Road to Reality solutions

There used to be a Road to Reality discussion forum, now archived. There's a sorted list of solutions from the forum.

Some solutions and comments of my own:

Sec. 9.7 Some more on hyperfunctions

Exercise 15.5 Mapping the 3-sphere to the tangent bundle on the 2-sphere

Exer.15.14 Model of a gauge connection on the complex plane

Section 16.2 The secret behind magic circles

Exer.16.8 A function from the quarter-plane to the naturals

Exer.18.5 Self-dual and anti-self-dual planes

Exer.18.7 Geometry on the velocity vector hyperboloid

Exer.19.14 Discrete analogue of the stress-energy tensor?

Exer.19.18 trace-reversed Ricci tensor has 0 divergence

Exer.19.16 Ricci tensor has info about volume acceleration: a nice illustration of Lie derivatives

Exer.19.21 Ricci tensor is 0 if trace-reversed Ricci tensor is 0

Exer.20.8 Taylor expansion of the equilibrium Hamiltonian

Exer.20.15 Symplectic form is unchanged by Hamiltonian evolution

Exer.22.9 Heisenberg equation of motion

Exer.22.11 Eigenvectors of a normal operator are orthogonal.

Exer.22.12 Amplitude <φ|ψ> = 1 only if φ proportional to ψ

Exer.23.3 Why does the singlet state have 0 spin?

Exer.23.4 Entangled state IS a product of states

Exer.23.9 Counting boson states

Exer.23.10 Quantum teleportation

Exer.24.3 Just a comment: An example of a normalizable state where momentum has a definite magnitude

Exer.24.7 relativistic invariance of the Dirac equation

Exer.24.9 Representing Clifford elements as matrices

Exer.25.6 Particle octet

Exer.25.9 Dual gauge curvature

Exer.26.5 Positive and negative frequency solutions to Maxwell equations

Exer.27.9 Putting MANY MANY little gas molecules back into Pandora's box

Exer.27.16 Isotropy and homogeneity: This problem has a counterexample!

Exer.28.2 Electroweak symmetry breaking

Exer.28.4 Exponential de Sitter metric

Exer.28.6 Ricci tensor is proportional to the metric tensor in (anti)de Sitter space

Exer.29.7 Pure-state density matrices

Exer.29.13 Density matrices for spin 1 EPR pairs

Exer.30.3 Black hole temperature

Exer.30.10 Gravitational time dilation

Exer.30.12 Uncertainty in ∂/∂t from energy to move mass distribution away from its potential

Exer.30.12 An easier proof

Exer.30.13 A free particle can't be in an energy eigenstate

Exer.31.6 Symplectic manifold from a Riemannian manifold with complex structure

Exer.32.2 Contracting a self-dual tensor with an anti self-dual tensor

Exer.33.2 Compactified Minkowski space!

Exer.33.5 Compactified Minkowski space as a conic section

Exer.33.8 The celestial sphere is a conformal manifold

Exer.33.11 A 0-length twistor is associated with (at least one) spacetime event

Exer. 33.16 The plane of points incident to a twistor is self-dual. Anti self-dual for dual twistor.

Exer. 33.18 The center of a twistor configuration can't be regarded as the path of a spinning particle

Exer. 33.19 Why is the twistor commutator a real number?

Exer. 33.23 See the answer to Exercise 33.24

Exer. 33.24 Massless free field equation for a photon = Maxwell's equations in empty space

Sec. 33.9 First analytic sheaf cohomology of the complex plane

Sec. 33.11 Making curved twistor space by drying paint. Also the answer to
Exer. 33.28.