MY-ASSIGNMENTEXPERT™可以为您提供my.uq.edu PHYS4040 Quantum field theory量子场论课程的代写代考和辅导服务！
这是昆士兰大学 量子场论课程的代写成功案例。
PHYS4040课程简介
Course Description: This course covers advanced topics from single-particle quantum mechanics, such as advanced quantum dynamics, path-integrals, and quantum decoherence. It will also cover introductory non-relativistic many-body quantum theory, relativistic quantum mechanics, and relativistic quantum field theory. We will look at selected applications from atom optics, condensed matter physics, and particle physics.
Assumed Background:
Students should have a sound understanding of quantum physics at the level of PHYS3040 (or equivalent). Background in special relativity (e.g. PHYS2100), electromagnetic fields (e.g. PHYS3051), condensed matter physics (e.g. PHYS2020) and statistical mechanics (e.g. PHYS3020) is strongly recommended.
Prerequisites
This course aims at a first introduction to relativistic quantum field theory. This plays a fundamental role in our understanding of particle physics but arises also in the study of statistical mechanics and second quantised condensed matter systems.
Course Changes in Response to Previous Student Feedback
The course has been modified to be more interactive, with more chance for students to work through problems with assistance.
PHYS4040 Quantum field theory HELP（EXAM HELP， ONLINE TUTOR）
Lorentz invariance.
(a) Show that
$$
\int_{-\infty}^{\infty} d k^0 \delta\left(k^2-m^2\right) \theta\left(k^0\right)=\frac{1}{2 \omega_k},
$$
where $\theta(x)$ is the unit step function and $\omega_k \equiv \sqrt{\vec{k}^2+m^2}$.
(b) Show that the integration measure $d^4 k$ is Lorentz invariant.
(c) Finally, show that
$$
\int \frac{d^3 k}{2 \omega_k}
$$
is Lorentz invariant.
Coherent states of the simple harmonic oscillator.
(a) Calculate $\partial_z\left(e^{-z a^{\dagger}} a e^{z a^{\dagger}}\right)$ where $z$ is a complex number.
(b) Show that $|z\rangle=e^{z a^{\dagger}}|0\rangle$ is an eigenstate of $a$. What is its eigenvalue?
(c) Calculate $\langle n \mid z\rangle$.
(d) Show that these “coherent states” are minimally dispersive: $\Delta p \Delta q=\frac{1}{2}$, where $\Delta q^2=\left\langle q^2\right\rangle-\langle q\rangle^2$ and $\Delta p^2=\left\langle p^2\right\rangle-\langle p\rangle^2$, where $\langle q\rangle=\frac{\langle z|q| z\rangle}{\langle z \mid z\rangle}$ and $\langle p\rangle=\frac{\langle z|p| z\rangle}{\langle z \mid z\rangle}$.
(e) Why can you not make an eigenstate of $a^{\dagger}$ ?
Lorentz currents.
(a) Calculate the conserved currents $K_{\mu \nu \alpha}$ associated with (global) Lorentz transformations $x_\mu \rightarrow \Lambda_{\mu \nu} x_\nu$. Express the currents in terms of the energymomentum tensor.
(b) Evaluate the currents for $\mathcal{L}=\frac{1}{2} \phi\left(\square+m^2\right) \phi$. Check that these currents satisfy $\partial_\alpha K_{\mu \nu \alpha}=0$ on the equations of motion.
(c) What is the physical interpretation of the conserved quantities $Q_i=\int d^3 x K_{0 i 0}$ associated with boosts?
(d) Show that $\frac{d Q_i}{d t}=0$ can still be consistent with $i \frac{\partial Q_i}{\partial t}=\left[Q_i, H\right]$. Thus, although these charges are conserved, they do not provide invariants for the equations of motion. This is one way to understand why particles have spin, corresponding to representations of the rotation group, and not additional quantum numbers associated with boosts.
Ambiguities in the energy-momentum tensor.
(a) If you add a total derivative to the Lagrangian $\mathcal{L} \rightarrow \mathcal{L}+\partial_\mu X^\mu$, how does the energy-momentum tensor change?
(b) Show that the total energy $Q=\int \mathcal{T}{00} d^3 x$ is invariant under such changes. (c) Show that $T{\mu \nu} \neq T_{\nu \mu}$ is not symmetric for $\mathcal{L}=-\frac{1}{4} F_{\mu \nu}^2$. Can you find an $X_\mu$ so that $T_{\mu \nu}$ is symmetric in this case?
MY-ASSIGNMENTEXPERT™可以为您提供MY.UQ.EDU PHYS4040 QUANTUM FIELD THEORY量子场论课程的代写代考和辅导服务！
