Basics on theoretical physics Flashcards
What are Yang-Mills theories?
Theories where the Lagrangian only contains a Maxwell term. These are gauge theories of based on special unitary groups.
Continuous symmetries can be described by ___ while discrete symmetries are described by ____.
Lie groups, finite groups
Arguably the most important example of a symmetry in physics is that the speed of light has the same value in all frames of reference, which is described in special relativity by a group of transformations of the spacetime known as the ____.
Poincaré group.
State Noether’s theorem
Every differentiable symmetry of the action of a physical system with conservative forces has a corresponding conservation law.
The Virasoro algebra is a complex Lie algebra and the unique central extension of the ____.
Witt algebra
What is a diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are smooth.
How are theories constructed?
- Use Hamilton’s principle on the Lagrangian density
- Fourier transforming to momentum space
- Solve the equation of motion in momentum space for different coordinates under possible gauge transformations.
- Quantize with creation operator(s) and polarisation tensor
The ____ is an antisymmetric gauge field that generalises the electromagnetic potential to strings.
Kalb-Ramond field
Describe the Einstein-Hillbert action mathematically
S=1/(2kappa)\int d^Dxsqrt(-g)R
It produces Einstein Field Equations
In natural units, write length and time in units of mass
L=T=1/M
Conformal gauge condition
h_{alpha, beta}=rho^2*eta_{alpha, beta}
What are ghosts?
Non-physical (statistically violating), anticommuting tensor fields introduced by Faddeev and Popov to maintain the Feynman formalism
What is a Wick rotation?
tau –> -i tau
Given a current, how do we find the charge?
Integrate the time-like components. In string theory we integrate over j^{0i} so the charge becomes a (conserved) vector.
What forces did the Glashow-Weinberg-Salam model unify?
Weak force and electromagnetism
What is the idea behind Kaluza-Klein theory?
That generalising relativity to five dimensions adds electromagnetism to the equations
Explain the idea behind the swampland program?
Some 10^500 compactifications from 10 to 4 dimensions are possible. Other 4-dimensional field theories that aren’t part of compatible with quantum gravity. They exist in the swampland instead of the landscape
What is an orbifold?
A generalisation of a manifold to a space with fixed point that is obtained by identification.
What is Born-Infeld theory about?
Non-linear electrodynamics. This solves the infinite self-energy problem
