“…The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. Although a great variety of methods for evaluating Feynman integrals has been developed over a span of more than fifty years, this book is a first attempt to summarize them. …”
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“…This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. …”
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“…We give a simple argument showing that in any sensible quantum field theory the masses of black holes cannot assume continuous values and must be quantized. …”
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“…Its computation has been made feasible through the development of the on-shell approach to perturbative quantum field theory. We present the total cross section for pp collisions at sqrt{s} = 7 TeV, after folding in the decay of the Z boson, or virtual photon, to a charged-lepton pair. …”
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“…Feynman integrals are central to all calculations in perturbative Quantum Field Theory. They often give rise to iterated integrals of $d\log$-forms with algebraic arguments, which in many cases can be evaluated in terms of multiple polylogarithms. …”
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“…We first revisit impact-parameter dependent collisions of ultra-relativistic particles in quantum field theory. Two conditions sufficient for defining an impact-parameter dependent cross section are given, which could be violated in proton-proton collisions. …”
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“…For more than half a century, covariant and differential geometric methods have been playing a central role in the development of Quantum Field Theory (QFT). After a brief historic overview of the major scientific achievements using these methods, we will focus on the covariant and differential geometric formalism originally proposed by Vilkovisky and DeWitt (VDW). …”
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“…Keywords: Automata Theory/ Sequential Machines, Bioinformatics, Complex Biological Systems, Complex Systems Biology, Computer Simulations and Modeling, Dynamical Systems , Quantum Dynamics, Quantum Field Theory, Quantum Groups,Topological Quantum Field Theory (TQFT), Quantum Automata, Quantum Dots, Cognitive Systems, Graph Transformations, Logic, Mathematical Modeling; applications of the Theory of Categories, Functors and Natural Transformations; pushouts, pullbacks, presheaves, sheaves, Categories of sheaves, Topos, n-valued Logic, N-categories/ higher dimensional algebra, Homotopy theory; applications to quantum field theories, quantum gravity, complex systems biology, bioengineering, informatics, Bioinformatics, Computer simulations, Mathematical Biology of complex systems and phenomena in various types of Dynamical Systems; bioengineering, Computing, Neurosciences, Bioinformatics, biological and/or social networks; quantitative ecology and quantitative biology/…”
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“…This redefinition becomes especially important in high-energy quantum regimes and quantum field theory and allows this article to define a new concept of quantum field. …”
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“…According to quantum field theory, empty space—the ground state with all real excitations removed—is not empty, but filled with quantum-vacuum fluctuations. …”
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“…Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. …”
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“…The $S$-matrix of a quantum field theory is unchanged by field redefinitions, and so only depends on geometric quantities such as the curvature of field space. …”
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“…Starting with the hadron spectrum, the reader becomes familiar with the representations of SU(N). Relativistic quantum field theory is recapitulated, and scattering theory is discussed in the framework of scalar quantum electrodynamics. …”
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“…The introduction of new material, and modification of existing material, appears in a way that better prepares the student for the next course in quantum field theory. You will still find such classic developments as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell’s inequality. …”
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“…This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics-- such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics-- and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. …”
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“…Streamlined content, chapters on semiconductors, Dirac equation and quantum field theory, as well as a robust pedagogy and ancillary package, including an accompanying website with computer applets, assist students in learning the essential material. …”
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“…--HTML-->Scale anomalies are present in conformal field theory very much like in any other quantum field theory. The anomaly coefficients in a CFT are numbers, known to "count the degrees of freedom" of the theory. …”
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“…With string theory being a multidisciplinary field interfacing with high energy physics, mathematics and quantum field theory, this book is ideal for both students with no previous knowledge of the field and scholars from other disciplines who are looking for an introduction to basic concepts.…”
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“…It aims to deliver a unique combination of classical and quantum field theory in one compact course.…”
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