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COMPUTING SCIENCE

Getting Your Quarks in a Row

A tidy lattice is the key to computing with quantum fields

Brian Hayes

The Particle Exchange

Field%20theories%20describe%20forces%20between%20particlesClick to Enlarge Image Bring two electrons close together, and they repel each other. Nineteenth-century theories explained such effects in terms of fields, which are often represented as lines of force that emanate from an electron and extend throughout space. The field produced by each particle repels other particles that have the same electric charge and attracts those with the opposite charge.

QED is a quantum field theory, and it takes a different view of the forces between charged particles. In QED electrons interact by emitting and absorbing photons, which are the quanta, or carriers, of the electromagnetic field. It is the exchange of photons that accounts for attractive and repulsive forces. Thus all those ethereal fields permeating the universe are replaced by localized events—namely the emission or absorption of a photon at a specific place and time. The theory allows for some wilder events as well. A photon—a packet of energy—can materialize to create an electron and its antimatter partner, a positron ( e e + ). In the converse event an e e + pair annihilates to form a photon.

QCD is also a quantum field theory; it describes the same kinds of events, but with a different cast of characters. Where QED is a theory of electrically charge particles, QCD applies to particles that have a property called color charge (hence the name chromo dynamics). And forces in QCD are transmitted not by photons but by particles known as gluons, the quanta of the color field.

The%20lattice%20version%20of%20a%20quantum%20field%20theoryClick to Enlarge Image Yet QCD is not just a version of QED with funny names for the particles. There are at least three major differences between the theories. First, the electric charges of QED come in just two polarities (positive and negative), but there are three varieties of color charge (usually labeled red, green and blue). Second, the photons that carry the electromagnetic force are themselves electrically neutral; gluons not only carry the color force but also have color of their own. As a result, gluons respond to the very force they carry. Finally, the color force is intrinsically stronger than electromagnetism. The strength is measured by a numerical coupling constant, α, which is less than 0.01 for electromagnetism. The corresponding constant for color interactions, α c , is roughly 1.

These differences between QED and QCD have dramatic consequences. Electromagnetism follows an inverse-square law: The force between electrically charged particles falls off rapidly with increasing distance. In contrast, the force between color-charged quarks and gluons remains constant at long distances. Furthermore, it's quite a strong force, equal to about 14 tons. A constant force means the energy needed to separate two quarks grows without limit as you pull them apart. For this reason we never see a quark in isolation; quarks are confined to the interior of protons and neutrons and the other composite particles known as hadrons.


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