Quantum electrodynamics

Flo Lindenbauer
Quiz by Flo Lindenbauer, updated more than 1 year ago
Flo Lindenbauer
Created by Flo Lindenbauer about 2 years ago
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Description

A quiz about quantum electrodynamics

Resource summary

Question 1

Question
Given the Schrödinger equation, \( i\partial_t |\psi\rangle = H|\psi\rangle,\) which of the following is true?
Answer
  • The Schrödinger equation is a purely nonrelativistic equation, as it is not possible to find a relativistic Hamiltonian
  • The Schrödinger equation can be made relativistic by chosing a relativistic Hamiltonian
  • The Schrödinger equation cannot be Lorentz covariant because of its special role of time
  • The Schrödinger equation requires that the time development of \(\psi\) follows a hermitian operation

Question 2

Question
What is the problem with the Klein-Gordon equation? Why can't we interpret it as a relativistic single particle equation?
Answer
  • The probability density is not positive definite
  • It is a linear equation, we wan't a nonlinear one
  • The Klein-Gordon equation is not relativistic
  • The Klein-Gordon equation has no real solutions

Question 3

Question
Which relation do the Dirac \(\gamma\)-matrices satisfy?
Answer
  • \([\gamma^\mu,\gamma^\nu]=2g^{\mu\nu}\)
  • \([\gamma^\mu,\gamma^\nu]=g^{\mu\nu}\)
  • \(\{\gamma^\mu,\gamma^\nu\}=2g^{\mu\nu}\)
  • \(\{\gamma^\mu,\gamma^\nu\}=g^{\mu\nu}\)
  • \(\{\gamma^\mu,\gamma^\nu\}=\delta^{\mu\nu}\)
  • \([\gamma^\mu,\gamma^\nu]=\delta^{\mu\nu}\)

Question 4

Question
What properties do the Dirac matrices satisfy? \(\gamma^\mu=(\gamma^0,\gamma^m)=(\beta,\beta\alpha_m)\)
Answer
  • \(\gamma^\mu\) are hermitian
  • \(\gamma^\mu\) are anti-hermitian
  • \(\gamma^i\) are hermitian
  • \(\gamma^i\) are anti-hermitian
  • The eigenvalues of \(\gamma^i\) are \(\pm i\)
  • The eigenvalues of \(\gamma^i\) are \(\pm 1\)
  • The eigenvalues of \(\beta\) are 0 and 1
  • The eigenvalues of \(\beta\) are 1 and -1
  • The eigenvalues of \(\beta\) are 1

Question 5

Question
Which operation creates a particle with momentum k?
Answer
  • \(a^\dagger(k)|0\rangle\)
  • \(a(k)|0\rangle\)

Question 6

Question
The quantization of the free electromagnetic field poses a problem which can be solved by adding a gauge breaking term to the Lagrangian. Which one? \(\mathcal L\to\mathcal L + G\)
Answer
  • \(G=(\lambda-1)(\partial\cdot A)^2\)
  • \(G=-\frac{\lambda}{2}(\partial\cdot A)^2\)
  • \(G=-\lambda g^{\mu0}(\partial\cdot A)\)
  • \(G=-(1-\lambda)\partial_\mu(\partial\cdot A)\)
  • \(G=\langle\psi|\partial\cdot A|\psi\rangle\)

Question 7

Question
Which field is given by this Lagrangian \(\mathcal L=(\partial_\mu \varphi^\ast)(\partial^\mu\varphi)-m^2\varphi^\ast\varphi\)?
Answer
  • a free scalar field
  • a fermionic field
  • the photon field
  • none of these answers

Question 8

Question
What is the canonical quantization procedure for a scalar field \(\varphi(t,\vec x)\) with conjugate momentum \(\pi(t,\vec y)\)?
Answer
  • \([\varphi(t,\vec x),\pi(t,\vec y)]=i\delta(\vec x-\vec y)\)
  • \(\{\varphi(t,\vec x),\pi(t,\vec y)\}=i\delta(\vec x-\vec y)\)
  • \([\varphi(t,\vec x),\pi(t,\vec y)]=\frac{i}{(2\pi)^3}\delta(\vec x-\vec y)\)
  • \(\{\varphi(t,\vec x),\pi(t,\vec y)\}=\frac{i}{(2\pi)^3}\delta(\vec x-\vec y)\)

Question 9

Question
What gives \(\gamma^0\gamma^\mu\gamma^0\)?
Answer
  • \(\gamma^\mu\)
  • \(\gamma^{\mu\dagger}\)
  • \(-\gamma^\mu\)
  • \(-\gamma^{\mu\dagger}\)
  • \(-\gamma^{\mu T}\)
  • \(\gamma^{\mu T}\)

Question 10

Question
In order for the Dirac equation to be covariant, a spinor has to transform according to \(\psi'_\alpha(x')=S_{\alpha\beta}(L)\psi_\beta(x)\) under a Lorentz transformation. Which relation must these matrices S satisfy?
Answer
  • \(S^{-1}\gamma^\mu S={L^\mu}_\nu\gamma^\nu\)
  • \(S\gamma^\mu S^{-1}={L^\mu}_\nu\gamma^\nu\)

Question 11

Question
Choose the right name for basis elements of Dirac field bilinears: \(1\): [blank_start]scalar[blank_end] \(\gamma^5\): [blank_start]pseudoscalar[blank_end] \(\gamma^\mu\gamma^5\): [blank_start]axial vector[blank_end] \(\gamma^\mu\): [blank_start]vector[blank_end] \(\frac{i}{2}\[\gamma^\mu,\gamma^\nu]\): tensor
Answer
  • scalar
  • pseudoscalar
  • axial vector
  • vector
  • antisymmetric tensor
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