Materias:

Materias:

“…In this book some current applications of Quantum Field Theory to those areas of modern physics and mathematics are collected, in order to offer a deeper understanding of known facts and unsolved problems…”

Tabla de Contenidos: “…Introduction -- Dimensional analysis in quantum field theory -- Renormalization as reparametrization -- Non-invariant approximations and the principle of minimal sensitivity -- Induced convergence -- Preliminaries : RG invariance, int-[beta] equation, [lambda with superscript] definition, and CG relation -- Parametization of RS dependence and the [correlation p subscript n] invariants -- Finite orders and optimization -- Solution for the optimized [r subscript m] coefficients and optimization algorithm -- Numerical examples for [R subscript e+e−] in QCD -- Infrared limit : fixed and unfixed points -- Optimization of factorized quantities -- Exploring all-orders OPT in the small-b (BZ) limit…”

Tabla de Contenidos: “…Large orders in perturbation theory; 8. Quantum electrodynamics in 1+1 dimensions; 9. …”

Materias:

Tabla de Contenidos: “…Path integrals in non-relativistic quantum mechanics. Classical field theory. Quantum field theory of a scalar field. …”

Tabla de Contenidos: “…Quantum Brain Dynamics and Quantum Field Theory -- 1. Motivation -- 2. Why Quantum Field Theory? …”

Tabla de Contenidos: “…Ginzburg-Landau effective action for a fluctuating holographic superconductor -- Complex Langevin studies of the emergent spacetime in the type IIB matrix model -- Digital quantum simulation of the Schwinger model with topological term -- Multi-soliton scattering of the anti-self-dual Yang-Mills equations in 4-dimensional split signature -- Aspects of 5D Seiberg-Witten theories on s1 -- Jacobi forms on even positive definite unimodular lattices -- De Sitter duality and holographic renormalization -- Non-invertible topological duality defects in 4-dimensional pure z2 gauge theory -- Conifold transition and matter in non-split models in F-theory -- Entanglement entropy in Schwarzschild spacetime -- Holographic index calculation for Argyres-Douglas and Minahan-Nemeschansky theories -- Topological defect junctions in 4-dimensional pure z2 lattice gauge theory -- Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena -- Entanglement entropy in interacting field theories -- The AdS5 x s5 supercoset sigma model from 4D Chern-Simons theory -- Wall-crossing of TBA equations and WKB periods for the higher order ODE -- Target space entanglement in quantum mechanics of fermions and matrices…”

“…By combining different empirical methods on the same questions, essentially the book sets forth a mixed-method design across chapters, allowing for a more convincing body of evidence per underlying question Some theoretical contributions re-evaluate what has been learned from the experimental and field results about the strengths and weaknesses of the earlier theoretical propositions, and extend the theory in light of these findings…”

“…Beginning with elementary one-loop examples, this book goes on to extend the method to all orders, showing that the pinch technique is equivalent to calculations in the background field Feynman gauge. …”

“…Some of these orderings are routinely used in many applications in economics, finance, insurance, management science, operations research, statistics, and various other fields of study. …”

Tabla de Contenidos: “…3.5 Inclusion of electromagnetic interactions via the gauge principle: the Dirac prediction of g = 2 for the electron -- Problems -- 4 Lorentz Transformations and Discrete Symmetries -- 4.1 Lorentz transformations -- 4.1.1 The KG equation -- 4.1.2 The Dirac equation -- 4.2 Discrete transformations: P, C and T -- 4.2.1 Parity -- 4.2.2 Charge conjugation -- 4.2.3 CP -- 4.2.4 Time reversal -- 4.2.5 CPT -- Problems -- II Introduction to Quantum Field Theory -- 5 Quantum Field Theory I: The Free Scalar Field -- 5.1 The quantum field: (i) descriptive -- 5.2 The quantum field: (ii) Lagrange-Hamilton formulation -- 5.2.1 The action principle: Lagrangian particle mechanics -- 5.2.2 Quantum particle mechanics à la Heisenberg-Lagrange-Hamilton -- 5.2.3 Interlude: the quantum oscillator -- 5.2.4 Lagrange-Hamilton classical field mechanics -- 5.2.5 Heisenberg-Lagrange-Hamilton quantum field mechanics -- 5.3 Generalizations: four dimensions, relativity and mass -- Problems -- 6 Quantum Field Theory II: Interacting Scalar Fields -- 6.1 Interactions in quantum field theory: qualitative introduction -- 6.2 Perturbation theory for interacting fields: the Dyson expansion of the S-matrix -- 6.2.1 The interaction picture -- 6.2.2 The S-matrix and the Dyson expansion -- 6.3 Applications to the 'ABC' theory -- 6.3.1 The decay C A + B -- 6.3.2 A + B A + B scattering: the amplitudes -- 6.3.3 A + B A + B scattering: the Yukawa exchange mechanism, s and u channel processes -- 6.3.4 A + B A + B scattering: the differential cross section -- 6.3.5 A + B A + B scattering: loose ends -- Problems -- 7 Quantum Field Theory III: Complex Scalar Fields, Dirac and Maxwell Fields -- Introduction of Electromagnetic Interactions -- 7.1 The complex scalar field: global U(1) phase invariance, particles and antiparticles -- 7.2 The Dirac field and the spin-statistics connection…”