
An Introduction to NonPerturbative Foundations of Quantum Field Theory
Franco Strocchi

Últimas novedades física cuántica física general

Quantum Field Theory (QFT) has proved to be the most useful strategy for the description of elementary particle interactions and as such is regarded as a fundamental part of modern theoretical physics. In most presentations, the emphasis is on the effectiveness of the theory in producing experimentally testable predictions, which at present essentially means Perturbative QFT. However, after more than fifty years of QFT, we still are in the embarrassing situation of not knowing a single nontrivial (even nonrealistic) model of QFT in 3+1 dimensions, allowing a nonperturbative control. As a reaction to these consistency problems one may take the position that they are related to our ignorance of the physics of small distances and that QFT is only an effective theory, so that radically new ideas are needed for a consistent quantum theory of relativistic interactions (in 3+1 dimensions).
The book starts by discussing the conflict between locality or hyperbolicity and positivity of the energy for relativistic wave equations, which marks the origin of quantum field theory, and the mathematical problems of the perturbative expansion (canonical quantization, interaction picture, nonFock representation, asymptotic convergence of the series etc.). The general physical principles of positivity of the energy, Poincare’ covariance and locality provide a substitute for canonical quantization, qualify the nonperturbative foundation and lead to very relevant results, like the Spinstatistics theorem, TCP symmetry, a substitute for canonical quantization, noncanonical behaviour, the euclidean formulation at the basis of the functional integral approach, the nonperturbative definition of the Smatrix (LSZ, HaagRuelleBuchholz theory).
A characteristic feature of gauge field theories is Gauss’ law constraint. It is responsible for the conflict between locality of the charged fields and positivity, it yields the superselection of the (unbroken) gauge charges, provides a nonperturbative explanation of the Higgs mechanism in the local gauges, implies the infraparticle structure of the charged particles in QED and the breaking of the Lorentz group in the charged sectors.
A nonperturbative proof of the Higgs mechanism is discussed in the Coulomb gauge: the vector bosons corresponding to the broken generators are massive and their two point function dominates the Goldstone spectrum, thus excluding the occurrence of massless Goldstone bosons.
The solution of the U(1) problem in QCD, the theta vacuum structure and the inevitable breaking of the chiral symmetry in each theta sector are derived solely from the topology of the gauge group, without relying on the semiclassical instanton approximation.
Readership : Suitable for graduate students and researchers in theoretical and mathematical physics.

indíce 
1. Relativistic quantum mechanics 2. Mathematical problems of the perturbative expansion 3. Nonperturbative foundations of quantum eld theory 4. General nonperturbative results and examples 5. Euclidean quantum eld theory 6. Nonperturbative Smatrix 7. Quantization of Gauge Field Theories 8. Chiral symmetry breaking and vacuum structure in QCD There are no Instructor/Student Resources available at this time. Franco Strocchi is Senior Research Fellow at INFN. He received his Laurea in Physics at the University of Pisa and Diploma in Physics at Scuola Normale Superiore, Pisa (1961). He has taught as Professor of Theoretical Physics at SISSA, Trieste (19831994), and as Professor of Theoretical Physics at Scuola Normale Superiore (19942009). His main research interests include the theory of quantized fields and spontaneous breaking of symmetries.
Making Sense  Margot Northey and Joan McKibbin Introduction to 3+1 Numerical Relativity  Miguel Alcubierre Quantum Gravity  Dr. Claus Kiefer Supersymmetry  Pierre Binetruy
Special Features
Provides general physical principles and a mathematically sound approach to QFT.Covers the general structure of gauge theories.Presents the charge superselection rules.Gives a nonperturbative treatment of the Higgs mechanism.Covers chiral symmetry breaking in QCD without instantons.


