4445 4446

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Ma444 Quantum Field Theory

Prof. Samson Shatashvili & Dr. Sergey Cherkis

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

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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 ...
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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)


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