Curvature tensors of higher-spin gauge theories derived from general Lagrangian densities

Curvature tensors of higher-spin gauge theories have been known for some time. In the past, they were postulated using a generalization of the symmetry properties of the Riemann tensor (curl on each index of a totally symmetric rank-$n$ field for each spin-$n$). For this reason they are sometimes referred to as the generalized 'Riemann' tensors. In this article, a method for deriving these curvature tensors from first principles is presented; the derivation is completed without any a priori knowledge of the existence of the Riemann tensors or the curvature tensors of higher-spin gauge theories. To perform this derivation, a recently developed procedure for deriving exactly gauge invariant Lagrangian densities from quadratic combinations of $N$ order of derivatives and $M$ rank of tensor potential is applied to the $N = M = n$ case under the spin-$n$ gauge transformations. This procedure uniquely yields the Lagrangian for classical electrodynamics in the $N = M = 1$ case and the Lagrangian for higher derivative gravity (`Riemann' and `Ricci' squared terms) in the $N = M = 2$ case. It is proven here by direct calculation for the $N = M = 3$ case that the unique solution to this procedure is the spin-3 curvature tensor and its contractions. The spin-4 curvature tensor is also uniquely derived for the $N = M = 4$ case. In other words, it is proven here that, for the most general linear combination of scalars built from $N$ derivatives and $M$ rank of tensor potential, up to $N=M=4$, there exists a unique solution to the resulting system of linear equations as the contracted spin-$n$ curvature tensors. Conjectures regarding the solutions to the higher spin-$n$ $N = M = n$ are discussed.Comment: 12 page

Field theories from physical requirements: Noether\u27s first theorem, energy-momentum tensors and the question of uniqueness

An axiomatic approach to physics is proposed for obtaining classical gauge theories from a common set of physical requirements based on standard features of special relativistic field theories such as gauge invariance, conformal invariance and being in four dimensions. This approach involves the use of Noether\u27s first theorem to directly obtain a unique, complete set of equations from the symmetries of the action. However, implementation of this procedure is obstructed by issues of ambiguity and non-uniqueness associated with the conserved tensors in the majority of special relativistic field theories. In the introductory chapter, we outline the three major problems which are considered in this thesis. Each of these three problems are addressed separately in the three central chapters of the thesis, which consist of eight integrated articles. These three problems are (i) the failure of the canonical Noether energy-momentum tensor to obtain known physical conservation laws, and the ad-hoc ``improvement\u27\u27 of the energy-momentum tensors occurring in the literature, (ii) the ambiguities and non-uniqueness associated with multiple different methods for derivation of the energy-momentum tensor, and (iii) the procedure required for converting a set of axioms to a set of Lagrangian densities. The concluding chapter summarizes our major results, such as proper variational ``Noetherian\u27\u27 symmetries for several completely gauge invariant models using the Bessel-Hagen method, a formal disproof of the equivalence of the Noether and Hilbert energy-momentum tensors in Minkowski spacetime, a proof that there are infinitely many solutions for energy-momentum tensors in linearized gravity obtained from the ``improvement\u27\u27 method, and a derivation of the curvature tensors of higher spin gauge theories without referring to the symmetry properties of the Riemann curvature tensor. Future research that could follow from our results is discussed

PHARMABULLETIN Issue 3, Fall 2005

On August 15, 2005, the Food and Drug Administration (FDA) and the Association of American Medical Colleges released a joint report that examines possible steps to accelerate drug discovery and development. The report, entitled Drug Development Science: Obstacles and Opportunities for Collaboration Among Academia, Industry and Government, is the product of a two-day conference among leaders from the pharmaceutical industry, academia, and FDA. The goal of the conference and the report was to explore means of overcoming the high failure rate for tentative drug candidates

Pharma Bulletin - Spring 2005

FDA to Create Drug Safety Board In February 2005, the Food and Drug Administration (FDA) announced that it will create a new independent Drug Safety Oversight Board (DSB) to oversee the management of drug safety issues within the Center for Drug Evaluation and Research (CDER). The FDA Commissioner will appoint individuals from the FDA and medical experts from other Health and Human Services agencies and government departments to the DSB, which also will consult with other medical experts and patient and consumer group representatives. Additionally, the FDA is proposing a new “Drug Watch” web page for emerging data and risk information, and anticipates an increased use of information sheets written for healthcare professionals and patients. Because of the potential concerns associated with disseminating emerging information prior to regulatory action, the agency has stated it will solicit public input. The FDA will issue draft guidance on procedures and criteria for identifying drugs and information for the Drug Watch web page

PHARMABULLETIN Issue 2, Summer 2005

In May 2005, the Food and Drug Administration (FDA) issued draft guidance on the type of information to be posted on its new “Drug Watch” website—a site intended to identify drugs for which it is actively evaluating early safety signals. At this time, the FDA plans only to post information on drug products regulated by the Center for Drug Evaluation and Research, therefore vaccines, blood products and medical devices shall be excluded

Finishing Steers in a Deep-bedded Hoop Barn and a Conventional Feedlot: Effects on Performance and Carcass Characteristics during Winter in Iowa

As the Iowa beef industry invests in environmental management, there has been increasing interest in systems that minimize runoff. A possible housing option used previously for pigs and sheep to help mitigate some of these environmental concerns are hoops. The objective of this study was to compare steer performance and carcass characteristics between two housing treatments; hoop confinement barn (HP n=3; 4.65m 2 /steer) vs. conventional feedlot (FD n=3; 14.7m 2 /steer). A total of 240 crossbred Bos taurus steers were used. Steers were ear tagged, implanted, and weighed (400 ± 23.38 kg) on arrival and allotted to balance weight and breed. Performance measures; average daily gain (ADG), average daily feed intake (ADFI), and feed to gain ratio (F:G) were collected over the trial. Carcass characteristics; dressing percentage, hot carcass weight (HCW), fat depth over the 12 rd rib, kidney pelvic and heart fat (KPH), ribeye area (REA), marbling score, quality grade, and USDA yield grade were collected at processing by the packing plant. ADG, ADFI and F:G did not differ (P \u3e 0.05) between housing treatments. Dressing percentage (P = 0.02) and HCW (P = 0.01) were higher for HP steers vs. FD steers between housing treatments. All other carcass characteristics did not differ (P \u3e 0.05) between housing treatments. Therefore, housing steers in a hoop does not result in detrimental alterations in either performance or carcass characteristics when compared to steers in a conventional feedlot

Finishing Steers in a Deep-bedded Hoop Barn and a Conventional Feedlot: Effects on Behavior and Temperament during Summer in Iowa

As the Iowa beef industry invests in environmental management, there has been increasing interest in systems where runoff is minimized. A possible housing option used previously for pigs and sheep to help mitigate some of these environmental concerns are hoops. The objective of this study was to compare steer behavior and temperament between two treatments; hoop building (HP; n=3; 4.65m 2 / steer) vs. conventional feedlot (FD; n=3; 14.7m 2 / steer) during the summer months. A total of 240 crossbred Bos taurus steers were used. Steers were ear tagged, implanted, and weighed (445 ± 31.7 kg) on arrival and allotted to balance weight and breed. Behavioral data were collected using a 10 min scan sampling technique using live observation by two experienced observers from 0700 h to 1600 h on d 34, 56 and 91 of the trial. Two behaviors (head in bunk and head in waterer) and three postures (lying, walking and standing) were recorded. One day postbehavior collection, steers were moved through a squeeze chute for subjective temperament scoring. Scores ranged from 1 (exits chute calmly) to 6 (very aggressive, charges handlers). There were no (P = 0.22) differences for head in bunk behavior between treatments, however there was a difference (P = 0.02) for drinking, with HP steers spending more time at the waterer than FD steers. Lying incidence was greater (P = 0.004) for HP vs. FD steers. Fewer (P \u3c 0.05) HP steers exhibited walking or standing behavior compared to their FD counterparts. Temperament scores were not different between treatments (P = 0.13) but day and day*treatment (P \u3c 0.001) were sources of variation for temperament measures. In conclusion, overall time budget differences were observed with HP steers being less active but spending more time engaged in drinking related behaviors. Temperament scores increased during the trial but did not differ between the two housing treatments. Therefore, housing steers in a hoop barn does not result in detrimental alterations in either behavior or temperament when compared to steers in a conventional feedlot