Physics 230A In-Class Problems:
Interactions II
1. Consider the meson-nucleon theory with interaction
Lint = g .
(1)
Here is a real scalar eld of mass M
(x) =
(dp)M eipx (p) + h.c.
(2)
and is a comple
Chapter Outline
Chapter 1
Why Quantum
Field Theory?
Paths to quantum field theory (QFT)
Tension between QFT and special relativity (SR)
Causality
Paths to QFT
Dirac (1930s)
Apply rules of quantum m
Physics 230A Assignment 6
Due May 19
Quantum field theory is also useful in cases where special relativity is not important,
and particles are neither created nor destroyed. Non-relativistic quantum f
Physics 230a
Homework 1 Solutions
1. (10 points)
(a) (2 points) At t = 0, our particle is in state (~, t = 0). To get the particles
p
state at a later time, we solve the time-dependent Schrdinger equa
Physics 230a
Homework 2 Solutions
1. (10 points)
(a) (3 points)The smallest dimension term allowed by both shift symmetry and
Lorentz invariance is
( )2 .
Rearranging indices, we could also have the t
Physics 230a
Final Solutions
1. (a) Our Noether current is
J = i i
So our normal ordered version, with
(x) =
(dp) (p)eipx + (p)eipx
(x) =
(dp) (p)eipx + (p)eipx
(x) =
(x) =
(dp)(ip ) (p)eipx (p)ei
Physics 230a
Homework 3 Solutions
1. (10 points) Our interaction Lagrangian is
Lint = g.
(a) (5 points) We want to compute the scattering amplitude for fermion-antifermion goes to fermionantifermion.
Physics 230A In-Class Problems:
Lorentz Transformations and Index Gymnastics
1. Write the following Lorentz transformations of 2-index tensors in index-free matrix
notation:
A = A
B
1
(1)
= ( ) B ,
(
Physics 230A In-Class Problems:
Relativistic Particle States
1. Consider the theory of a single relativistic particle dened in the lectures. Just as in
non-relativistic quantum mechanics, the states c
Physics 230A In-Class Problems:
Symmetries in Quantum Mechanics
1. (a) Use the creation and annihilation operator formalism to show that for a simple
harmonic oscillator in Heisenberg picture
i
0|[q(t
Physics 230A In-Class Problems:
Interactions I
1. Consider a real scalar eld theory with interaction term
Lint = 4 .
(1)
4!
In this problem you will compute the O(0 ) and O() contribution to the S-mat
Physics 230A In-Class Problems:
Continuous Groups and Representations
1. A group representation is dened by a linear transformation R(g) that acts on a
vector space of states, such that the group mult
Physics 230A In-Class Problems:
Feynman Rules for Dirac Fermions
1. Consider the theory of a Dirac fermion coupled to a real scalar eld. The
interaction Lagrangian is
Lint = g.
(1)
(a) Compute the sca
Physics 230A In-Class Problems:
Feynman Rules for Dirac Fermions II
Suppose that the electron is coupled to a new kind of scalar by a Yukawa coupling
Lint = y .
(1)
Compute the spin-averaged squared a
Physics 230A In-Class Problems:
Symmetry II
1. Consider a complex scalar with classical Lagrangian density
L = m2 ( )2 .
4
(1)
This Lagrangian is invariant under the U (1) symmetry
ei ,
(2)
where is
Chapter Outline
Chapter 2
Spacetime
Symmetry
What is Symmetry?
Definition of symmetry in QM
The most general transformation that leaves the circle invariant has the form
We can represent these transf