Renormalization Group (eBook)

Giuseppe Benfatto, Giovanni Gallavotti (Autoren)

eBook Download: PDF

2020
140 Seiten
Princeton University Press (Verlag)
978-0-691-22169-4 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 10.11.2020
• Reihe/Serie: Physics Notes
• Reihe/Serie: Physics Notes
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Schlagworte: absolute value • Almost surely • Anomalous dimension • Approximation • asymptotic analysis • asymptotic freedom • Auxiliary field • Beta function • Beta function (physics) • Big O notation • Bose Condensation • Bose–Einstein condensate • Bose Gas • Boundary problem (spatial analysis) • Calculation • Characteristic function (probability theory) • chemical potential • coefficient • Complex conjugate • Computation • conjecture • Constant term • Convergence of Fourier series • Convergent series • Creation and annihilation operators • Critical dimension • critical exponent • Critical point • Critical point (mathematics) • Cumulant • Derivative • Determinant • Dimension • Dimensional potential • Dimension (vector space) • effective potential • Eigenvalues and Eigenvectors • Equation • Euclidean field • exponential function • Fermi–Dirac statistics • Fermi Gas • Fermi liquid • Fermi Liquid Theory • Fermi surface • Feynman Graph • Formal power series • Fourier transform • Free parameter • functional integration • Gauge Theory • Gaussian integral • Gaussian measure • Generating functional • Grassmannian • Grassmannian variable • ground state • Hadamard inequality • Harmonic Analysis • hilbert space • holomorphic function • Hubbard Model • Infrared problem • instability • Integration by parts • Irrelevant part • Ising Model • Iteration • Kernel • Kondo effect • Kosterlitz–Thouless transition • Landau-Ginsburg model • length scale • Linear Approximation • Linear combination • Linearity • Linearization • Linear map • localization operator • many-body theory • Marginal operator • Mathematical Physics • Mean field theory • Monomial • Normal critical behavior • Oscillation • Periodic boundary conditions • Permutation • perturbation theory • Perturbation theory (quantum mechanics) • polynomial • power law • power series • probability measure • Projection (linear algebra) • Propagator • Propagator matrix • Proportionality (mathematics) • Quantity • quantum field theory • quantum mechanics • Random field • Recursion (computer science) • Renormalizable theory • renormalization • Renormalization Group • Scale Parameter • Schwinger function • scientific notation • Semigroup • Series expansion • stable manifold • Statistical Physics • Superfluid behavior • Taylor series • tensor product • theoretical physics • theory • Total derivative • Tree formalism • Triviality (mathematics) • Ultraviolet problem • Variable (mathematics) • Wick monomial
• ISBN-10: 0-691-22169-3 / 0691221693
• ISBN-13: 978-0-691-22169-4 / 9780691221694