Bohr-Sommerfeld Quantization of Space

We introduce semiclassical methods into the study of the volume spectrum in loop gravity. The classical system behind a 4-valent spinnetwork node is a Euclidean tetrahedron. We investigate the tetrahedral volume dynamics on phase space and apply Bohr-Sommerfeld quantization to find the volume spectrum. The analysis shows a remarkable quantitative agreement with the volume spectrum computed in loop gravity. Moreover, it provides new geometrical insights into the degeneracy of this spectrum and the maximum and minimum eigenvalues of the volume on intertwiner space.Comment: 32 pages, 10 figure

Spectrum, volume 32, number 04

Guy Bailey named as UM-Kansas City chancellor -- Board approves changes to medical benefits plan -- University of Missouri briefs -- Board approves FY07 appropriations requests

Spectrum, volume 32, number 05

President Floyd reports on statewide tuition tour -- UM faculty & staff benefits announce plan changes, open enrollment -- University of Missouri briefs -- Gardner named vice president for research & economic development

Spectrum, volume 32, number 02

John F. Carney III named as next UM-Rolla chancellor -- Floyd addresses budget, campus accomplishments in report to board -- Atkins praises Chancellor Thomas' service, leadership to University -- UM technology transfer showcase honors faculty -- Floyd appoints UM-Kansas City chancellor search committee -- Alumni Alliance gives awards for outstanding service to UM -- University of Missouri briefs

Spectrum, volume 32, number 03

Floyd reports on University priorities, legislative session -- Board approves FY06 operating budget -- FY07 state appropriations request reviewed -- February 2005 research board awards announced -- UM faculty honored for outstanding work -- University of Missouri briefs -- Lehmkuhle appointed interim chancellor at UM-Kansas City

Spectrum, volume 32, number 06

Board elects Bennett and Walsworth as 2006 officers -- Atkins highlights year of accomplishments in final board report -- UM-Columbia graduate Wasinger takes place on board -- Floyd focuses on partnerships and efficiencies in board report -- Economic development vice president brings focus to fourth mission -- Floyd introduces alternative tuition proposal -- University of Missouri briefs

Spectrum, volume 32, number 01

Atkins discusses goals for 2005 in first report to board -- Gov. Blunt announces appointments of three UM curators -- Board approves educational fees, room & board rates for next year -- October 2004 research board award announced -- President Floyd addresses tuition, efficiencies in report to board -- University surplus property available online at eBay -- University of Missouri briefs -- Gilliland leaves UM-Kansas City chancellor post

Spectrum, Volume 32, Issue 6

Highlights include: Students Give Meaning to the Alternative Spring Break -- Career Fair Gives Students Opportunity to Succeed -- Sacred Heart Ranked Platinum for Promoting a Healthy Workplace -- Blackbear Saloon Closing -- Students Tap Into UNICEF -- Jacqueline ZIevor Travels to Kenya -- Kappa Sigma Hosts America 4 Boston Even

Spectrum, Volume 32, Issue 11

Highlights include: Women Can Have It All : Linda and Stephanie McMahon speak to Welch Coiiege of Business --New minor in business developed specifically for students who are non-business majors --Cruisin\u27 Through Senior Week activities --Senior perspectives --BuzzFeed --Students sing out at the 2nd annual Concert Against Bullying --Sixth annual Relay For Life fundraiser (photos) --Spring Fest 2014 --SHU L.O.V.E. pops concert --Men\u27s lacrosse: Cody Marquis --Women\u27s soccer: Alyssa Brandofino --Track and cross country: Brianna Castrogivanni --Sports Class of 2014

Spectrum, Volume 32, Issue 6

Highlights include: Students Give Meaning to the Alternative Spring Break -- Career Fair Gives Students Opportunity to Succeed -- Sacred Heart Ranked Platinum for Promoting a Healthy Workplace -- Blackbear Saloon Closing -- Students Tap Into UNICEF -- Jacqueline ZIevor Travels to Kenya -- Kappa Sigma Hosts America 4 Boston Even