Gauge theoryIn physics, a gauge theory is a field theory in which the Lagrangian is invariant under local transformations according to certain smooth families of operations (Lie groups). The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators.
Course of Theoretical PhysicsThe Course of Theoretical Physics is a ten-volume series of books covering theoretical physics that was initiated by Lev Landau and written in collaboration with his student Evgeny Lifshitz starting in the late 1930s. It is said that Landau composed much of the series in his head while in an NKVD prison in 1938–1939. However, almost all of the actual writing of the early volumes was done by Lifshitz, giving rise to the witticism, "not a word of Landau and not a thought of Lifshitz".
Spin–orbit interactionIn quantum physics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion inside a potential. A key example of this phenomenon is the spin–orbit interaction leading to shifts in an electron's atomic energy levels, due to electromagnetic interaction between the electron's magnetic dipole, its orbital motion, and the electrostatic field of the positively charged nucleus.
Negative massIn theoretical physics, negative mass is a hypothetical type of exotic matter whose mass is of opposite sign to the mass of normal matter, e.g. −1 kg. Such matter would violate one or more energy conditions and show some strange properties such as the oppositely oriented acceleration for an applied force orientation. It is used in certain speculative hypothetical technologies, such as time travel to the past and future, construction of traversable artificial wormholes, which may also allow for time travel, Krasnikov tubes, the Alcubierre drive, and potentially other types of faster-than-light warp drives.
Dirac seaThe Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons (electrons traveling near the speed of light). The positron, the antimatter counterpart of the electron, was originally conceived of as a hole in the Dirac sea, before its experimental discovery in 1932.
Continuity equationA continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described using continuity equations. Continuity equations are a stronger, local form of conservation laws.
Lorentz groupIn physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz. For example, the following laws, equations, and theories respect Lorentz symmetry: The kinematical laws of special relativity Maxwell's field equations in the theory of electromagnetism The Dirac equation in the theory of the electron The Standard Model of particle physics The Lorentz group expresses the fundamental symmetry of space and time of all known fundamental laws of nature.
Four-momentumIn special relativity, four-momentum (also called momentum–energy or momenergy) is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle with relativistic energy E and three-momentum p = (px, py, pz) = γmv, where v is the particle's three-velocity and γ the Lorentz factor, is The quantity mv of above is ordinary non-relativistic momentum of the particle and m its rest mass.
Momentum operatorIn quantum mechanics, the momentum operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example of a differential operator. For the case of one particle in one spatial dimension, the definition is: where ħ is Planck's reduced constant, i the imaginary unit, x is the spatial coordinate, and a partial derivative (denoted by ) is used instead of a total derivative (d/dx) since the wave function is also a function of time. The "hat" indicates an operator.
Path integral formulationThe path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization.
ZitterbewegungIn physics, the zitterbewegung (ˈtsɪtɐ.bəˌveːɡʊŋ, ) is the theoretical prediction of a rapid oscillatory motion of elementary particles that obey relativistic wave equations. This prediction was first discussed by Gregory Breit in 1928 and later by Erwin Schrödinger in 1930 as a result of analysis of the wave packet solutions of the Dirac equation for relativistic electrons in free space, in which an interference between positive and negative energy states produces an apparent fluctuation (up to the speed of light) of the position of an electron around the median, with an angular frequency of 2mc2/ħ, or approximately 1.
