Techniques and Applications of Path Integration by L. Schulman

Author:L. Schulman
Language: eng
Format: epub
ISBN: 9780486137025
Publisher: Dover Publications
Published: 2012-10-11T00:00:00+00:00

(25.7)

where Fµv is the electromagnetic field and σµν is (essentially) a commutator of γ matrices. If one again replaces m2 by — 2i∂/∂λ the resulting equation is formally similar to the Schrödinger equation for a particle with spin and can be handled (clumsily) exactly as done for the Hamiltonian in (22.2).

We turn next to the use of relativistic propagators on curved space-times. The physical problem concerns the emission of radiation from black holes. Since the first thing one learns about black holes—as an explanation of their name—is that they absorb everything, the possibility of emission may be surprising. However, it is only classically that emission is forbidden, and the emission to be derived below is the result of a quantum tunneling process.

Actually even before the emission mechanism described below was worked out, there was reason to expect radiation from black holes. This was because black holes had certain properties best understood in terms of thermodynamics, and when one tried to push the thermodynamic analogy as far as possible, the need for some sort of emission arose. Specifically, Bekenstein, beginning from the fact that when black holes collide the area of the event horizon can never decrease, was led to identify (some multiple of) the area of the event horizon as an entropy so that the nondecrease of area was an expression of the second law of thermodynamics. He then formulated a generalized second law, in which the sum of the black hole entropy and the usual entropy never decreases. Going further, there is also an analogue of the first law in that nearby equilibrium states of a black hole are related by

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.