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Foodborne illness outbreaks linked to unpasteurised milk and relationship to changes in state laws – United States, 1998–2018
- Lia Koski, Hannah Kisselburgh, Lisa Landsman, Rachel Hulkower, Mara Howard-Williams, Zainab Salah, Sunkyung Kim, Beau B. Bruce, Michael C. Bazaco, Michael B. Batz, Cary Chen Parker, Cynthia L. Leonard, Atin R. Datta, Elizabeth N. Williams, G. Sean Stapleton, Matthew Penn, Hilary K. Whitham, Megin Nichols
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- Epidemiology & Infection / Volume 150 / 2022
- Published online by Cambridge University Press:
- 25 October 2022, e183
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Consumption of unpasteurised milk in the United States has presented a public health challenge for decades because of the increased risk of pathogen transmission causing illness outbreaks. We analysed Foodborne Disease Outbreak Surveillance System data to characterise unpasteurised milk outbreaks. Using Poisson and negative binomial regression, we compared the number of outbreaks and outbreak-associated illnesses between jurisdictions grouped by legal status of unpasteurised milk sale based on a May 2019 survey of state laws. During 2013–2018, 75 outbreaks with 675 illnesses occurred that were linked to unpasteurised milk; of these, 325 illnesses (48%) were among people aged 0–19 years. Of 74 single-state outbreaks, 58 (78%) occurred in states where the sale of unpasteurised milk was expressly allowed. Compared with jurisdictions where retail sales were prohibited (n = 24), those where sales were expressly allowed (n = 27) were estimated to have 3.2 (95% CI 1.4–7.6) times greater number of outbreaks; of these, jurisdictions where sale was allowed in retail stores (n = 14) had 3.6 (95% CI 1.3–9.6) times greater number of outbreaks compared with those where sale was allowed on-farm only (n = 13). This study supports findings of previously published reports indicating that state laws resulting in increased availability of unpasteurised milk are associated with more outbreak-associated illnesses and outbreaks.
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. Bernad, Henley Bernard, Alan E. Bernstein, Jon L. Berquist, Johannes Beutler, Ana María Bidegain, Matthew P. Binkewicz, Jennifer Bird, Joseph Blenkinsopp, Dmytro Bondarenko, Paulo Bonfatti, Riet en Pim Bons-Storm, Jessica A. Boon, Marcus J. Borg, Mark Bosco, Peter C. Bouteneff, François Bovon, William D. Bowman, Paul S. Boyer, David Brakke, Richard E. Brantley, Marcus Braybrooke, Ian Breward, Ênio José da Costa Brito, Jewel Spears Brooker, Johannes Brosseder, Nicholas Canfield Read Brown, Robert F. Brown, Pamela K. Brubaker, Walter Brueggemann, Bishop Colin O. Buchanan, Stanley M. Burgess, Amy Nelson Burnett, J. Patout Burns, David B. Burrell, David Buttrick, James P. Byrd, Lavinia Byrne, Gerado Caetano, Marcos Caldas, Alkiviadis Calivas, William J. Callahan, Salvatore Calomino, Euan K. Cameron, William S. Campbell, Marcelo Ayres Camurça, Daniel F. Caner, Paul E. Capetz, Carlos F. Cardoza-Orlandi, Patrick W. Carey, Barbara Carvill, Hal Cauthron, Subhadra Mitra Channa, Mark D. Chapman, James H. Charlesworth, Kenneth R. Chase, Chen Zemin, Luciano Chianeque, Philip Chia Phin Yin, Francisca H. Chimhanda, Daniel Chiquete, John T. Chirban, Soobin Choi, Robert Choquette, Mita Choudhury, Gerald Christianson, John Chryssavgis, Sejong Chun, Esther Chung-Kim, Charles M. A. Clark, Elizabeth A. Clark, Sathianathan Clarke, Fred Cloud, John B. Cobb, W. Owen Cole, John A Coleman, John J. Collins, Sylvia Collins-Mayo, Paul K. Conkin, Beth A. Conklin, Sean Connolly, Demetrios J. Constantelos, Michael A. Conway, Paula M. Cooey, Austin Cooper, Michael L. Cooper-White, Pamela Cooper-White, L. William Countryman, Sérgio Coutinho, Pamela Couture, Shannon Craigo-Snell, James L. Crenshaw, David Crowner, Humberto Horacio Cucchetti, Lawrence S. Cunningham, Elizabeth Mason Currier, Emmanuel Cutrone, Mary L. Daniel, David D. Daniels, Robert Darden, Rolf Darge, Isaiah Dau, Jeffry C. Davis, Jane Dawson, Valentin Dedji, John W. de Gruchy, Paul DeHart, Wendy J. Deichmann Edwards, Miguel A. De La Torre, George E. Demacopoulos, Thomas de Mayo, Leah DeVun, Beatriz de Vasconcellos Dias, Dennis C. Dickerson, John M. Dillon, Luis Miguel Donatello, Igor Dorfmann-Lazarev, Susanna Drake, Jonathan A. Draper, N. Dreher Martin, Otto Dreydoppel, Angelyn Dries, A. J. Droge, Francis X. D'Sa, Marilyn Dunn, Nicole Wilkinson Duran, Rifaat Ebied, Mark J. Edwards, William H. Edwards, Leonard H. Ehrlich, Nancy L. Eiesland, Martin Elbel, J. Harold Ellens, Stephen Ellingson, Marvin M. Ellison, Robert Ellsberg, Jean Bethke Elshtain, Eldon Jay Epp, Peter C. Erb, Tassilo Erhardt, Maria Erling, Noel Leo Erskine, Gillian R. Evans, Virginia Fabella, Michael A. Fahey, Edward Farley, Margaret A. Farley, Wendy Farley, Robert Fastiggi, Seena Fazel, Duncan S. Ferguson, Helwar Figueroa, Paul Corby Finney, Kyriaki Karidoyanes FitzGerald, Thomas E. FitzGerald, John R. Fitzmier, Marie Therese Flanagan, Sabina Flanagan, Claude Flipo, Ronald B. Flowers, Carole Fontaine, David Ford, Mary Ford, Stephanie A. Ford, Jim Forest, William Franke, Robert M. Franklin, Ruth Franzén, Edward H. Friedman, Samuel Frouisou, Lorelei F. Fuchs, Jojo M. Fung, Inger Furseth, Richard R. Gaillardetz, Brandon Gallaher, China Galland, Mark Galli, Ismael García, Tharscisse Gatwa, Jean-Marie Gaudeul, Luis María Gavilanes del Castillo, Pavel L. Gavrilyuk, Volney P. Gay, Metropolitan Athanasios Geevargis, Kondothra M. George, Mary Gerhart, Simon Gikandi, Maurice Gilbert, Michael J. Gillgannon, Verónica Giménez Beliveau, Terryl Givens, Beth Glazier-McDonald, Philip Gleason, Menghun Goh, Brian Golding, Bishop Hilario M. Gomez, Michelle A. Gonzalez, Donald K. Gorrell, Roy Gottfried, Tamara Grdzelidze, Joel B. Green, Niels Henrik Gregersen, Cristina Grenholm, Herbert Griffiths, Eric W. Gritsch, Erich S. Gruen, Christoffer H. Grundmann, Paul H. Gundani, Jon P. Gunnemann, Petre Guran, Vidar L. Haanes, Jeremiah M. Hackett, Getatchew Haile, Douglas John Hall, Nicholas Hammond, Daphne Hampson, Jehu J. Hanciles, Barry Hankins, Jennifer Haraguchi, Stanley S. Harakas, Anthony John Harding, Conrad L. Harkins, J. William Harmless, Marjory Harper, Amir Harrak, Joel F. Harrington, Mark W. Harris, Susan Ashbrook Harvey, Van A. Harvey, R. Chris Hassel, Jione Havea, Daniel Hawk, Diana L. Hayes, Leslie Hayes, Priscilla Hayner, S. Mark Heim, Simo Heininen, Richard P. Heitzenrater, Eila Helander, David Hempton, Scott H. Hendrix, Jan-Olav Henriksen, Gina Hens-Piazza, Carter Heyward, Nicholas J. Higham, David Hilliard, Norman A. Hjelm, Peter C. Hodgson, Arthur Holder, M. Jan Holton, Dwight N. Hopkins, Ronnie Po-chia Hsia, Po-Ho Huang, James Hudnut-Beumler, Jennifer S. Hughes, Leonard M. Hummel, Mary E. Hunt, Laennec Hurbon, Mark Hutchinson, Susan E. Hylen, Mary Beth Ingham, H. Larry Ingle, Dale T. Irvin, Jon Isaak, Paul John Isaak, Ada María Isasi-Díaz, Hans Raun Iversen, Margaret C. Jacob, Arthur James, Maria Jansdotter-Samuelsson, David Jasper, Werner G. Jeanrond, Renée Jeffery, David Lyle Jeffrey, Theodore W. Jennings, David H. Jensen, Robin Margaret Jensen, David Jobling, Dale A. Johnson, Elizabeth A. Johnson, Maxwell E. Johnson, Sarah Johnson, Mark D. Johnston, F. Stanley Jones, James William Jones, John R. Jones, Alissa Jones Nelson, Inge Jonsson, Jan Joosten, Elizabeth Judd, Mulambya Peggy Kabonde, Robert Kaggwa, Sylvester Kahakwa, Isaac Kalimi, Ogbu U. Kalu, Eunice Kamaara, Wayne C. Kannaday, Musimbi Kanyoro, Veli-Matti Kärkkäinen, Frank Kaufmann, Léon Nguapitshi Kayongo, Richard Kearney, Alice A. Keefe, Ralph Keen, Catherine Keller, Anthony J. Kelly, Karen Kennelly, Kathi Lynn Kern, Fergus Kerr, Edward Kessler, George Kilcourse, Heup Young Kim, Kim Sung-Hae, Kim Yong-Bock, Kim Yung Suk, Richard King, Thomas M. King, Robert M. Kingdon, Ross Kinsler, Hans G. Kippenberg, Cheryl A. Kirk-Duggan, Clifton Kirkpatrick, Leonid Kishkovsky, Nadieszda Kizenko, Jeffrey Klaiber, Hans-Josef Klauck, Sidney Knight, Samuel Kobia, Robert Kolb, Karla Ann Koll, Heikki Kotila, Donald Kraybill, Philip D. W. Krey, Yves Krumenacker, Jeffrey Kah-Jin Kuan, Simanga R. Kumalo, Peter Kuzmic, Simon Shui-Man Kwan, Kwok Pui-lan, André LaCocque, Stephen E. Lahey, John Tsz Pang Lai, Emiel Lamberts, Armando Lampe, Craig Lampe, Beverly J. Lanzetta, Eve LaPlante, Lizette Larson-Miller, Ariel Bybee Laughton, Leonard Lawlor, Bentley Layton, Robin A. Leaver, Karen Lebacqz, Archie Chi Chung Lee, Marilyn J. Legge, Hervé LeGrand, D. L. LeMahieu, Raymond Lemieux, Bill J. Leonard, Ellen M. Leonard, Outi Leppä, Jean Lesaulnier, Nantawan Boonprasat Lewis, Henrietta Leyser, Alexei Lidov, Bernard Lightman, Paul Chang-Ha Lim, Carter Lindberg, Mark R. Lindsay, James R. Linville, James C. Livingston, Ann Loades, David Loades, Jean-Claude Loba-Mkole, Lo Lung Kwong, Wati Longchar, Eleazar López, David W. 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- The Cambridge Dictionary of Christianity
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- 20 September 2010, pp xi-xliv
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Conventions and notation
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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Quantum Field Theory in Curved Spacetime
- Quantized Fields and Gravity
- Leonard Parker, David Toms
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Quantum field theory in curved spacetime has been remarkably fruitful. It can be used to explain how the large-scale structure of the universe and the anisotropies of the cosmic background radiation that we observe today first arose. Similarly, it provides a deep connection between general relativity, thermodynamics, and quantum field theory. This book develops quantum field theory in curved spacetime in a pedagogical style, suitable for graduate students. The authors present detailed, physically motivated, derivations of cosmological and black hole processes in which curved spacetime plays a key role. They explain how such processes in the rapidly expanding early universe leave observable consequences today, and how in the context of evaporating black holes, these processes uncover deep connections between gravitation and elementary particles. The authors also lucidly describe many other aspects of free and interacting quantized fields in curved spacetime.
1 - Quantum fields in Minkowski spacetime
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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Summary
The theory of quantum fields in curved spacetime is a generalization of the well-established theory of quantum fields in Minkowski spacetime. To a great extent, the behavior of quantum fields in curved spacetime is a direct consequence of the corresponding flat spacetime theory. Local entities, such as the field equations and commutation relations, are to a large extent determined by the principle of general covariance and the principle of equivalence. However, global entities which are unique in Minkowski spacetime lose that uniqueness in curved spacetime. For example, the vacuum state, which in Minkowski spacetime is determined by Poincaré invariance, is not unambiguously determined in curved spacetime. This ambiguity is closely tied to the phenomenon of particle creation by certain gravitational fields, as in the expanding universe or near a black hole.
It is logical, therefore, to review the relevant aspects of flat spacetime quantum field theory. This will serve to establish the necessary background, to fix our notation, and to highlight those aspects of the theory which can be carried over to curved spacetime, as well as those which lose their meaning in curved spacetime. We will often be brief, emphasizing concepts while omitting many derivations, and only touch on particular topics. Our discussion of the curved spacetime theory in later chapters will be more detailed.
In this initial chapter, we discuss the canonical formulation, including the Schwinger action principle and the relation between symmetry transformations and conserved currents (Schwinger 1951b, 1953).
7 - The effective action: Gauge theories
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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References
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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3 - Expectation values quadratic in fields
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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Adiabatic subtraction and physical quantities
A number of quantities of physical interest, such as the action S and the energy-momentum tensor Tµν, are quadratic in the fields and their derivatives evaluated at a single point. As discussed in Chapter 1, the expectation values of such quantities diverge and can be regularized in the case of free fields in Minkowski spacetime by normal ordering. In curved spacetime, even for free fields, the implicit gravitational interaction introduces additional divergences. Furthermore, vacuum energy must be treated more carefully because it can give rise to gravitational effects through the gravitational field equations.
Various methods have been developed to regularize and renormalize quantities that involve squares or higher powers of fields or their derivatives evaluated at a single point of spacetime. Among them are proper-time regularization, dimensional regularization, zeta-function regularization, point-splitting regularization, particularly by the Hadamard method, and adiabatic regularization in homogeneous spacetimes. In this chapter we employ several of the above methods of regularization, including adiabatic, Hadamard, point-splitting, proper-time, and dimensional regularization as applied to curved spacetime. The trace anomaly of the energy-momentum tensor of the conformally coupled free field in a Robertson–Walker spacetime is derived using adiabatic regularization and compared with the equivalent result obtained from the proper-time series. It is shown that the expectation values of all the components of the energy-momentum tensor then follow from the trace anomaly by using the conformal symmetry of the spacetime.
4 - Particle creation by black holes
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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Introduction
We have already seen how time-dependent gravitational fields, such as occur in cosmology, can give rise to the creation of elementary particles. The time development of a quantum field induces a redefinition of creation and annihilation operators that correspond to physical particles. For example, the annihilation operators of particles at late times can be expressed as superpositions of annihilation and creation operators of particles at early times. This superposition is known as a Bogolubov transformation. The coefficients in the superposition determine the probability of creation of pairs of elementary particles by the gravitational field.
This method of using Bogolubov transformations to analyze particle creation by gravitational fields was first introduced by Parker (1965, 1968, 1969, 1971) in the cosmological context. Fulling (1972, 1973) found that the creation and annihilation operators defined in an accelerated coordinate system (known as Rindler coordinates (Rindler 1966)) in Minkowski spacetime were related to the usual Minkowski creation and annihilation operators through a Bogolubov transformation. This was shown by Unruh (1976) to imply that an accelerated particle detector in empty Minkowski spacetime would respond as if it were observing a flux of particles. The particle spectrum corresponding to the Bogolubov transformation of Fulling was a thermal spectrum with a temperature determined by the acceleration (Davies 1975).
Several investigations of particle creation by black holes were also in progress at this time.
2 - Basics of quantum fields in curved spacetimes
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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The successful predictions of general relativity are convincing evidence that gravitational phenomena are most clearly understood by regarding spacetime as curved. In general relativity matter exerts its gravitational influence by curving spacetime, and we study the propagation of particles and waves on this curved background. It is then natural to study the propagation of quantum fields in curved spacetimes in order to search for new effects of gravitation. At this level, the gravitational field itself is not quantized, and the methods of Minkowski spacetime quantum field theory are carried over as much as possible. As we shall see, this modest extension of quantum field theory has turned out to be richer in consequences than we could have anticipated.
Among other things, it gives rise to the physically important processes of particle creation in cosmological and black hole spacetimes. The same amplification process that creates particles in an expanding universe is responsible for creating, in the context of an early inflationary expansion, the primordial fluctuations that are now observed with astonishing accuracy in the cosmic microwave background (CMB) radiation. These same primordial fluctuations also appear responsible for the large-scale structure of the universe. The creation of particles by black holes is necessary for maintaining the second law of thermodynamics in their presence. This process of radiation and evaporation of black holes is an important facet in the fundamental search for a microscopic explanation of the entropy of black holes; a search which appears to be leading to new and exciting physics connecting gravitation and quantum theory.
Preface
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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The success of Einstein's theory of general relativity convincingly demonstrates that the classical gravitational field is a manifestation of the curvature of spacetime. Similarly, quantum field theory in Minkowski spacetime successfully describes the behavior of elementary particles over a wide range of energies. It has proved notoriously difficult to understand how gravity fits with the quantum attribute of the fields that transmit the other forces of nature. Leading attempts to combine gravitation and quantum field theory include string theory and loop quantum gravity. String theory attempts to describe elementary particles, including the graviton, as quantized excitations of systems of strings and D-branes in a higher-dimensional space. Loop quantum gravity attempts to describe the structure of spacetime itself in terms of quantized loops. At energies much below the Planck scale, these theories reduce to descriptions of quantized fields propagating in a curved spacetime having a metric described by Einstein's gravitational field equations with additional higher-order curvature corrections.
Quantum field theory in curved spacetime is the framework for describing elementary particles and gravitation at energies below the Planck scale. This theory has had striking successes. It has shown how gravitation and quantum field theory are intimately connected to give a consistent description of black holes having entropy and satisfying the second law of thermodynamics; and it has shown how the inhomogeneities and anisotropies we observe today in the cosmic microwave background and in the large-scale structure of the universe were created in a brief stage of very rapid expansion of the universe, known as inflation.
6 - The effective action: Non-gauge theories
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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5 - The one-loop effective action
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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- 20 August 2009, pp 184-267
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Summary
Introduction
The main purpose of this chapter is to provide a link between the methods used in previous chapters and the more general methods contained in the following chapters necessary to study interacting fields. These more general methods, which may be applied to a wide class of theories, are based on the background field approach to the effective action. In this chapter we will concentrate on free fields, or fields interacting with background, or external, fields which are not quantized, as we did in the previous four chapters. We will defer the quantization of gauge fields to Chapter 7.
We begin this chapter by presenting the relation between the Schwinger action principle and the Feynman functional, or path, integral for the basic 〈out∣in〉 transition amplitude. Regularization of the one-loop effective action, which is simply related to the in-out transition amplitude, is discussed using a number of popular methods. (Cut-off, dimensional, and ς-function regularization are presented to complement our earlier treatment of regularization in Chapter 3.) Two explicit scalar field examples are given: the Schwinger effective Lagrangian for a constant electromagnetic field in flat Minkowski spacetime and the effective potential for a constant gauge field background in the spacetime ℝn−1 × S1. In these two cases it is possible to calculate an exact result for the effective action. The conformal anomaly for a scalar field, considered earlier in four spacetime dimensions, is analyzed from the Feynman path integral viewpoint.
Frontmatter
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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- 25 January 2011
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- 20 August 2009, pp i-vi
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Index
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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- 25 January 2011
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- 20 August 2009, pp 445-455
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Acknowledgments
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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- 25 January 2011
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- 20 August 2009, pp xiii-xiv
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Contents
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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- 25 January 2011
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- 20 August 2009, pp vii-x
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Appendix: Quantized Inflaton Perturbations
- Leonard Parker, University of Wisconsin, Milwaukee, David Toms, University of Newcastle upon Tyne
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- Quantum Field Theory in Curved Spacetime
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- 25 January 2011
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- 20 August 2009, pp 422-425
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Nonviral gene delivery: techniques and implications for molecular medicine
- Alan L. Parker, Christopher Newman, Simon Briggs, Leonard Seymour, Paul J. Sheridan
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- Expert Reviews in Molecular Medicine / Volume 5 / Issue 22 / 3 September 2003
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- 13 February 2004, pp. 1-15
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Medical research continues to illuminate the origins of many human diseases. Gene therapy has been widely proposed as a novel strategy by which this knowledge can be used to deliver new and improved therapies. Viral gene transfer is relatively efficient but there are concerns relating to the use of viral vectors in humans. Conversely, nonviral vectors appear safe but inefficient. Therefore, the development of an efficient nonviral vector remains a highly desirable goal. This review focuses on the numerous challenges preventing efficient nonviral gene transfer in vivo and discusses the many technologies that have been adopted to overcome these problems.
2 - Vortices
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- By J. M. Lopez, A. D. Perry, P. Koumoutsakos, A. Leonard, M. P. Escudier, G. J. F. Van Heijst, R. C. Kloosterziel, C. W. M. Williams, H. Higuchi, H. Balligand, M. Visbal, G. D. Miller, C. H. K. Williamson, H. Higuchi, F. M. Payne, R. C. Nelson, T. T. Ng, Q. Rahaman, A. Alvarez-Toledo, B. Parker, C. M. Ho, T. Leweke, M. Provansal, D. Ormières, R. Lebescond, J. C. Owen, A. A. Szewczyk, P. W. Bearman, G. J. F. Van Heijst, J. B. Flór, C. Seren, M. V. Melander, N. J. Zabusky, P. Petitjeans, R. Hancock
- M. Samimy, Ohio State University, K. S. Breuer, Brown University, Rhode Island, L. G. Leal, University of California, Santa Barbara, P. H. Steen, Cornell University, New York
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- A Gallery of Fluid Motion
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- 25 January 2010
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- 12 January 2004, pp 11-27
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Summary
Periodic axisymmetric vortex breakdown in a cylinder with a rotating end wall
When the fluid inside a completely filled cylinder is set in motion by the rotation of the bottom end wall, steady and unsteady axisymmetric vortex breakdown is possible. The onset of unsteadiness is via a Hopf bifurcation.
Figure 1 is a perspective view of the flow inside the cylinder where marker particles have been released from an elliptic ring concentric with the axis of symmetry near the top end wall. This periodic flow corresponds to a Reynolds number Re=2765 and cylinder aspect ratio H/R=2.5. Neighboring particles have been grouped to define a sheet of marker fluid and the local transparency of the sheet has been made proportional to its local stretching. The resultant dye sheet takes on an asymmetric shape, even though the flow is axisymmetric, due to the unsteadiness and the asymmetric release of marker particles.When the release is symmetric, as in Fig. 2, the dye sheet is also symmetric. These two figures are snapshots of the dye sheet after three periods of the oscillation (a period is approximately 36.3 rotations of the end wall). Figure 3 is a cross section of the dye sheet in Fig. 2 after 26 periods of the oscillation. Here only the marker particles are shown. They are colored according to their time of release, the oldest being blue, through green and yellow, and the most recently released being red. Comparison with Escudier's experiment shows very close agreement.
The particle equations of motion correspond to a Hamiltonian dynamical system and an appropriate.