1. Symmetries and Conservation Laws Flashcards
What are symmetries?
Regularities of physical systems
What are the two classes of symmetries, and briefly describe them?
Space time symmetries - Transformation of s-t coords
Internal symmetries - Translations of non s-t degrees of freedom
State some examples of the two classes of symmetries
s-t: Translations, rotations, Lorentz transformations, parity
Internal: Isospin, flavour, gauge transformations
For every unitary symmetry…
There exists a conservation law
How does the wavefunction change under a spatial transformation?
The wavefunction changes according to the identity matrix
What is a basis?
A complete orthonormal set of states
What is the QM definition of symmetry?
The Hamiltonian is invariant under the transformation concerned
What are axial vectors?
Vectors which are invariant under the parity transformation e.g. angular momentum
What does it mean if a particle has intrinsic parity?
They are eigenstates of the parity operator
What are scalar and pseudoscalar particles?
Scalar particles: Spin 0 particles with a parity eigenvalue of +1
pseudoscalar particles: Spin 0 particles with a parity eigenvalue of -1
What is the fundamental scalar boson?
The Higgs
What does it mean if an equation is covariant?
The expression of the law takes the same form when using the variables which express the new frame of reference,
What are vectors, or polar vectors in relation to parity>
When they transform as
r -> r’ = -r
What is the parity of gauge bosons?
-1 as they are vector particles
