# Physics: QED Gauge Theory and Renormalization

# Physics: QED Gauge Theory and Renormalization

## Introduction

Quantum electrodynamics (QED) is a mathematical theory describing the interaction of electromagnetic radiation with matter. The development of QED theory was essential in the refinement of quantum field theory in the early twentieth century. QED is a fundamental scientific theory that accounts for most observed particle phenomena with extremely high precision. QED can be characterized as an extension of quantum theory to include special relativity. It is termed a gauge-invariant theory because its predictions are not affected by variations in space or time.

The practical value of QED is that it allows physicists to precisely describe the absorption and emission of light by atoms. QED also makes accurate predictions regarding the interactions between photons and charged atomic particles such as electrons. These abilities allow scientists to predict the properties of some molecules, to design highly sensitive sensors of electromagnetic fields, and to build single-atom memory-storage devices that will probably be used in future computer systems based on quantum principles.

## Historical Background and Scientific Foundations

During the first half of the twentieth century, physicists struggled to reconcile Scottish physicist James Clerk Maxwell's (1831–1879) equations regarding electromagnetism with the emerging quantum and relativistic theories advanced by German physicist Maxwell Planck (1858–1947), Danish physicist Niels Bohr (1885–1962), German-American physicist Albert Einstein (1879–1955), and others. Prior to World War II, British physicist Paul Dirac (1902–1984), German physicist Werner Heisenberg (1901–1976), and Austrian-born American physicist Wolfgang Pauli (1900–1958) made significant independent contributions to the mathematical foundations of QED.

Working with QED was difficult at first, however, because infinite values kept appearing in the mathematical calculations (e.g., for emission rates or determinations of mass). Infinite values do not correspond to anything that can be meaningfully observed and may even point to places where a physical theory predicts the impossible and so fails. Thus, early predictions of particle behavior based on QED often failed to match experimental observations. Later, however, QED was rescued by a mathematical procedure termed renormalization, which allows positive infinities to cancel out negative infinities, and by other advances developed independently by American physicists Richard Feynman (1918–1988) and Julian Schwinger (1918–1994) and Japanese physicist Shin'ichiro Tomonaga (1906–1979).

The use of renormalization initially allowed QED theorists to use measured values of mass and charge in QED calculations. The result made QED a highly reliable theory with regard to its ability to predict and reflect the observed interactions of electrons and photons. QED theory was, however, revolutionary in theoretical physics because of the nature and methodology of its predictions. QED reflected a growing awareness of limitations on the ability to make predictions regarding behaviors of subatomic particles. Instead of making predictions based on mechanistic cause-and-effect interactions, QED relies on the probabilities associated with the quantum properties and behavior of subatomic particles: this allows the calculation of probabilities regarding outcomes of subatomic interactions. No one outcome is necessarily determined: rather, there is a range of possible outcomes, having different, definite probabilities.

Renormalization was long viewed, even by Feynman and others, as a sort of sleight-of-hand trick to save QED from some hidden flaw. Upon receiving his Nobel Prize in 1965, Feynman said he thought that “the renormalization theory is simply a way to sweep the difficulties of the divergences of electrodynamics under the rug,” though he could not, he added, be sure. In the end, his hunch turned out to be wrong: today, renormalization is considered a valid method in several areas of quantum physics.

As quarks, gluons, and other subatomic particles became known to physicists in the early- and mid-twentieth century, QED became increasingly important in explaining the structure, properties, and reactions of these particles. QED, also known as the quantum theory of light, eventually became one of the most precise, accurate, and well-tested theories in all science. QED-based predictions of the mass of some subatomic particles, for example, offer results accurate to six or more significant figures—one part in a million or better.

QED describes the phenomenon of light in ways that are counterintuitive (not typical of everyday experience) because it treats quantum properties of light. Considered as a quantum phenomenon rather than as an electromagnetic wave, light has certain properties that are conserved and that occur in discrete amounts called quanta. According to QED theory, light exists in a state of

particle-wave dualism (i.e., the electromagnetic wave has both particle and wave-like properties). Electromagnetism—the phenomena of electrical charge and magnetism on which much of our technology depends—results from the quantum properties of the photon, the fundamental particle responsible for the transmission or propagation of electromagnetic radiation. Unlike the particles of everyday experience, photons can also exist as virtual particles that are constantly exchanged between charged particles: indeed, all the fundamental forces of nature are understood, in quantum mechanics, as exchanges of virtual particles. The relatively familiar forces of electricity and magnetism arise from the exchange of these virtual photons between charged particles. The exchange of these virtual photons is the explanatory domain of QED. According to QED theory, virtual photons are passed back and forth between the charged particles somewhat like basketball players passing a ball between them as they run down the court. The force caused by the exchange of virtual photons results from changes to the velocity (speed and/or direction of travel) of the charged particles as they absorb or emit virtual photons. Only in this covert or hidden state, flashing between particles, do photons act as mediators of force: otherwise, they travel freely through space as light or other forms of radiation.

As virtual particles, photons are cloaked from observation and measurement: that is, they can only be detected by their effects. The naked transformation of a virtual particle to a real particle would violate the laws of physics specifying the conservation of energy and momentum (i.e., energy and momentum would emerge from below the threshold of quantum uncertainty and become a permanent part of the universe: this is not possible). Photons themselves are electrically neutral and only under special circumstances and as a result of specific interactions that preserve conservation do virtual photons become real photons observable as light.

Among other phenomena, QED accounts for the interactions of electrons, positrons (the positively charged antiparticle to the electron), and photons. In electron-positron fields, electron-positron pairs come into existence as photons interact with these fields. According to QED, the process also operates in reverse to allow photons to create a particle and its antiparticle (e.g., an electron and a positron).

QED's concept of forces such as electromagnetism arising from the exchange of virtual particles may carry profound implications regarding the advancement of theories relating to the strong, electroweak, and gravitational forces. Some physicists assert that if a unified theory can be found—a mathematical description of all known physical forces as aspects of a single, underlying force—it will rest on the foundations and methodologies established during the development of QED theory.

## Modern Cultural Connections

Because QED is highly mathematical, only specialists with advanced, specialized schooling ever encounter its equations directly. Like some other areas of advanced physics, its cultural impact is primarily indirect.

In the early twentieth century, no practical uses for much of quantum physics, including QED, were yet imaginable: physicists pursued their understanding of these fundamental matters both from pure curiosity and from a historically founded confidence that uses would be found for such knowledge someday. In the early twenty-first century, as precise manipulation of single atoms and photons became commonplace in laboratories, QED became the basis of new sensors and computing devices. This new technological revolution—still in its early stages—depended on the refinement since the 1960s of techniques for building extremely small structures connected to complex electronic circuits on tiny chips of silicon. Such a circuit-on-a-chip is termed an integrated circuit because its parts are all integral to (a seamless part of) a single crystal of a semiconducting substance such as silicon or gallium arsenide.

In the late 1980s and early 1990s, integrated-circuit techniques allowed the creation of tiny superconducting (zero-electrical-resistance) cavities on chips. Methods for manipulating single atoms using lasers allowed researchers to place single atoms inside such cavities, where their interactions with photons—as described by QED—could be carefully observed and controlled. This field became known as cavity quantum electrodynamics (cavity QED or c-QED). Super-sensitive optical and microwave detectors, capable of detecting electromagnetic fields consisting of only a few photons, have been developed using cavity QED. Perhaps more importantly, in the early 2000s researchers were busily engaged in demonstrating how, using cavity QED methods, quantum information (in the form of quantum bits or “cubits”) could be stored in single atoms. In 2007, researchers reported that they could imprint the state of a single photon on a single atom, force the atom to retain that information for a significant period of time, and then release the information at will in the form of a new photon. Such technologies will probably be needed in the development of future computer chips that greatly exceed today's most powerful computers in memory capacity and number of calculations per second. Just as today's computer technology has had profound effects on society, future leaps to quantum computers with hundreds or thousands of times the power of today's machines are likely to have further effects, some unforeseen.

**See Also** Physics: The Quantum Hypothesis.

bibliography

**Books**

Feynman, Richard. *QED: The Strange Theory of Light and Matter.* Princeton University Press, 2006.

Feynman, Richard. *Quantum Electrodynamics.* Boulder, CO: Westview Press, 1998.

**Periodicals**

Haroche, Serge, and Jean-Michel Raimond. “Cavity Quantum Electrodynamics.” *Scientific American* (April 1993): 54–62.

**Web Sites**

Feynman, Richard. “The Development of the Space-Time View of Quantum Electrodynamics.” Nobel Prize.org. December 11, 1965. http://nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html (accessed January 23, 2008).

*K. Lee Lerner*

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