Short Descriptions of Quantum Field Theory

Lisa Randall

Warped Passages, Harper Perennial (2005)

“Quantum field theory, the tool with which we study particles, is based on eternal, omnipresent objects that can create and destroy those particles. These objects are the ‘fields’ of quantum field theory. Like the classical electromagnetic fields that inspired their name, quantum fields are objects that permeate spacetime. But quantum fields play a different role. They create or absorb elementary particles. According to quantum field theory, particles can be produced or destroyed anywhere and anytime.”

You should also check out the interview with Lisa Randall at the Smithsonian Magazine.

A. Zee

Quantum Field Theory in a Nutshell, Princeton University Press (2003)

“In quantum mechanics the uncertainty principle tells us that the energy can fluctuate wildly over a small interval of time. According to special theory of relativity, energy can be converted into mass and vica versa. With quantum mechanics and special relativity, wildly fluctuating energy can metamorphose into mass, that is into new particles not previously present.”

Matt Strassler

“A field is something that 1) is present everywhere in space and time, 2) can be, on average,  zero or not zero, and 3) can have waves in it. 4) And if it is a quantum field, its waves are made from particles.”

“One example of a field is the wind.  Another is the electric field.  A third is the Higgs field.  And there are many more.  In particular, every type of elementary particle is a ripple in a corresponding quantum field.”

“The general class of equations that we use to calculate the behavior of quantum fields — quantum field theory — is therefore crucial in particle physics.  In fact, you can’t do much particle physics or string theory without running into the mathematics of QFT. The subject also has a big role to play in cosmology (the history of the universe) and in the research area known as “condensed matter physics”, which includes as a big subset the physics of solid materials.”

“An aside: in quantum field theory, quantum fluctuations are sometimes called, or attributed to, the “appearance and disappearance of two (or more) ‘virtual particles’ “. This technical bit of jargon is unfortunate, as these things (whatever we choose to call them) are certainly not particles — for instance, they don’t have a definite mass — and also, more technically, because the notion of “a virtual particle” is only precisely defined in the  presence of relatively weak forces.”

“Every elementary particle (I speak of real particles now) in our universe is a ripple — a small wave, the wave of smallest possible intensity — in a corresponding elementary quantum field. A W particle is a ripple in a W field; a photon [a particle of light, which you may think of as the dimmest possible flash] is a ripple in the electric field; an up quark is a ripple in the up quark field.”

Stephen Wolfram

Stephen Wolfram’s notes in his book “New Kind of Science” are freely available online. This is a great resource: There is is a note on Quantum Field Theory:  Here is a quote from that note.

“In standard approaches to quantum field theory one tends to think of particles as some kind of small perturbations in a field. Normally for calculations these perturbations are on their own taken to be plane waves of definite frequency, and indeed in many ways they are direct analogs of waves in classical field theories like those of electromagnetism or fluid mechanics. To investigate collisions between particles, one thus looks at what happens with multiple waves. In a system described by linear equations, there is always a simple superposition principle, and waves just pass through each other unchanged. But what in effect leads to non-trivial interactions between particles is the presence of nonlinearities. If these are small enough then it makes sense to do a perturbation expansion in which one approximates field configurations in terms of a succession of arrangements of ordinary waves – as in Feynman diagrams. But just as one cannot expect to capture fully turbulent fluid flow in terms of a few simple waves, so in general as soon as there is substantial nonlinearity it will no longer be sufficient just to do perturbation expansions. And indeed for example in QCD there are presumably many cases in which it is necessary to look at something closer to actual complete field configurations – and correlations in them.”


“In theoretical physics, quantum field theory (QFT) is a theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics, by treating a particle as an excited state of an underlying physical field. These excited states are called field quanta. For example, quantum electrodynamics (QED) has one electron field and one photon field, quantum chromodynamics (QCD) has one field for each type of quark, and in condensed matter there is an atomic displacement field that gives rise to phonon particles.”

“Because the fields are continuous quantities over space, there exist excited states with arbitrarily large numbers of particles in them, giving QFT systems an effectively infinite number of degrees of freedom. Infinite degrees of freedom can easily lead to divergences of calculated quantities (i.e., the quantities become infinite) in a straightforward approach to QFT calculations. Techniques such as renormalization of QFT parameters and discretization of spacetime, as in lattice QCD, are used to avoid such infinities and to yield physically meaningful results.”


About Suresh Emre

I have worked as a physicist at the Fermi National Accelerator Laboratory and the Superconducting Super Collider Laboratory. I am a volunteer for the Renaissance Universal movement. My main goal is to inspire the reader to engage in Self-discovery and expansion of consciousness.
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