Modular Groups of Quantum Fields in Thermal States

For a quantum field in a thermal equilibrium state we discuss the group generated by time translations and the modular action associated with an algebra invariant under half-sided translations. The modular flows associated with the algebras of the forward light cone and a space-like wedge admit a simple geometric description in two dimensional models that factorize in light-cone coordinates. At large distances from the domain boundary compared to the inverse temperature the flow pattern is essentially the same as time translations, whereas the zero temperature results are approximately reproduced close to the edge of the wedge and the apex of the cone. Associated with each domain there is also a one parameter group with a positive generator, for which the thermal state is a ground state. Formally, this may be regarded as a certain converse of the Unruh-effect.Comment: 28 pages, 4 figure

Middle Ground? Book Review Of: Same Sex Different States: When Same-Sex Marriages Cross State Lines. by Andrew Koppelman

Book review: Same Sex Different States: When Same-Sex Marriages Cross State Lines. By Andrew Koppelman. Yale University Press. 2006. Pp. xviii + 204. Reviewed by: Patrick J. Borcher

The Internationalization of Contractual Conflicts Law

Professor Borchers maintains that United States conflict of laws rules regarding contracts have long had an international character. This Article reviews the development of contractual conflicts law and examines how, through Joseph Story\u27s treatises, the United States law in this area assumed an international perspective. These international influences have played and will increasingly play an important role in the development of U.S. contractual conflicts rules. This influence can be seen in both choice-of-forum and choice-of-law agreements. Both have been upheld by U.S. courts initially in international cases, which presented starker contrasts in choice of law or choice of forum. Once courts accepted these clauses in international cases, they soon extended these principles to domestic cases as well. While contractual conflicts law has been accepted in the United States, the extent of its acceptance has not been exactly the same as in other states. Limitations imposed on party autonomy have been the focus of discussion in the revision to the Uniform Commercial Code, Section 1-105. The author endorses a liberal view on party autonomy: his approach of conflicts pragmatism suggests that commercial activities may play a role in defining legal rights and duties. He therefore concludes that parties should not be limited in choosing the law that they want applied to resolve any dispute to those states having a relation to their transaction. Given the particular importance of choice of law in international transactions, where each party may fear the application of the others\u27 law, allowing parties to choose the law of a neutral forum that has no relation to the transaction may be more important. Moreover, the author suggests that law developed by private institutions, such as the UNIDROIT Principles, may offer parties a neutral, superior body of law that developed through consensus