[QUE/QFT-04003] QFT-PROBLEM

Define \(a(k,t)\) and \(a^\dagger(k,t)\) as Fourier coefficients of free field \(\psi(x,t)\). \[ \psi(x,t)= \frac{1}{(2\pi)^3}\int dx e^{ikx} a(k);\psi^\dagger(x,t)= \frac{1}{(2\pi)^3}\int dx e^{-ikx} a^\dagger(k); \]

• Use ETCR to show that \[ [(a(k,t), a^\dagger(k{'},t)]= \delta(k-k{'}).\] What are the values of equal time commutators \([a(k,t), a(k{'},t) ], [a^\dagger(k,t), a^\dagger(k{'},t) ].\)