\contentsline {section}{\numberline {0}Preface}{2}{section.2}
\contentsline {section}{\numberline {1}September 23}{7}{section.4}
\contentsline {subsection}{Units; Translational invariance, Rotational invariance and Lorentz invariance for a single free particle.}{7}{section*.3}
\contentsline {section}{\numberline {2}September 25}{14}{section.6}
\contentsline {subsection}{Position operator; Violation of Causality; Pair Production; Fock Space; Occupation number representation; SHO; Oscillator-like formalism for Fock space.}{14}{section*.14}
\contentsline {section}{\numberline {3}September 30}{21}{section.8}
\contentsline {subsection}{Causality, observables and quantum fields; Constructing the quantum field from Fock space operators axiomatically; Translational invariance; Lorentz invariance and Relativistic normalization; Field constructed satisfies Klein-Gordon equation.}{21}{section*.19}
\contentsline {section}{\numberline {4}October 2}{28}{section.10}
\contentsline {subsection}{Constructing Fock space from the quantum field axiomatically; The Method of the Missing Box, Classical Particle Mechanics, Quantum Particle Mechanics, Classical Field Theory, Quantum Field Theory; Quantum field from free scalar theory.}{28}{section*.20}
\contentsline {section}{\numberline {5}October 7}{38}{section.12}
\contentsline {subsection}{Hamiltonian recovered in free scalar theory up to infinite constant; Normal ordering; Symmetries and conservation laws, Noether's theorem; Noether's theorem in field theory, conserved currents; ambiguity in currents; Energy-momentum tensor.}{38}{section*.29}
\contentsline {section}{\numberline {6}October 9}{49}{section.14}
\contentsline {subsection}{Lorentz transformations; Angular momentum conservation; Internal symmetries; $SO(2)$ internal symmetry; Charged field; $SO(n)$ internal symmetry.}{49}{section*.37}
\contentsline {section}{\numberline {7}October 14}{58}{section.16}
\contentsline {subsection}{Lorentz transformation, properties of conserved quantities; Discrete symmetries; $\phi \rightarrow -\phi $; Charge conjugation; Parity; Ambiguity of choice of parity; Time reversal; Unitary and anti-unitary operators, angular momentum; Dilatations.}{58}{section*.40}
\contentsline {section}{\numberline {8}October 16}{70}{section.18}
\contentsline {subsection}{Scattering theory overview; Low budget scattering theory; Turning on and off function; Schr\"odinger picture, Heisenberg picture and interaction picture; Evolution operator; Time ordered product; Three models; Wick's theorem.}{70}{section*.48}
\contentsline {section}{\numberline {9}October 21}{83}{section.20}
\contentsline {subsection}{Diagrammatic perturbation theory in Model 3; Vertex in model 1; Connected diagrams; Thm: $\DOTSB \sum@ \slimits@ $ all Wick diagrams = $:e^{\DOTSB \sum@ \slimits@ \text {connected Wick diagrams}}:$; Model 1 solved; Model 2 begun.}{83}{section*.57}
\contentsline {section}{\numberline {10}October 23}{93}{section.22}
\contentsline {subsection}{Model 2 finished; Vacuum energy c.t.; $S$ matrix is 1; Ground state energy; Yukawa potential; Ground state wave function; Model 3 and Mass renormalization; Renormalized perturbation theory.}{93}{section*.61}
\contentsline {section}{\numberline {11}October 28}{103}{section.24}
\contentsline {subsection}{Feynman diagrams in Model 3; Feynman rules in model 3; A catalog of all Feynman diagrams in model 3 to $\mathcal {O}(g^2)$; Scattering amplitude at $\mathcal {O}(g^2)$; Direct and exchange Yukawa potentials.}{103}{section*.67}
\contentsline {section}{\numberline {12}October 30}{112}{section.26}
\contentsline {subsection}{``Nucleon''-anti``nucleon'' scattering at $\mathcal {O}(g^2)$; Energy eigenstate probe; Meson-``nucleon'' scattering; ``Nucleon''-anti``nucleon'' annihilation; Assembling the amplitudes for various processes into one amplitude; Mandelstam variables; Mandelstam-Kibble plot; crossing symmetry; CPT; Phase space and the $S$ matrix; $\frac {\text {Differential tran. prob.}}{\text {unit time}}$.}{112}{section*.70}
\contentsline {section}{\numberline {13}November 4}{131}{section.28}
\contentsline {subsection}{Applications of $\frac {\text {Differential tran. prob.}}{\text {unit time}}$; Decay; Cross sections, flux; Final state phase space simplified for two bodies; $\frac {d\sigma }{d\Omega }$; Optical theorem; Final state phase space for three bodies; Feynman diagrams with external lines off the mass shell; they could be an internal part of a larger diagram.}{131}{section*.77}
\contentsline {section}{\numberline {14}November 6}{144}{section.30}
\contentsline {subsection}{Fourier transform of the new blob; A second interpretation of Feynman diagrams with lines off the mass shell; they are the coefficients of $\rho ^n$ in $\delimiter "426830A 0|S|0\delimiter "526930B _\rho $; A third interpretation of the blob; they are the Fourier transform of the VEV of a string of Heisenberg fields; Reformulation of scattering theory; $S$ matrix elements without the turning on and off function; LSZ formula stated.}{144}{section*.89}
\contentsline {section}{\numberline {15}November 13}{163}{section.32}
\contentsline {subsection}{LSZ formula proved; A second look at Model 3 and its renormalization; Renormalization conditions.}{163}{section*.100}
\contentsline {section}{\numberline {16}November 18}{171}{section.34}
\contentsline {subsection}{Perturbative determination of a c.t.; Problems with derivative couplings; Rephrasing renormalization conditions in terms of Green's functions; Lehmann-Kallen spectral representation for the propagator; Rephrasing renormalization conditions in terms of 1PI functions.}{171}{section*.101}
\contentsline {section}{\numberline {17}November 20}{182}{section.36}
\contentsline {subsection}{Perturbative determination of c.t.; Corrections to external lines in the computation of $S$ matrix elements; One loop correction to meson self energy; Feynman's trick for combining 2 denominators; Shift to make denominator $SO(3,1)$ invariant; Wick notation to make denominator $O(4)$ invariant; Integral tables for convergent combinations; Self-energy at one loop studied; Combining lots of denominators; The shift in the general case to reduce any multi-loop integral to an integral over Feynman parameters.}{182}{section*.105}
\contentsline {section}{\numberline {18}November 25}{196}{section.38}
\contentsline {subsection}{Rephrasing coupling constant renormalization in terms of a 1PI function; Experimental significance of the definition; Renormalization versus the infinities; Renormalizable Lagrangians; Unstable particles, Decay products.}{196}{section*.108}
\contentsline {section}{\numberline {19}December 2}{207}{section.40}
\contentsline {subsection}{Unstable particles, lifetime, method of stationary phase; Where it begins again; Lorentz transformation laws of fields; Equivalent representations; Reducible reps; The finite dimensional inequivalent irreducible representations of SO(3); Unitarity; Complex conjugation; Direct product; Projection operators and reducibility.}{207}{section*.123}
\contentsline {section}{\numberline {20}December 4}{226}{section.42}
\contentsline {subsection}{Parametrizing the Lorentz group; Commutation relations for the generators; decomposition into two sets obeying $SO(3)$ commutation relations; The catalog; Complex conjugation properties; Tensor product properties; Restriction to $SO(3)$; The vector; Rank 2 tensors; Spinors.}{226}{section*.130}
\contentsline {section}{\numberline {21}December 9}{240}{section.44}
\contentsline {subsection}{Lagrangian made of two component spinors; Solution of Weyl equations of motion; Weyl particles; Dirac Lagrangian; Four-component spinors; Weyl basis, Dirac basis; Plane wave solutions of the Dirac equation.}{240}{section*.131}
\contentsline {section}{\numberline {22}December 11}{249}{section.46}
\contentsline {subsection}{Plane wave solutions of the Dirac equation; Pauli's theorem; Dirac adjoint; Pauli-Feynman notation; Parity; Bilinears; Orthogonality; Completeness; Summary.}{249}{section*.132}
\contentsline {section}{\numberline {23}December 16}{267}{section.48}
\contentsline {subsection}{Canonical quantization of the Dirac Lagrangian.}{267}{section*.133}
\contentsline {section}{\numberline {24}December 18}{273}{section.50}
\contentsline {subsection}{Perturbation theory for spinors; Time ordered product; Wick's theorem; Calculation of the contraction (propagator); Wick diagrams; Feynman diagrams; Matrix multiplication; Spin averages and spin sums.}{273}{section*.134}
\contentsline {section}{\numberline {25}January 6}{289}{section.52}
\contentsline {subsection}{Parity for spinors; Fermion and antifermion have opposite intrinsic parity; Charge conjugation; Majorana basis; Charge conjugation properties of fermion bilinears; Decay of ortho and para positronium; $U_PU_C=U_CU_P(-1)^{N_F}$; PT.}{289}{section*.147}
\contentsline {section}{\numberline {26}January 8}{301}{section.54}
\contentsline {subsection}{Effect of PT on states; Proof of CPT theorem in perturbation theory; Renormalization of spinor theories; Propagator.}{301}{section*.148}
\contentsline {section}{\numberline {27}January 13}{313}{section.56}
\contentsline {subsection}{1PI part of propagator; Spectral representation for propagator; $\DOTSB \sum@ \slimits@ \prime (p')$ to $\mathcal {O}(g^2)$ in meson-nucleon theory; Coupling constant renormalization; Is renormalization sufficient to eliminate $\infty $'s.}{313}{section*.150}
\contentsline {section}{\numberline {28}January 15}{323}{section.58}
\contentsline {subsection}{Regularization; Regulator fields; Dim'l regularization; Minimal subtraction; BPHZ renormalizability; Renormalization and symmetry; Renormalization of composite operators.}{323}{section*.152}