Baryons are strongly interacting fermions — that is, they experience the strong nuclear force and are described by Fermi − Dirac statistics, which apply to all particles obeying the Pauli exclusion principle.

Systems of many identical fermions are described by Fermi – Dirac statistics.

There are important differences between the statistical behavior of bosons and fermions, which are described by Bose – Einstein statistics and Fermi – Dirac statistics respectively.

The principle was described by Paul Dirac as follows:

In the Dirac notation, ( projective ) measurements are described via eigenvalues and eigenstates, both purely formal objects.

The Dirac sea has a direct analog to the electronic band structure in crystalline solids as described in solid state physics.

( It does not hold for matter described by a super-field, i. e., the Dirac field ) The energy condition required for the black-hole singularity theorem is weak: it says that light rays are always focused together by gravity, never drawn apart, and this holds whenever the energy of matter is non-negative.

* Magnetic monopole, or Dirac monopole, a hypothetical particle that may be loosely described as a magnet with only one pole, or related concepts in physics and mathematics:

As a consequence, at low energies, even neglecting the true spin, the electrons can be described by an equation which is formally equivalent to the massless Dirac equation.

The situation around 1930 is described by Paul Dirac:

In group representation theory, a quark is described by a Dirac spinor, which can be thought of as a pair of Weyl spinors describing the left-handed ( negative chirality ) and the right-handed ( positive chirality ) quark.

A consequence of this apparent paradox is that the electric field of a point-charge can only be described in a limiting sense by a carefully constructed Dirac delta function.

The wave function Ψ in the Breit equation is a spinor with 4 < sup > N </ sup > elements, since each electron is described by a Dirac bispinor with 4 elements as in the Dirac equation and total wave function is the cartesian product of these.

The Dirac field can be described as either a 4-component spinor or as a pair of 2-component Weyl spinors.

This term is also used in condensed matter physics to describe low-energy excitations in graphene and topological insulators, among others, which in this regime are described by a pseudo-relativistic Dirac equation.

( It does not hold for matter described by a super-field, i. e., the Dirac field!

Using quantum theory Dirac showed that if magnetic monopoles exist, then one could explain the quantization of electric charge --- that is, why the observed elementary particles carry charges that are multiples of the charge of the electron.

In his PhD thesis project, Paul Dirac discovered that the equation for the operators in the Heisenberg representation, as it is now called, closely translates to classical equations for the dynamics of certain quantities in the Hamiltonian formalism of classical mechanics, when one expresses them through Poisson brackets, a procedure now known as canonical quantization.

* 1931 Paul Dirac shows that charge quantization can be explained if magnetic monopoles exist

The Dirac string acts as the solenoid in the Aharonov-Bohm effect, and the requirement that the position of the Dirac string should not be observable implies the Dirac quantization rule: the product of a magnetic charge and an electric charge must always be an integer multiple of.

The quantization forced by the Dirac string can be understood in terms of the cohomology of the fibre bundle representing the gauge fields over the base manifold of space-time.

Historically, this was not quite Werner Heisenberg's route to obtaining quantum mechanics, but Paul Dirac introduced it in his 1926 doctoral thesis, the " method of classical analogy " for quantization, and detailed it in his classic text.

He extended the Dirac quantization condition to the dyon and used the model to predict the existence of a particle with the properties of the J / ψ meson prior to its discovery in 1974.

The allowed charges of dyons are restricted by the Dirac quantization condition.

This particular star product is also sometimes called Weyl-Groenewold product, as it was introduced by H. J. Groenewold in 1946, in a trenchant appreciation of Weyl quantization — Moyal actually appears to not know about it in his celebrated paper, and in his legendary correspondence with Dirac, as adduced in his biography.

Dirac tried to argue that this was due to the electromagnetic interactions with the sea, until Hermann Weyl proved that hole theory was completely symmetric between negative and positive charges.

Following the work of Paul Dirac in quantum field theory, George Sudarshan, Roy J. Glauber, and Leonard Mandel applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light.

The left-hand side is like the original Dirac equation and the right-hand side is the interaction with the electromagnetic field.

On introducing the external electromagnetic 4-vector potential into the Dirac equation in a similar way, known as minimal coupling, it takes the form ( in natural units )

Supposed to transmit a single, ideal Dirac pulse of electromagnetic power at time 0, i. e.

Like the electromagnetic potential A the Dirac string is not gauge invariant ( it moves around with fixed endpoints under a gauge transformation ) and so is also not directly measurable.

Following the work of Dirac in quantum field theory, George Sudarshan, Roy J. Glauber, and Leonard Mandel applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light ( see degree of coherence ).

" This means that there is a component of the quantum vacuum respectively for each component field ( considered in the conceptual absence of the other fields ), such as the electromagnetic field, the Dirac electron-positron field, and so on.

In quantum field theory, the kinetic term for real scalar fields, electromagnetic field and Dirac field are

Dirac met this difficulty by introducing into the Einstein field equations a gauge function that describes the structure of spacetime in terms of a ratio of gravitational and electromagnetic units.

As in the case of the Dirac equation, electromagnetic interaction can be added by promoting the partial derivative to gauge covariant derivative:

The spin g-factor g < sub > s </ sub > = 2 comes from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties.

On introducing the external electromagnetic 4-potential into the Dirac equation in a similar way, known as minimal coupling, it takes the form ( in natural units ħ

In a general case ( if a certain linear function of electromagnetic field does not vanish identically ), three out of four components of the spinor function in the Dirac equation can be algebraically eliminated, yielding an equivalent fourth-order partial differential equation for just one component.

The history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s.

The first reasonably complete theory of quantum electrodynamics, which included both the electromagnetic field and electrically charged matter ( specifically, electrons ) as quantum mechanical objects, was created by Paul Dirac in 1927.

Following the work of Dirac in quantum field theory, George Sudarshan, Roy J. Glauber, and Leonard Mandel applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light ( see degree of coherence ).