New Use of Dimensional Continuation Illustrated by dE/dx in a Plasma and the Lamb Shift
arXiv:physics/9911056 · doi:10.1103/PhysRevD.62.045026
Abstract
Physical processes ranging from the Lamb shift to the energy loss dE/dx of a charged particle traversing a plasma entail processes that occur over a wide range of energy or length scales. Different physical mechanisms dominate at one or the other end of this range. For example, in the energy loss problem, soft collisions that are screened by collective effects are important at large distances, while at short distances hard collisions are important where the exact details of the single-particle interactions must be taken into account. We introduce a novel application of dimensional continuation. The soft processes dominate at all scales when the spatial dimension νis less than 3, and we use them to compute the result to leading order for ν< 3. On the other hand, the hard processes dominate at all scales for ν> 3, and we use them to compute the result to leading order for these spatial dimensions. We then explain why the sum of the analytic continuation of these disparate mechanisms yields the correct leading-order result for the physical limit at ν= 3 dimensions. After applying this new method to the energy loss problem in some detail, we then show how it also provides a very short and easy way to compute the Lamb shift.
arXiv commentNew title, Lamb shift calculation included, paper expanded to 16 pages
Cited by in corpus (8)
- O(g) plasma effects in jet quenching
- Heavy quark diffusion in QCD and N=4 SYM at next-to-leading order
- Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
- Charged Particle Stopping Power Effects on Ignition: Some Results from an Exact Calculation
- Temperature Equilibration Rate with Fermi-Dirac Statistics
- The Lamb shift and the gravitational binding energy for binary black holes
- The energy partitioning of non-thermal particles in a plasma: or the Coulomb logarithm revisited
- Calculating the Charged Particle Stopping Power Exactly to Leading and Next-to-leading Order