Topological Aspects of Spin and Statistics in Nonlinear Sigma Models

We study the purely topological restrictions on allowed spin and statistics of topological solitons in nonlinear sigma models. Taking as space the connected $d$-manifold $X$, and considering nonlinear sigma models with the connected manifold $M$ as target space, topological solitons are given by elements of $pi_d(M)$. Any topological soliton $\alpha \in \pi_d(M)$ determines a quotient \Stat_n(X,\alpha) of the group of framed braids on $X$, such that choices of allowed statistics for solitons of type $\alpha$ are given by unitary representations of \Stat_n(X,\alpha) when $n$ solitons are present. In particular, when $M = S^2$, as in the $O(3)$ nonlinear sigma model with Hopf term, and $\alpha \in \pi_2(S^2)$ is a generator, we compute that \Stat_n(\R^2,\alpha) = \Z, while \Stat_n(S^2,\alpha) = \Z_{2n}. It follows that phase $\exp(i\theta)$ for interchanging two solitons of type $\alpha$ on $S^2$ must satisfy the constraint $\theta = k\pi/n$, $k \in \Z$, when $n$ such solitons are present.Comment: 14 page

12th Annual Conference on Recent Developments in IP Law and Policy

Program booklet and handouts for the IP Law Center at Golden Gate University School of Law\u27s 12th Annual Conference on Recent Developments in IP Law and Policy

The IP Law Book Review, Vol. 3 #1, November, 2012

REVIEWS AND REVIEWERS: MORAL RIGHTS: PRINCIPLES, PRACTICE AND NEW TECHNOLOGY, by Mira T. Sundara Rajan Reviewed by Cyrill P. Rigamonti, University of Bern CLEAN TECH INTELLECTUAL PROPERTY: ECO-MARKS, GREEN PATENTS, AND GREEN INNOVATION, by Eric L. Lane Reviewed by Joshua D. Sarnoff, De Paul University College of Law COMPLEX COPYRIGHT: MAPPING THE INFORMATION ECOSYSTEM, by Deborah Tussey Reviewed by Shubha Ghosh, University of Wisconsin Law School IMITATION TO INNOVATION IN CHINA: THE ROLE OF PATENTS IN BIOTECHNOLOGY AND PHARMACEUTICAL INDUSTRIES, by Yahong Li Reviewed by Benjamin P. Liu, John Marshall Law Schoo

12th Annual Conference on Recent Developments in IP Law and Policy

Program booklet and handouts for the IP Law Center at Golden Gate University School of Law\u27s 12th Annual Conference on Recent Developments in IP Law and Policy

The IP Law Book Review, Vol. 3 #1, November, 2012

REVIEWS AND REVIEWERS: MORAL RIGHTS: PRINCIPLES, PRACTICE AND NEW TECHNOLOGY, by Mira T. Sundara Rajan Reviewed by Cyrill P. Rigamonti, University of Bern CLEAN TECH INTELLECTUAL PROPERTY: ECO-MARKS, GREEN PATENTS, AND GREEN INNOVATION, by Eric L. Lane Reviewed by Joshua D. Sarnoff, De Paul University College of Law COMPLEX COPYRIGHT: MAPPING THE INFORMATION ECOSYSTEM, by Deborah Tussey Reviewed by Shubha Ghosh, University of Wisconsin Law School IMITATION TO INNOVATION IN CHINA: THE ROLE OF PATENTS IN BIOTECHNOLOGY AND PHARMACEUTICAL INDUSTRIES, by Yahong Li Reviewed by Benjamin P. Liu, John Marshall Law Schoo

10th Annual Conference on Recent Developments in Intellectual Property Law & Policy

Welcome to the 10 Annual Conference on Recent Developments in Intellectual Property Law andPolicy, presented by the Intellectual Property Law Center of Golden Gate University School of Law

Advanced EHF Technologies for Lightweight Augmentation / Restoration Communications Satellites

Small EHF satellites can significantly complement the anti-jam service provided by basic EHF MILSATCOM space segments. Mobile/survivable launch vehicles with rapid launch preparations can be utilized to responsively deploy these small satellites into high altitude elliptical or circular orbits. From such orbits, only a few satellites are needed to provide high duty cycle coverage of a critical area. The communications capabilities provided by these EHF payloads can range from low data rate services (75 to 2400 bps per channel) to high data rate links (10 Mbps or more per link) depending on the payload configuration. Through the use of EHF waveform standards, these augmentation/ restoration satellites will be compatible with existing and planned EHF terminals. Advanced technologies permit the development of the highly capable lightweight payloads required for these roles. Some of the key payload technologies include adaptive uplink antennas; high speed low power digital signal processing subsystems; lightweight frequency hopping synthesizers; and efficient solid-state transmitters