A01=Giovanni Gallavotti
A01=Giuseppe Benfatto
Absolute value
Almost surely
Approximation
Asymptotic analysis
Asymptotic freedom
Author_Giovanni Gallavotti
Author_Giuseppe Benfatto
Auxiliary field
Beta function
Big O notation
Bose gas
Boundary problem (spatial analysis)
Calculation
Category=PDE
Category=PH
Coefficient
Conjecture
Constant term
Convergence of Fourier series
Creation and annihilation operators
Critical dimension
Critical exponent
Critical point (mathematics)
Cumulant
Effective potential
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
Equation
Exponential function
Fermi liquid theory
Fermi surface
Fermi-Dirac statistics
Formal power series
Free parameter
Functional integration
Gauge theory
Gaussian integral
Gaussian measure
Grassmannian
Harmonic analysis
Holomorphic function
Hubbard model
Instability
Integration by parts
Iteration
Kosterlitz-Thouless transition
Length scale
Linear approximation
Linear combination
Linear map
Linearization
Mathematical physics
Mean field theory
Monomial
Perturbation theory
Perturbation theory (quantum mechanics)
Polynomial
Power series
Probability measure
Projection (linear algebra)
Propagator
Proportionality (mathematics)
Quantum field theory
Random field
Renormalization
Renormalization group
Scale parameter
Schwinger function
Scientific notation
Series expansion
Stable manifold
Taylor series
Theory
Total derivative
Triviality (mathematics)
Variable (mathematics)
Product details
- ISBN 9780691044460
- Weight: 227g
- Dimensions: 197 x 254mm
- Publication Date: 30 Jul 1995
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
Giuseppe Benfatto is Professor of Mathematical Physics at the University of Rome-Tor Vergata, and Giovanni Gallavotti is Professor of Rational Mechanics at the University of Rome-La Sapienza.
