Leseprobe
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Renormalization Group
Giovanni Gallavotti, Giuseppe Benfatto
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Naturwissenschaften, Medizin, Informatik, Technik / Physik, Astronomie
Beschreibung
Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems.
The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties.
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Kosterlitz–Thouless transition, Gaussian measure, Hubbard model, Boundary problem (spatial analysis), Triviality (mathematics), Propagator, Mean field theory, Scale parameter, Functional integration, Length scale, Almost surely, Series expansion, Instability, Equation, Integration by parts, Quantum field theory, Formal power series, Effective potential, Cumulant, Stable manifold, Linear map, Variable (mathematics), Calculation, Gauge theory, Beta function, Big O notation, Free parameter, Fermi surface, Holomorphic function, Perturbation theory (quantum mechanics), Critical point (mathematics), Constant term, Asymptotic freedom, Total derivative, Projection (linear algebra), Random field, Convergence of Fourier series, Monomial, Taylor series, Auxiliary field, Exponential function, Linear combination, Power series, Polynomial, Scientific notation, Mathematical physics, Absolute value, Gaussian integral, Probability measure, Renormalization group, Bose gas, Conjecture, Iteration, Critical dimension, Proportionality (mathematics), Asymptotic analysis, Fermi liquid theory, Theory, Coefficient, Approximation, Harmonic analysis, Linear approximation, Creation and annihilation operators, Renormalization, Grassmannian, Fermi–Dirac statistics, Perturbation theory, Linearization, Critical exponent, Schwinger function