Quantum Field Theory
Quantum Field Theory (QFT) is a fundamental framework in physics that merges classical field theory with quantum mechanics to describe the behavior and interactions of subatomic particles. It posits that particles are not discrete entities but are excitations within continuous physical fields, such as electromagnetic or gravitational fields. QFT encompasses various fundamental forces, with quantum electrodynamics (QED) governing electromagnetic interactions, and quantum chromodynamics (QCD) addressing the strong interactions among quarks and gluons. The standard model of particle physics synthesizes these theories, explaining three of the four fundamental forces, while gravity remains an unsolved challenge within this framework.
A notable subtype of QFT is conformal field theory (CFT), which is scale-invariant and exclusively supports massless excitations. The mathematics of QFT involves an infinite number of degrees of freedom due to the continuity of fields, with techniques like renormalization employed to manage infinities and approximate the theory for specific scales. Despite its complexity, QFT has proven successful in predicting particle behaviors, continually verified through high-energy experiments at facilities like CERN. As technology advances, understanding QFT is increasingly essential, influencing fields from electronics to astrophysics, demonstrating its real-world relevance despite its theoretical nature.
Quantum Field Theory
FIELDS OF STUDY: Quantum Field Theory; Quantum Physics
ABSTRACT: Quantum field theory has its origins in quantum mechanics. It is a mathematical model designed to explain the behavior of subatomic particles in terms of physical fields. Examples of quantum field theories include quantum chromodynamics, quantum electrodynamics, and conformal field theory. Valid descriptions of the behavior of electrons and other matter at the atomic scale in electronic devices is an important application of quantum field theory.
PRINCIPAL TERMS
- conformal field theory: a quantum field theory that is independent of the scale of the system and supports only massless excitations.
- degrees of freedom: the number of physical parameters required to specify the position and configuration of a particle or other body.
- quantum chromodynamics: a quantum field theory that describes the interactions of quarks and gluons, subatomic particles that are responsible for the strong interaction.
- quantum electrodynamics: a quantum field theory that describes the interactions of photons and electrically charged particles, which are responsible for electromagnetism.
- quantum mechanics: the branch of physics that deals with matter interactions on a subatomic scale, based on the concepts that energy is quantized, not continuous, and that elementary particles exhibit wavelike behavior.
- renormalization: a mathematical procedure by which processes occurring on very different scales can be aligned.
- standard model: a generally accepted unified framework of particle physics that explains electromagnetism, the weak interaction, and the strong interaction as products of interactions between different types of elementary particles.
- superposition: in quantum mechanics, the concept that a particle exists in all possible states at the same time until either its position or its energy is known.
Quantization of Physical Fields
One significant aspect of quantum mechanics is the tendency of subatomic particles to behave as waves under some conditions and as particles under others. This concept is called wave-particle duality. Quantum field theory arises from the idea that such behavior can be described as the product of continuous physical fields rather than as interactions between individual entities.
A physical field is a region of space-time in which each point has a specific value for some physical quantity, such as electric potential or gravitational force. The voltage difference between two points in space, such as the terminals of a battery, is an example of an electric field, because electric potential exists between the two points. Similarly, the region between two magnetic poles is an example of a magnetic field, because magnetic potential exists between the poles. A quantum field theory explains particle interactions by treating particles not as discrete units but as energy excitations, or "field quanta," in fields such as these.
There are four fundamental forces that underlie all of physics: electromagnetism, the strong interaction, the weak interaction, and gravity. The standard model of particle physics is a unifying framework that brings together the quantum field theories of the first three of those forces. The theory of electromagnetism is quantum electrodynamics (QED), which describes the behavior of charged particles in an electromagnetic field. The theory of the strong interaction is quantum chromodynamics (QCD); it describes the interactions of elementary particles called quarks and gluons, which come together to form hadrons. (Hadrons are relatively massive composite particles, such as protons and neutrons.) The theory of the weak interaction is the electroweak theory, which unites it with electromagnetism.
As yet, there is no complete quantum field theory describing gravity. A model has been proposed, but it relies on hypothetical particles called gravitons, the existence of which has yet to be confirmed. A viable quantum field theory of gravity would be the first step toward a unified "theory of everything" that would incorporate gravity into the standard model. The lack of such a theory is one of the major unsolved problems in physics.
One subset of quantum field theory is conformal field theory (CFT). A quantum field theory is considered to be a CFT if it is scale invariant—that is, if the interactions it describes are independent of the scale of the system. In other words, if a CFT is either increased or decreased in size, the physics of the system it describes will remain the same. A CFT can only support massless excitations (i.e., particles), because having mass would make the system behave differently at different scales.
Mathematics of Quantum Fields
In general, a quantum mechanical system will contain a finite number of particles, each with a finite number of degrees of freedom. Degrees of freedom are the number of parameters required to precisely identify and locate an individual particle. For example, a point particle in three-dimensional space has three degrees of freedom, because three coordinates (x, y, z) are necessary to describe its location. If the point particle were instead a rigid body, it would have six degrees of freedom, because another three parameters would be needed to describe its orientation in space.
However, because fields are continuous, they have an effectively infinite number of degrees of freedom. Moreover, quantum fields can support any number of particles. One way to avoid dealing with these infinities is renormalization. This involves "integrating out," or removing from consideration, any parameters that do not apply to the length and energy scales being studied. Renormalization allows for the creation of an effective field theory, which is an approximation of a field theory that holds true for the lengths and energies of interest.
Quantum field theories are mathematics-intensive models that have had success in predicting the behaviors of subatomic particles. However, as models, they do not constitute proof of the behaviors they predict. The validity of these models must constantly be tested against experimentation and observation.
The observation of effects on the quantum scale requires very high-energy collision experiments, such as those carried out at the European Organization for Nuclear Research (CERN) facilities in Switzerland and at the Stanford Linear Accelerator Center (SLAC) facility in Connecticut. Calculation of wave properties in quantum mechanics begins with a statement of the general wave equation relating position and velocity. For a one-dimensional application only, this equation is relatively simple. However, it becomes increasingly complex as more degrees of freedom are involved.
One problem in quantum mechanics is that exact solutions involving more than one particle are effectively impossible to calculate. The principle of superposition can be used to simplify the situation by invoking a certain uniformity. Because the equation is linear, any combination of linear solutions is also a linear solution of the appropriate wave equation. The entire range of linear solutions to a particular wave equation represents the field corresponding to that wave equation.
Fundamental Physics
For the vast majority of people, quantum field theory is of no consequence. Because quantum theory deals with matter at the most fundamental level, classical Newtonian physics is sufficient on a macroscopic scale. However, ongoing developments in quantum theory have increasing significance as technology becomes functional at ever-smaller scales.
As the transistor circuits imprinted on silicon computer chips approach the lower size limits dictated by atomic size, quantum field effects become more important. Understanding these effects will be vital to ensuring that digital electronics of this type will be functional. New materials such as graphene raise the possibility of more efficient functioning on an even smaller scale. Development of devices using such materials will depend on the ability of theoretical models to predict the quantum behavior of particles within them.
Quantum field theory can also address questions on a much larger scale. It may help scientists understand the processes occurring within stars and the interactions of cosmic particles with Earth’s atmosphere. Accordingly, seemingly esoteric theoretical models do in fact have relevance in the real world.
Bibliography
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Lancaster, Tom, and Stephen J. Blundell. Quantum Field Theory for the Gifted Amateur. Oxford: Oxford UP, 2014. Print.
Teller, Paul. An Interpretive Introduction to Quantum Field Theory. Princeton: Princeton UP, 1995. Print.
Zee, A. Quantum Field Theory in a Nutshell. 2nd ed. Princeton: Princeton UP, 2010. Print.