A unified interpretation of antiparticles is now available in quantum field theory, which solves both these problems.

This is an example of renormalization in quantum field theory — the field theory being necessary because the number of particles changes from one to two and back again.

In quantum field theory, this process is allowed only as an intermediate quantum state for times short enough that the violation of energy conservation can be accommodated by the uncertainty principle.

These processes are important in the vacuum state and renormalization of a quantum field theory.

This section draws upon the ideas, language and notation of canonical quantization of a quantum field theory.

This technique is the most widespread method of computing amplitudes in quantum field theory today.

Practical applications are made impossible due to the no-cloning theorem, and the fact that quantum field theories preserve causality, so that quantum correlations cannot be used to transfer information.

The analogy was completed when Hawking, in 1974, showed that quantum field theory predicts that black holes should radiate like a black body with a temperature proportional to the surface gravity of the black hole.

* Canonical anticommutation relation, a concept in quantum field theory

The physical model behind cosmic inflation is extremely simple, however it has not yet been confirmed by particle physics, and there are difficult problems reconciling inflation and quantum field theory.

* An introduction including more on general relativity and quantum field theory than most.

After World War II, several ideas from quantum field theory were applied to condensed matter problems.

These ideas were unified by Kenneth Wilson in 1972, under the formalism of the renormalization group in the context of quantum field theory.

Theoretical models have also been developed to study the physics of phase transitions, such as the Landau-Ginzburg theory, Critical exponents and the use of mathematical techniques of quantum field theory and the renormalization group.

Goldstone's theorem in quantum field theory states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone bosons.

In 1929, Heisenberg gave a series of invited lectures at the University of Chicago explaining the new field of quantum mechanics.

The problem of thinking in terms of classical measurements of a quantum system becomes particularly acute in the field of quantum cosmology, where the quantum system is the universe.

The general concept of a chemical reaction has been extended to non-chemical reactions between entities smaller than atoms, including nuclear reactions, radioactive decays, and reactions between elementary particles as described by quantum field theory.

He discovered that the so-called Weil representation, previously introduced in quantum mechanics by Irving Segal and Shale, gave a contemporary framework for understanding the classical theory of quadratic forms.

A 2008 quantum physics experiment performed in Geneva, Switzerland has determined that in any hypothetical nonlocal hidden-variables theory the speed of the quantum non-local connection would have to be at least 10, 000 times the speed of light.

Sakharov also proposed the idea of induced gravity as an alternative theory of quantum gravity.

In computational complexity theory, BQP ( bounded error quantum polynomial time ) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1 / 3 for all instances.

Apparently a new unified theory of quantum gravitation is needed to break this barrier.

Bootstrapping is using very general consistency criteria to determine the form of a quantum theory from some assumptions on the spectrum of particles.

Linear operators are ubiquitous in the theory of quantum mechanics.

Albert Einstein, in 1922, said regarding contemporary theories of superconductivity that “ with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas ”

Quantum effects such as the Casimir effect cannot violate the averaged null energy condition in any neighborhood of space with zero curvature, but calculations in semiclassical gravity suggest that quantum effects may be able to violate this condition in curved spacetime.

It is true that certain experimentally verified quantum phenomena, such as the Casimir effect, when described in the context of the quantum field theories, lead to stress – energy tensors that also violate the energy conditions, such as negative mass-energy, and thus one can hope that Alcubierre-type warp drives can be physically realized by clever engineering taking advantage of such quantum effects.

Morris, Thorne and Yurtsever pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally mass-negative region of space-time.

In quantum field theory the existence of virtual particles is proposed, which lead to the so called Casimir effect.

Scientists have discovered a way of levitating ultra small objects by manipulating the so-called Casimir force, which normally causes objects to stick together due to forces predicted by quantum field theory.

* Casimir effect, an attraction between parallel plates best explained by quantum mechanics

Despite the sniping, he is well known for many invaluable contributions, in particular to quantum electrodynamics, where he calculated the Casimir force in an arbitrary macroscopic configuration of metals and dielectrics.

Applying these ladder operators to the eigenstates of the total angular momentum, azimuthal angular momentum and energy operators, the eigenvalues of the first Casimir operator C < sub > 1 </ sub > are n < sup > 2 </ sup > − 1 ; importantly, they are independent of the l and m quantum numbers, making the energy levels degenerate.

He postulates that such naturally occurring quantum events are exceptions to this premise, like the Casimir effect and radioactive decay.

The effect of device and quantum noise, associated with such low input levels, will be described.

The standard ampere is most accurately realized using a watt balance, but is in practice maintained via Ohm's Law from the units of electromotive force and resistance, the volt and the ohm, since the latter two can be tied to physical phenomena that are relatively easy to reproduce, the Josephson junction and the quantum Hall effect, respectively.

Further investigation and theoretical work showed that the effect was a radiationless effect more than an internal conversion effect by use of elementary quantum mechanics and transition rate and transition probability calculations.

The quantum Hall effect was discovered by Klaus von Klitzing in 1980 when he observed the Hall conductivity to be integer multiples of a fundamental constant.

Shortly after, in 1982, Störmer and Tsui observed the fractional quantum Hall effect where the conductivity was now a rational multiple of a constant.

The quantum hall effect is another example of measurements with high magnetic fields where topological properties such as Chern-Simons angle can be measured experimentally.

In most materials diamagnetism is a weak effect, but in a superconductor a strong quantum effect repels the magnetic field entirely, apart from a thin layer at the surface.

Although modern quantum optics tells us that there also is a semi-classical explanation of the photoelectric effect — the emission of electrons from metallic surfaces subjected to electromagnetic radiation — the photon was historically ( although not strictly necessarily ) used to explain certain observations.

In some contexts it is meaningful to speak of fractions of a charge ; for example in the charging of a capacitor, or in the fractional quantum Hall effect.

Heisenberg's principle was an attempt to provide a classical explanation of a quantum effect sometimes called non-locality.

Wavefunction collapse can be viewed as an epiphenomenon of quantum decoherence, which in turn is nothing more than an effect of the underlying local time evolution of the wavefunction of a system and all of its environment.

The quasiparticles of the fractional quantum Hall effect are also known as composite fermions, which are electrons with an even number of quantized vortices attached to them.

In a few materials, a much stronger interaction between spins arises because the change in the direction of the spin leads to a change in electrostatic repulsion between neighboring electrons, due to a particular quantum mechanical effect called the exchange interaction.

This is a direct effect of quantum mechanics: specifically, the zero point energy of the system is too high to allow freezing.

Experimental evidence for the existence of anyons exists in the fractional quantum Hall effect, a phenomenon observed in the two-dimensional electron gases that form the inversion layer of MOSFETs.

BCS theory views superconductivity as a macroscopic quantum mechanical effect.

:* Nanotechnology – rigorously, the study of materials where the effects of quantum confinement, the Gibbs – Thomson effect, or any other effect only present at the nanoscale is the defining property of the material ; but more commonly, it is the creation and study of materials whose defining structural properties are anywhere from less than a nanometer to one hundred nanometers in scale, such as molecularly engineered materials.

Study of the photoelectric effect led to important steps in understanding the quantum nature of light and electrons and influenced the formation of the concept of wave – particle duality.

Since the complex algebra is responsible for the striking interference effect of quantum mechanics, phase of particles is therefore ultimately related to their quantum behavior.