Quantum Field Theory for MathematiciansTicciati's approach to quantum field theory falls between building a mathematical model of the subject and presenting the mathematics that physicists actually use. It begins with the need to combine special relativity and quantum mechanics and culminates in a basic understanding of the standard model of electroweak and strong interactions. The book is divided into five parts: canonical quantization of scalar fields, Weyl, Dirac and vector fields, functional integral quantization, the standard model of the electroweak and strong interactions, renormalization. This should be a useful reference for those interested in quantum theory and related areas of function theory, functional analysis, differential geometry or topological invariant theory. |
Contents
1 Relativistic Quantum Mechanics | 1 |
2 Fock Space the Scalar Field and Canonical Quantization | 13 |
3 Symmetries and Conservation Laws | 36 |
4 From Dysons Formula t o Feynman Rules | 79 |
5 Differential Transition Probabilities and Predictions | 121 |
6 Representations of the Lorentz Group | 136 |
7 TwoComponent Spinor Fields | 166 |
8 FourComponent Spinor Fields | 207 |
14 SU3 Representation Theory | 438 |
15 The Structure of the Standard Model | 454 |
16 Hadrons Flavor Symmetry and NucleonPion Interactions | 480 |
17 TreeLevel Applications of the Standard Model | 507 |
18 Regular izat ion and Re normalization | 532 |
Three Primitive Divergences | 564 |
20 Renormalization and Preservation of Symmetries | 596 |
21 The Renormalization Group Equations | 631 |
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Common terms and phrases
action amplitude annihilation operators anomaly apply axial baryon basis bosons canonical quantization Chapter charge conjugation classical coefficients compute conserved quantity counterterm coupling covariant decay defined definition derivative differential dimensional regularization Dirac algebra divergent energy equations of motion evaluate example external lines factor Faddeev-Popov Fermi fields fermions Feynman diagrams Feynman integrals Feynman rules finite functional integral functional integral quantization gauge fields gauge group gauge invariance gauge theories Green functions hadrons Hamiltonian Hence hermitian Homework integrand Lagrangian density lepton Lie algebra linear loop Lorentz group mass term massless matrix element momenta momentum parameters parity particle photon polarization spinors propagator quantum numbers quarks renormalization conditions representation scalar field scattering tensor product Theorem transformation unitary vacuum variables vector field vector space vertex Weyl spinors Wick diagram zero µ²