Siva Swaminathan
November 23, 2015
91

What is quantum field theory?

Invited talk at the gathering of the Society of Physics Students (at UT Austin). Intended as an introduction, for physics undergraduate students with varying levels of familiarity with classical and quantum mechanics, but no prior knowledge of field theory.

Siva Swaminathan

November 23, 2015

Transcript

1. What is quantum eld theory? From wooden blocks to the

building blocks of nature @ Siva Swaminathan SPS
2. Quantum eld theory is a framework to describe systems which

evolve quantum mechanically (unitarity) have many degrees of freedom (excitations) which respect locality (causality) That's basically it.

4. Let's back up for a bit... Classical Mechanics Quantum Mechanics

Classical Field theory Quantum Field theory h → 0 reducing DOFs (c → ∞) h → 0 reducing DOFs (c → ∞)

6. Newton's laws What is a force? That thing which causes

acceleration. What is mass? That thing which tells you how hard it is to produce acceleration. = m (actually ) F ⃗ a⃗ dp ⃗ dt

move?

9. How to do physics? Guess the differential equation describing a

system Specify the state (initial conditions) Predict dynamics (solving the differential equation) { , } x i x ˙i x(t)

11. Principle of "least" stationary action S = ∫ dt L(

, ) x i x ˙i Action is the price paid by a physical system

13. Symmetries = Conservation laws (Noether) Conserved quantities help specify/constrain states

Think of symmetries as "frame invariance"
14. How to do physics? Guess a Lagrangian Fix and Solve

for Derive the equations of motion and conserved quantities L(x, ) x ˙ x i x f x ˙i (Euler-Lagrange) ( ) − = 0 d dt ∂L ∂x ˙ ∂L ∂x eg: for mechanical systems L = KE − PE

17. Superpositions Enlarge your notion of a system's state |state of

cat⟩ ∼ |dead cat⟩ + |alive cat⟩ |pointing direction⟩ = |X⟩ + |Y⟩ − |Z⟩ 1 3 − − √ 1 3 − − √ 1 3 − − √
18. Wavefunctions |particle position⟩ = |position 1⟩ + |position 4⟩ −

|position 1 3 − − √ 1 3 − − √ 1 3 − − √ ⟨x|ψ⟩ ∼ sin(2π ) x L
19. Measurements "Collapse of the wavefunction" Physicists don't discuss this in

polite company.
20. In a random world, what are the observables? How do

you characterize random variables?
21. Democrazy Everything that can happen should be considered. Z ∼

∫ [Dx(t)]e iS/ℏ Every possibility gets to vote (with strength ) Contributions will interfere (reinforce/cancel) e iS/ℏ
22. How to do physics Specify an initial quantum state Find

Find the probability amplitude to evolve to putative Unitarity : |initial state⟩ ⟨observable⟩ = ⟨state|observable|state⟩ |final state⟩ ∑ = 1 p f

∂t ∂ 2 ∂x2
24. All the magic of quantum mechanics is arguably a consequence

of linearity/unitarity
25. Oh, by the way... Spookiness ✗ Nonlocality ✗ Democracy ✔

Determinism ✗ Predictability ✔

28. Local degrees of freedom A eld is a set of

values: a quantity at each point of space (and time) How do those degrees of freedom in uence each other?

Nonlinear

32. How to do physics? Guess the correct PDE Specify appropriate

initial/boundary conditions Solve the PDE!

39. Scattering amplitudes It's like trying to collide together two mechanical

watches, to understand their structure, by observing the gears that y out.

41. What are the fundamental degrees of freedom? Particles are just

different manifestations of energy

43. Classical Mechanics Quantum Mechanics Classical Field theory Quantum Field theory

h → 0 reducing DOFs (c → ∞) h → 0 reducing DOFs (c → ∞)
44. Quantum eld theory is a framework to describe systems which

evolve quantum mechanically (unitarity) have many degrees of freedom (excitations) which respect locality (causality) That's basically it.
45. Thank you "The rst principle is that you must not

fool yourself — and you are the easiest person to fool." -- Richard Feynman