SERC Lectures on Quantum Field Theory

## Official Syllabus

1. Quantization of free fields: scalars, fermions, gauge fields.
2. Propagators.
3. Interactions: $\phi^4$, Yukawa.
4. Wick's theorem. Feynman rules.
5. Tree-level processes, $2\rightarrow 2$ scattering in QED, cross section and helicity amplitudes; e.g. Bhabha scattering.
6. Feynman rules for $SU(2)$ gauge theory.

The above material has to be covered in 12 lectures each of duration 1.5 hours and supplemented by 12 tutorials of the same duration. The tutorials will be conducted by Prof. Bala Sathiapalan of the Institute of Mathematical Sciences, Chennai. I have also been briefed to NOT use the path-integral approach and hence will stick to canonical quantization.

### Prerequisites

Mark Srednicki has a wonderful way of describing the prerequisites to do Quantum Field Theory in his book (see the preface for students) and I will quote him rather than give my list.

In order to be prepared to undertake the study of quantum field theory, you should recognize and understand the following equations:

(1)
\begin{eqnarray} \frac{d\sigma}{d\Omega}&=& |f(\theta,\phi)|^2 \nonumber \\ a^\dagger |n\rangle &=& \sqrt{n+1} |n+1\rangle \\ J_\pm |j,m\rangle &=& \sqrt{j(j+1)-m(m\pm1)}|j,m\pm1\rangle \\ A(t) &=& e^{+iHt/\hbar}\ A \ e^{-iHt/\hbar} \\ H &=& p \dot{q}-L \\ ct' &=& \gamma (ct -\beta x) \\ E &=& (\mathbf{p}^2 c^2 + m^2c^4)^{1/2}\\ \mathbf{E} &=& -\dot{\mathbf{A}}/c -\mathbf{\nabla}\varphi \end{eqnarray}

### Problem Sets and Handouts

Problem Sets: PS 1 PS 2 PS 3 PS 4 PS 5 PS 6 PS 7 PS 8 PS 9

Handouts: (i) Green Functions for the Klein-Gordon operator;

### References

David Tong has put up his QFT Lectures on the web. You can also download (scanned) pdf files of Brian Hill's transcription of the classic QFT lectures of Sidney Coleman from his page in addition to pointers to other resources on QFT.

1. M. Srednicki, Quantum Field Theory, Cambridge Univ. Press (Feb. 2007)
2. M. E. Peskin & D. V. Schroeder, An introduction to Quantum Field Theory, Westview Press (Oct. 1995)
3. C. Itzykson and J. B. Zuber, Quantum Field Theory, (Orginally by McGraw Hill) Dover Pub. (Feb. 2006)
4. P. Ramond, Field Theory : A Modern Primer, Westview Press; 2nd ed. (Dec. 2001)

There are many more books on QFT that I have not listed here.