Commutator Anomaly in Noncommutative Quantum Mechanics

In this letter, firstly, the Schr$\ddot{o}$dinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.Comment: 7 page

Four-Point One-Loop Amplitude Computation in the Pure Spinor Formalism

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism.Comment: 10 pages harvmac te

Bosonic Field Propagators on Algebraic Curves

In this paper we investigate massless scalar field theory on non-degenerate algebraic curves. The propagator is written in terms of the parameters appearing in the polynomial defining the curve. This provides an alternative to the language of theta functions. The main result is a derivation of the third kind differential normalized in such a way that its periods around the homology cycles are purely imaginary. All the physical correlation functions of the scalar fields can be expressed in terms of this object. This paper contains a detailed analysis of the techniques necessary to study field theories on algebraic curves. A simple expression of the scalar field propagator is found in a particular case in which the algebraic curves have $Z_n$ internal symmetry and one of the fields is located at a branch point.Comment: 26 pages, TeX + harvma

Hadron-nucleus scattering in the local reggeon model with pomeron loops for realistic nuclei

Contribution of simplest loops for hadron-nucleus scattering cross-sections is studied in the Local Reggeon Field Theory with a supercritical pomeron. It is shown that inside the nucleus the supercritical pomeron transforms into a subcritical one, so that perturbative treatment becomes possible. The pomeron intercept becomes complex, which leads to oscillations in the cross-sections.Comment: 13 pages, 6 figure

Finite nuclei in the reggeon “toy model”

Hadron-nucleus amplitudes at high energies are studied in the "toy" Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and looses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprizing result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite well in spite of the fact that in reality the series should be cut and as such deprived of any physical sense at high energies

Regge Field Theory in zero transverse dimensions: loops versus "net" diagrams

Toy models of interacting Pomerons with triple and quaternary Pomeron vertices in zero transverse dimension are investigated. Numerical solutions for eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained, providing the quantum solution for the scattering amplitude in both models. The equations of motion for the Lagrangians of the theories are also considered and the classical solutions of the equations are found. Full two-point Green functions ("effective" Pomeron propagator) and amplitude of diffractive dissociation process are calculated in the framework of RFT-0 approach. The importance of the loops contribution in the amplitude at different values of the model parameters is discussed as well as the difference between the models with and without quaternary Pomeron vertex.Comment: 34 pages, 36 figure

Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring

A ten-dimensional super-Poincare covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincare covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and to construct a suitable $b$ ghost. A super-Poincare covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N<4, confirming the perturbative finiteness of superstring theory. One can also prove the Type IIB S-duality conjecture that $R^4$ terms in the effective action receive no perturbative contributions above one loop.Comment: 45 pages harvmac tex, added minor clarification

The life and scientific work of William R. Evitt (1923-2009)

Occasionally (and fortunately), circumstances and timing combine to allow an individual, almost singlehandedly, to generate a paradigm shift in his or her chosen field of inquiry. William R. (‘Bill’) Evitt (1923-2009) was such a person. During his career as a palaeontologist, Bill Evitt made lasting and profound contributions to the study of both dinoflagellates and trilobites. He had a distinguished, long and varied career, researching first trilobites and techniques in palaeontology before moving on to marine palynomorphs. Bill is undoubtedly best known for his work on dinoflagellates, especially their resting cysts. He worked at three major US universities and spent a highly significant period in the oil industry. Bill's early profound interest in the natural sciences was actively encouraged both by his parents and at school. His alma mater was Johns Hopkins University where, commencing in 1940, he studied chemistry and geology as an undergraduate. He quickly developed a strong vocation in the earth sciences, and became fascinated by the fossiliferous Lower Palaeozoic strata of the northwestern United States. Bill commenced a PhD project on silicified Middle Ordovician trilobites from Virginia in 1943. His doctoral research was interrupted by military service during World War II; Bill served as an aerial photograph interpreter in China in 1944 and 1945, and received the Bronze Star for his excellent work. Upon demobilisation from the US Army Air Force, he resumed work on his PhD and was given significant teaching duties at Johns Hopkins, which he thoroughly enjoyed. He accepted his first professional position, as an instructor in sedimentary geology, at the University of Rochester in late 1948. Here Bill supervised his first two graduate students, and shared a great cameraderie with a highly motivated student body which largely comprised World War II veterans. At Rochester, Bill continued his trilobite research, and was the editor of the Journal of Paleontology between 1953 and 1956. Seeking a new challenge, he joined the Carter Oil Company in Tulsa, Oklahoma, during 1956. This brought about an irrevocable realignment of his research interests from trilobites to marine palynology. He undertook basic research on aquatic palynomorphs in a very well-resourced laboratory under the direction of one of his most influential mentors, William S. ‘Bill’ Hoffmeister. Bill Evitt visited the influential European palynologists Georges Deflandre and Alfred Eisenack during late 1959 and, while in Tulsa, first developed several groundbreaking hypotheses. He soon realised that the distinctive morphology of certain fossil dinoflagellates, notably the archaeopyle, meant that they represent the resting cyst stage of the life cycle. The archaeopyle clearly allows the excystment of the cell contents, and comprises one or more plate areas. Bill also concluded that spine-bearing palynomorphs, then called hystrichospheres, could be divided into two groups. The largely Palaeozoic spine-bearing palynomorphs are of uncertain biological affinity, and these were termed acritarchs. Moreover, he determined that unequivocal dinoflagellate cysts are all Mesozoic or younger, and that the fossil record of dinoflagellates is highly selective. Bill was always an academic at heart and he joined Stanford University in 1962, where he remained until retiring in 1988. Bill enjoyed getting back into teaching after his six years in industry. During his 26-year tenure at Stanford, Bill continued to revolutionise our understanding of dinoflagellate cysts. He produced many highly influential papers and two major textbooks. The highlights include defining the acritarchs and comprehensively documenting the archaeopyle, together with highly detailed work on the morphology of Nannoceratopsis and Palaeoperidinium pyrophorum using the scanning electron microscope. Bill supervised 11 graduate students while at Stanford University. He organised the Penrose Conference on Modern and Fossil Dinoflagellates in 1978, which was so successful that similar meetings have been held about every four years since that inaugural symposium. Bill also taught many short courses on dinoflagellate cysts aimed at the professional community. Unlike many eminent geologists, Bill actually retired from actively working in the earth sciences. His full retirement was in 1988; after this he worked on only a small number of dinoflagellate cyst projects, including an extensive paper on the genus Palaeoperidinium