Andrius Kulikauskas

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Introduction E9F5FC

Questions FFFFC0



  • How do twistor diagrams replace feynman diagrams?
  • Consider how gauge theory describes a field's impact upon itself and the multi-dimensional slack inherent in that.
  • There are 6x3 + 2 Maxwell equations where the 3 is for three-dimensional space. Do 6x3 express 10 + 8 ?



  • Özgür Ogan. Wick's theorem, Feynman diagrams.
  • Luis Gregorio Dias. Course on Quantum Many-Body Physics.
  • Peter-Weyl theorem in harmonic analysis is the analogous result for compact groups as compared to the finite groups. And when applied to SO(3) it gives the spherical harmonics which are crucial for the quantum mechanics of the Schroedinger equation for the hydrogen atom.
  • John Cardy. Introduction to Quantum Field Theory. 19 page overview of course.
  • Quantum field theory explains how a set of particles can be isolated from the rest of the universe regarding a set of their interactions. So it's the opposite of the collapse of the wave function, it's the unfolding of the buble which can ultimately collapse. Feynman diagram interactions-foursomes describe what is definite and thus allow for partial knowledge of the universe, total knowledge of a small part of a universe, namely, the interaction which is shielded (like by Faraday's pail) from the rest of the universe for the duration of the diagram. Making the diagram more sophisticated with "walkaways" allows the particles to "go outside of the pail" into the universe as a whole where something may change it (between alpha and beta) or there is no change (if beta is zero) or it changes to itself (if beta equals alpha) or it changes to its conjugate. The traveling can go to the "extra dimensions" of string theory.

Lorentz invariance

  • Lorentz invariance manifests in that an interaction in 4 dimensional space-time can't have more than 4 lines. There is a limited way of writing the potential.


  • Lagrangian relates the operators (the legs). Viewed, external legs and hidden, internal legs. Interactions (potential, local, at a point in space) and motions between them (kinectic, moving in space). There is slack between potential and kinetic, between external and internal.
  • Yukawa. Particle expresses slack in the field. Two bosonic particles can share slack, thus express an attractive force. Two fermionic particles must keep their slack separate, thus they experience a repulsive force, unless they are of different charge, in which case they don't need to keep their slack separate, and so they experience an attractive force.
  • Anthony Zee. Quantum Field Theory. African Summer Theory Institute. 2004. Four lectures
  • Mentioned by Anthony Zee.
  • Ricardo D'Elia Matheus. Quantum Field Theory. 30 lectures.
  • Wick's theorem is used extensively in quantum field theory to reduce arbitrary products of creation and annihilation operators to sums of products of pairs of these operators. A more general idea in probability theory is Isserlis' theorem. Isserlis' theorem or Wick's probability theorem is a formula that allows one to compute higher-order moments of the multivariate normal distribution in terms of its covariance matrix.
  • More formally, in the context of QFT, the S-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the in-states and the out-states) in the Hilbert space of physical states. A multi-particle state is said to be free (non-interacting) if it transforms under Lorentz transformations as a tensor product, or direct product in physics parlance, of one-particle states as prescribed by equation (1) below. Asymptotically free then means that the state has this appearance in either the distant past or the distant future. (Distant time!)
  • the possible interactions in quantum field theory are governed by a few basic principles: locality, symmetry and renormalization group flow (the decoupling of short distance phenomena from physics at larger scales). Fivesome.
  • Constructor theory counterfactuals global causality. Constructor is a coordinate space. It allows for remeasurement.


  • Quantum fluctuations (as per Heisenberg uncertainty principle) are like mutations.


Quantum field theory

  • What is a quantum field? It is expressed in particle contributions. Particles are or are not, as with the simplex vertices.

StackExchange: The Physical Meaning of Commutators in Quantum Mechanics

  • In field theory, vibrations are particles are symmetry breakings.

Quantum field theory

Sean Carroll or me? Quantum field theory. Instead of space and time, consider in terms of particles and their interactions. Particle clock steps take us from possible interaction to possible interaction. Problem: field theory is based on Minkowski spacetime rather than on particles.

Gerald B. Folland

  • Quantum Field Theory: A Tourist Guide for Mathematicians 2021
  • Quantum Field Theory 2008

Quantum Field Theory

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This page was last changed on March 30, 2024, at 11:47 AM