·Sergei D. Odintsov (ICREA)
·Diego Sáez Gómez (JdC PostDoc)
·Taishi Katsuragawa (PhD Student)
·Luis Gustavo T. Silva (PhD Student)
·Yi Zhong (PhD Student)
·Kerim Demirel (Master Thesis UAB)
·Alejandro Peñuela Díaz (Graduate Thesis UAB)
·Daniel Pérez Cervera (Graduate Thesis UAB)
·David Llorens (Graduate Thesis UAB)
·Aleix Calderón Usán (Graduate Thesis UAB)
·Gloria Garcia Cuadrado (PhD Student)
·Roger Oliva Balagué (PhD Student)
·Antonio Jesús López Revelles (PhD)
·A de la Cruz Dombriz (PostDoc B Pinos)
·Sergey Vernov (PostDoc CPAN)
·Pedro J. Silva (I3P, CSIC)
·Sante Carloni (PostDoc BPinos)
·Pau Amaro Seoane (PostDoc DGICYT)
·Bantipo Kamoua Kolani (Master Thesis UAB)
·Jofre Espigulé (Graduate Thesis UAB)
·Anna Escofet Pacreu (Graduate Thesis UAB)
·Marc Canals (Graduate Thesis UAB)
· Quantum fields in curved space-time
· Black hole structure
· String, brane, M-theory inspired models
· Uses of the renormalization group
· AdS/CFT correspondence and brane worlds
· Quantum vacuum fluctuations, also dynamical effects
· External fields, finite temperature QFT, chemical potentials
· Strong magnetic field effects in cosmology
· Zeta regularization and effective actions in QG
· Early time Universe, inflation
· Dark energy models
· Phantom cosmology, future singularities
· Braneworld cosmology and modified gravity
· Zeta functions of yDOs
· Heat-kernel techniques
· Zeta function regularization, Hadamard regularization
· Determinants, the multiplicative anomaly (or defect)
Zeta-function regularization is a powerful method in perturbation theory. This book is meant as a guide for the student of this subject. Everything is explained in detail, in particular the mathematical difficulties and tricky points, and several applications are given to show how the procedure works in practice (e.g. Casimir effect, gravity and string theory, high-temperature phase transition, topological symmetry breaking, noncommutative spacetime). The formulas some of which are new can be used for physically meaningful, accurate numerical calculations. The book is to be considered as a basic introduction and a collection of exercises for those who want to apply this regularization procedure in practice. This thoroughly revised, updated and expanded edition includes in particular new explicit formulas on the general quadratic, Chowla-Selberg series case, an interplay with the Hadamard calculus, and features a new chapter on recent cosmological applications including the calculation of the vacuum energy fluctuations at large scale in braneworld and other models. TABLE OF CONTENTS: --Introduction and Outlook. --Mathematical Formulas Involving the Different Zeta Functions. --A Treatment of the Non-Polynomial Contributions: Application to Calculate Partition Functions of Strings and Membranes. --Analytical and Numerical Study of Inhomogeneous Epstein and Epstein-Hurwitz Zeta Functions. --Physical Application: the Casimir Effect. --Five Physical Applications of The Inhomogeneous Generalized Epstein-Hurwitz Zeta Functions. --Miscellaneous Applications Combinig Zeta With Other Regularization Procedures. --Applications to Gravity, Strings and P-Branes.- Eleventh Application: Topological Symmetry Breaking in Self-Interacting Theories. --Twelth Application: Cosmology and The Quantum-Vacuum. --References. --Index.
Some major developments of physics in the last three decades are addressed by highly qualified specialists in different specific fields. They include renormalization problems in QFT, vacuum energy fluctuations and the Casimir effect in different configurations, and a wealth of applications. A number of closely related issues are also considered. The cosmological applications of these theories play a crucial role and are at the very heart of the book; in particular, the possibility to explain in a unified way the whole history of the evolution of the Universe: from primordial inflation to the present day accelerated expansion. Further, a description of the mathematical background underlying many of the physical theories considered above is provided. This includes the uses of zeta functions in physics, as in the regularization problems in QFT already mentioned, specifically in curved space-time, and in Casimir problems. The papers have been grouped into three main areas: Quantum field theory (QFT) and the Casimir effect, Gravity and Cosmology, and Zeta functions in Physics and Mathematics. Written by highly qualified specialists in the different specific fields, they cover some major developments of Physics in the last three decades and a wealth of applications. A number of closely related issues are also considered, such as the nature of dark energy, modified gravity models (f(R) and Gauss-Bonnet, for example), Horava-Lifshitz gravity, and a couple of non-standard approaches. The cosmological applications of these theories play a crucial role and are at the very heart of the book. In particular, the possibility to explain in a unified way the whole history of the evolution of the Universe, from primordial inflation to accelerated expansion, one of the landmark discoveries of the last century. Further, a nice and rigorous description of the mathematical background underlying many of the physical theories considered above is provided. This includes the uses of zeta functions in physics, as in the regularization problems in QFT already mentioned, specifically in curved space-time, and in Casimir problems as, e.g., those involving pistons, which are now very fashionable. The prerequisites to read this book are some good background knowledge of quantum physics, relativity, and basic functional analysis. Many of the articles give a detailed description of their subject and they try to be as pedagogical as possible.
On March 8, 2010, Professor Emilio Elizalde Rius, a renowned Spanish and Catalan scientist in the area of mathematical physics, quantum field theory and cosmology, is celebrating his sixtieth birthday. This special volume contains a selected collection of his more important articles written during the last thirty years. It is quite natural that such a book is being edited by Tomsk State Pedagogical University (TSPU). Professor Emilio Elizalde (ICE, CSIC-IEEC, Barcelona) has been collaborating very intensively with mathematical physics/cosmology researchers from Tomsk State Pedagogical University during the last twenty years. In total he has published more than one hundred papers written together with TSPU professors. Among his collaborators one can count the leaders of the aforementioned theoretical physics directions: Prof. V.V. Obukhov (General Relativity and Mathematical Physics), Prof. S.D. Odintsov (Cosmology and Quantum Gravity), Prof. K.E. Osetrin (General Relativity and Mathematical Physics) as well as several other professors of TSPU. The scientific relations between TSPU and ICE-IEEC were developed to a very high level during the last years. There was established a cooperation agreement between ICE-IEEC, Barcelona and TSPU, Tomsk. Our students and professors are often guests of ICE-IEEC, Barcelona. A number of common conferences has been organized. Moreover, Professor Emilio Elizalde is nominated to become honorary professor of TSPU in 2010. The research activity by Emilio Elizalde is very wide, as one can see from his brief CV attached at the end of this volume as well as from his publications list. He has got a number of fundamental results in zeta-regularization techniques (where three monographs are published), mathematical physics, observational and theoretical cosmology, quantum gravity and quantum field theory. We are proud of the fact that some of these fundamental results have been obtained together with his Tomsk colleagues. Needless to say that on his 60th birthday Prof. Emilio Elizalde is extremely active in research, publishing a dozen of scientific papers a year. This definitely means that we can expect a lot more brilliant results from him in the future. TSPU presents this special volume to Emilio as a gift on his 60th anniversary. All his Tomsk friends and colleagues wish him excellent health for many years to come and even more fundamental scientific achievements. Prof. V.V. Obukhov and Prof. S.D. Odintsov, Editors.
· Riemann and Related Zeta Functions
· Zeta-Function Regularization of Sums Over Known Spectrum
· Zeta Function Regularization Generalized
· The Casimir Effect in Flat Spacetime
· Heat-Kernel and Zeta-Function Regularization Techniques in the Theory of Quantum Fields on Hyperbolic Space
· Quantum Properties of Extended Objects
· Finite-Temperature Effects in Quantum Field Theory
· String Theory at Non-Zero Temperature
· Covariant Effective in 2D Gravity
· Calculation of Heat-Kernel Coefficients
Zeta-function regularization is a powerful method in perturbation theory. This book is meant as a guide for the student of this subject. Everything is explained in detail, in particular the mathematical difficulties and tricky points, and several applications are given to show how the procedure works in practice (e.g. Casimir effect, gravity and string theory, high-temperature phase transition, topological symmetry breaking). The formulas some of which are new can be used for accurate numerical calculations. The book is to be considered as a basic introduction and a collection of exercises for those who want to apply this regularization procedure in practice.
One of the aims of this book is to explain in a basic manner the seemingly difficult issues of mathematical structure using some specific examples as a guide. In each of the cases considered, a comprehensible physical problem is approached, to which the corresponding mathematical scheme is applied, its usefulness being duly demonstrated. The authors try to fill the gap that always exists between the physics of quantum field theories and the mathematical methods best suited for its formulation, which are increasingly demanding on the mathematical ability of the physicist.
Stuart Dowker is known, among different things, for his many applications in the context of zeta function regularization and its applications to quantum field theory under external conditions and spectral theory. He can be considered the world expert on particular case calculations with a knowledge of the literature, old and recent, that is not seen very often and which originated in the many hours spent at different (mostly British) libraries. His attitude towards explicit computations is nicely summarized by himself: 'I have always been interested in exact solutions, even if unphysical, so long as they are pretty. They seem to be working mechanisms that fit together, complete in themselves, like a watch.' This issue in honour of Stuart's 75th birthday contains contributions that touch upon the various topics he has worked on. Eds. Fay Dowker, Emilio Elizalde and Klaus Kirsten (IOP, London, 2012); DOI:10.1088/1751-8113/45/37/370301.
This volume contains the Proceedings of the 10th International Conference on Quantum Field Theory Under the Influence of External Conditions (QFEXT11) held at the Pedro Pascual Science Center in Benasque (Spain), 18–24 September 2011. The series of Workshops on Quantum Field Theory Under the Influence of External Conditions was started in 1989 by D. Robaschik and continued since 1995 by M. Bordag. The meetings have taken place mainly in Leipzig (1995, 1998, 2001, 2007), but also in Oklahoma (2003, 2009) and Barcelona (2005). One hundred and six leading scientists and junior researchers attended the Conference held in Benasque. Most of the world leading specialists on the subjects discussed participated in the meeting and presented new developments. The conference focussed on the following topics: 1. Casimir and van der Waals forces; theoretical and experimental aspects, with applications at the nanoscale. 2. Quantum vacuum effects in quantum field theory, with applications to particle physics, condensed matter physics, laser and atomic physics. 3. Quantum field theory in strong external fields and in curved space-time. 4. Vacuum energy in gravity, cosmology and astrophysics. 5. Mathematical physics techniques for quantum vacuum studies. The QFEXT11 conference also helped to broaden the interest of Spanish groups working on quantum field theory under background fields and cosmology. In particular, the conference pointed out the existence of a large Spanish community working on these topics. As a result, some more Spanish scientists have newly joined the Casimir European Network. A special session was devoted to analyse recent progress on the line of the seminal work by Euler and Heisenberg on the occasion of the 75th anniversary of their highly influential paper. Another session was devoted to Stuart Dowker for his important contributions to the development of the field, in special through zetafunction regularization. During the Conference especial attention was paid to junior researchers and their oral or poster presentations. Eds. M. Asorey, M. Bordag, and E. Elizalde (World Sci., Singapore, 2012). DOI: http://dx.doi.org/10.1142/S2010194512007726.
On April 7, 2009 Professor Iver Hakon Brevik, a world-known norwegian scientist in the area of theoretical physics and hydrodynamics, celebrated his seventieth birthday. This special volume represents the collection of articles devoted mainly to Casimir effect and Cosmology and written by his friends and colleagues who wish to pay tribute to this remarkable event. The research activity by Iver Brevik is very wide, however, this volume is devoted to only two of the several research directions by Iver Brevik: Casimir Effect and Cosmology. Prof. I.H. Brevik is still very active in science, especially in cosmology and Casimir effect at non-zero temperature. The editors and contributors presented this special volume to Iver as a gift on his 70th anniversary. Eds. S.D. Odintsov, E. Elizalde and O. Gorbunova (Ed. TSPU, Russia, 2009) ISBN 978-5-89428-415-6.
By kind agreement of the participants of the workshop QFEXT03, which took place in Oklahoma, USA in September 2003, I was commissioned to organize the seventh workshop on ‘Quantum Field Theory under the Influence of External Conditions’ (QFEXT05), in Barcelona, Spain. This was the follow-up meeting of a series of international workshops that started in 1989 in Leipzig. This workshop provided a unique opportunity to bring together scientists from eastern and western Europe, in numbers necessary to initiate serious collaborative work. Its success was due as much to the appropriateness of the location as to the friendly atmosphere generated. During the intervening years we witnessed the sudden changes experienced in eastern Europe with the fall of the Berlinwall and the emergence of a new European conscience and scientific society. I would like to recall that the subject of these meetings has always had much to do with the seminal contributions of the late Professor Hendrik Casimir to physics, in particular with the increasingly important Casimir effect (observable manifestations of the fluctuations of the quantum vacuum). Professor Casimir himself participated in some of the meetings, the last time just before his death. I had been corresponding with him during those last months about the possibility of him coming to Barcelona, but unfortunately there was no time to realize this visit. Now that finally the workshop took place here I felt I owed him this remembrance. I keep as a treasure a dedicated copy of one of his books. Both at terrestrial and at cosmological level the importance of quantum vacuum fluctuations is growing at a very fast pace. Over the last few years measurements of the Casimir force have attained high precision and applications in nanotechnology—hybrid devices integrating carbon nanotubes and their mass production, for instance—are important tasks for the near future. Actual progress in these fields is quickly reaching the standard of technological applications. The state of the art in these subjects is covered in the present proceedings, as reported at large at the Barcelona meeting QFEXT05. Moreover, at the cosmological scale, vacuum fluctuations have the potential to give rise to a simple and most natural explanation of the recently observed acceleration in the expansion of the Universe. More results, both at the theoretical and observational level, are needed in order to confirm such a possibility, which is explored in some of the papers here. E. Elizalde and S.D. Odintsov, Guest Editors.
These lectures were addressed to non-specialists willing to learn some basic facts, approaches, tools and observational evidence which conform modern cosmology. The aim is also to try to complement the many excellent treatises that exists on the subject (an exhaustive treatment being in any case impossible for lack of time, in the lectures, and of space here), instead of trying to cover everything in a telegraphic way. We start by recalling in the introduction a couple of philosophical questions that have always upset inquiring minds. We then present some original mathematical approaches to investigate a number of basic questions, as the comparison of two point distributions (each point corresponding to a galaxy or galaxy cluster), the use of non-standard statistics in the analysis of possible non-Gaussianities, and the use of zeta regularization in the study of the contributions of vacuum energy effects at the cosmological scale. And we also summarize a number of important issues which are both undoubtedly beautiful (from the physical viewpoint) and useful in present-day observational cosmology. To finish, the reader should be warned that, for the reasons already given and lack of space, some fundamental issues, as inflation, quantum gravity and string theoretical fundamental approaches to cosmology will not be dealt with here. A minimal treatment of any of them would consume more pages than the ones at disposal and, again, a number of excellent treatments of these subjects are available.
May 18, 2016