“…Laying a basis for our analysis, we first show how the conventional quantisation of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. …”
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“…On the other hand, ideas from string theory and quantum field theory have been a source of significant inspirations to reveal surprising mathematical structures and create new spectrums of mathematics. …”
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“…Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. …”
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“…--HTML-->Recent advances in Hamiltonian truncation have demonstrated it to be a useful tool for obtaining nonperturbative information about quantum field theories, even in the strongly-coupled regime. …”
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“…Over the last several years, the author and his colleagues have developed new, innovative methods for the exact analysis of a variety of spectral functions occurring in spectral geometry and under external conditions in statistical mechanics and quantum field theory. Spectral Functions in Mathematics and Physics presents a detailed overview of these advances. …”
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“…Computations in perturbative Quantum Field Theory (pQFT) feature several aspects which, although intrinsically non-physical, are traditionally successfully eluded by modifying the dimensions of the space-time. …”
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“…In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of quaternions used mainly in the quantum field theory. We apply this tool to speed up algorithms counting subgraphs parameterized by the treewidth of a graph. …”
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“…This paper discusses the empirical evidence and the ideas behind the Lifshitz theory of the cosmological constant without requiring prior knowledge of cosmology and quantum field theory. This article is part of a discussion meeting issue ‘The next generation of analogue gravity experiments’.…”
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“…The Renormalization Group (RG) is a set of methods that have been instrumental in tackling problems involving an infinite number of degrees of freedom, such as, for example, in quantum field theory and critical phenomena. What all these methods have in common—which is what explains their success—is that they allow a systematic search for those degrees of freedom that happen to be relevant to the phenomena in question. …”
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“…Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the state of which is described by a probability distribution. …”
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“…An effort has been made to provide a self-contained exposition of a restricted amount of material at the appropriate level of rigour which at the same time is accessible to graduate students with only basic knowledge of general relativity and quantum field theory on Minkowski space.…”
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“…Specializing in the theoretical physics of elementary particles, quantum field theory and astrophysics, Prof. Basdevant works in the Leprince-Ringuet Laboratory at the Ecole Polytechnique.…”
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“…The first volume on particles, fields, and quantum electrodynamics covers: The mathematical foundation of quantum field theory The interactions and particles of the Standard Model How accelerators, detectors, and neutrino telescopes are used in particle physics experiments The technique of renormalization in quantum electrodynamics The second volume on the Standard Model and beyond discusses: The technique of renormalization in quantum chromodynamics (QCD) The status of current QCD experiments Physics beyond the Standard Model, including composite models and a left-right model How solar and atmospheric neutrinos are detected and analyzed The books in this two-volume set enable readers not only to perform complicated and skilled calculations, but also to propose and elaborate new theories. …”
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“…Mechanics is one of the oldest and at the same time newest disciplines, in the sense that there are methods and principles developed first in mechanics but now widely used in almost all branches of physics: electrodynamics, quantum mechanics, classical and quantum field theory, special and general theory of relativity, etc. …”
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“…Last but not least, an important new theoretical tool that will be revisited and which made much of the progress surveyed in this book possible is the holographic principle - the correspondence between quantum field theory and gravity in extra dimensions. Edited and authored by the pioneers and leading experts in this newly emerging field, this book offers a valuable resource for a broad community of physicists and graduate students.…”
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“…This a book is for those who would like to learn something about special and general relativity beyond the usual textbooks, about quantum field theory, the elegant Fock-Schwinger-Stueckelberg proper time formalism, the elegant description of geometry by means of Clifford algebra, about the fascinating possibilities the latter algebra offers in reformulating the existing physical theories, and quantizing them in a natural way. …”
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“…Yet, paradoxically, its mathematical description resembles quantum field theory. The present book addresses the idealised problem posed by homogeneous, isotropic turbulence, in order to concentrate on the fundamental aspects of the general problem. …”
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“…In addition to providing a fundamental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and abstract algebra, topology and geometry, and real and complex analysis.…”
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“…--HTML-->The Two-Particle-Irreducible (2PI) formalism as introduced by Cornwall, Jackiw and Tomboulis provides a systematic analytic approach to consistently describing non-perturbative phenomena in Quantum Field Theory. In spite of its great success, one major problem of the 2PI approach is that its loopwise expansion gives rise to residual violations of symmetries and hence to massive Goldstone bosons in the spontaneously broken phase of the theory. …”
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