 0/ is independent of Q, and P (Q) is the spectral of the coherent state Psi of bremsstrahlung photons defined by a/sup ..mu../(k) Psi = i (2..pi..)/sup -3/2..sigma..sub a/u/sup ..mu..//sub a/(u/sub a/xk)/sup -1/Psi, where a/sup ..mu../(k) is the annihilation operator for a photon of four-momentum k, and e/sub a/ and u/sub a/ are the charges and four-velocities of the scattered charged particles. Although Psi is not in the Fock space, the evaluation ofP (Q) =, where P/sub op/ is the operator of total electromagnetic four-momentum, is straightforward. The resulting function P (Q) simplifies if Q is near the light cone, where the bulk of the probability is in fact located, P (Q) approx. theta (Q/sup 0/) theta (Q/sup 2/)(GAMMA (1+B))/sup -1/B (Q/sup 2//2)/sup B/-1I/sub 0/ (Q)exp(F (Q)), where I/sub 0/(Q) =-(2..pi..)/sup -3/(..sigma..sub a/e/sub a/u/sub a/ (u/sub a/xQ)/sup -1/)/sup 2/ > 0, B = ..integral..dk I/sub 0/(Q/sup 0/ = 1, Q = k), and F (Q) is given explicitly in the text, satisfies F (lambdaQ) = F (Q) - B lnlambda, and is a smooth function as the light cone is approached.

• Research Organization: Department of Physics, New York University, New York, New York 10003
• OSTI ID: 6002068
• Journal Information: Phys. Rev., D; (United States), Vol. 20:8
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BREMSSTRAHLUNG
SPECTRAL FUNCTIONS
ELECTRON-POSITRON INTERACTIONS
ANNIHILATION
PHOTONS
SCATTERING
COHERENT RADIATION
CROSS SECTIONS
INFRARED DIVERGENCES
LIGHT CONE
METRICS
PROBABILITY
Q-VALUE
SCALING LAWS
ULTRAVIOLET DIVERGENCES
BASIC INTERACTIONS
ELECTROMAGNETIC INTERACTIONS
ELECTROMAGNETIC RADIATION
ELEMENTARY PARTICLES
ENERGY
FUNCTIONS
INTERACTIONS
LEPTON-LEPTON INTERACTIONS
MASSLESS PARTICLES
PARTICLE INTERACTIONS
RADIATIONS
SPACE-TIME
645202* - High Energy Physics- Particle Interactions & Properties-Theoretical- Electromagnetic Interactions & Properties