# 4445 4446

Ma444 Quantum Field Theory

Prof. Samson Shatashvili & Dr. Sergey Cherkis

http://www.maths.tcd.ie/~cherkis/444/

## Differences in notation between Peskin and Schroeder and Mark Srednicki

Peskin and Schroeder Mark Srednicki
$g^{\mu\nu}$ $\mathrm{diag}(+,-,-,-)$ $\mathrm{diag}(-,+,+,+)$
Expansion of fields in plane waves $\phi(x)=\int \frac{\mathrm{d}^4k}{(2\pi)^4}\frac{1}{\sqrt{2\omega}}$etc. $\phi(x)=\int \frac{\mathrm{d}^4k}{(2\pi)^4}\frac{1}{2\omega}$etc.
Canonical commutation relations $[a(\vec{k}),a^\dagger(\vec{k^\prime})]=(2\pi)^3\delta^3(\vec{k}-\vec{k^\prime})$ $[a(\vec{k}),a^\dagger(\vec{k^\prime})]=(2\pi)^32\omega\delta^3(\vec{k}-\vec{k^\prime})$
One particle states $|k\rangle=\sqrt{2\omega}a^\dagger(k)|0\rangle$ $|k\rangle=a^\dagger(k)|0\rangle$
Symmetry Factors Consider sources fixed (smaller symmetry factors) Consider sources free (larger symmetry factors)
Spinor products $\chi^\top i\sigma^2\psi$ $-\chi \psi$
$\chi^{\dagger} i\sigma^2 \psi^*$ $\chi^\dagger\psi^\dagger$
Feynman slash $\gamma^\mu a_\mu$ $-\gamma^\mu a_\mu$
$\gamma^\mu \partial_\mu$ $\gamma^\mu \partial_\mu$
Scalar Propagator $(\partial_\mu \partial^\mu+m^2)\Delta(x-y)=\frac{1}{i}\delta^4(x-y)$ $(-\partial_\mu \partial^\mu+m^2)\Delta(x-y)=\delta^4(x-y)$
Fermionic Propagator $(-i\gamma^\mu \partial_\mu+m)S(x-y)=\frac{1}{i}\delta^4(x-y)$ $(-i\gamma^\mu \partial_\mu+m)S(x-y)=\delta^4(x-y)$
Free Propagators in general $\Delta(x-y)=\langle 0| \mathrm{T} \Phi(x) \Phi^\dagger (y) |0\rangle$ $\Delta(x-y)=i\langle 0| \mathrm{T} \Phi(x) \Phi^\dagger (y) |0\rangle$
$D\Delta(x-y)=\frac{1}{i}\delta(x-y)$ $D\Delta(x-y)=\delta(x-y)$
and many, many more ...

## References

1. Michael E. Peskin, Daniel V. Schroeder, "An introduction to quantum field theory," HarperCollins Publishers; Reissue edition (1995)
2. Paul A. M. Dirac, "Lectures on Quantum Mechanics," Dover Publications (2001)
3. Mark Srednicki, "Quantum Field Theory," Cambridge University Press, (2007)