In 1979 the ( non relativistic ) hydrogen atom was solved for the first time within Feynman's path integral formulation

Schopenhauer also points towards this inherently relativistic nature of mathematics and conventional science in his formulation of the ' World as Will '.

Also like Newton's Second law, the Schrödinger equation describes time in a way that is inconvenient for relativistic theories, a problem that is not as severe in matrix mechanics and completely absent in the path integral formulation.

This is in analogy to the 4 / 3 problem of the electromagnetic mass of electrons, where similar methods were employed by Enrico Fermi ( 1921 ) and Fritz Rohrlich ( 1960 ): In the standard formulation of relativistic dynamics the hyperplanes of simultaneity of any observer can be used, while in the Fermi / Rohrlich definition the hyperplane of simultaneity of the object's rest frame should be used.

He also introduced a trigonometric formulation of the relativistic velocity addition rule, which according to Sommerfeld, removes much of the strangeness of that concept.

The above formulation is inherently phrased in a non-relativistic language ; and it is noted that elementary particles have relativistic decay products.

The total energy is determined by approximate solutions of the time-dependent Schrödinger equation, usually with no relativistic terms included, and by making use of the Born – Oppenheimer approximation, which allows for the separation of electronic and nuclear motions, thereby simplifying the Schrödinger equation.

In order to obtain exact agreement with experiment, it is necessary to include relativistic and spin orbit terms, both of which are only really important for heavy atoms.

The time scale represented by T < sub > eph </ sub > has been characterized as a relativistic coordinate time that differs from Terrestrial Time only by small periodic terms with an amplitude not exceeding 2 milliseconds of time: it is linearly related to, but distinct ( by an offset and constant rate which is of the order of 0. 5 sec / yr ) from the TCB time scale adopted in 1991 as a standard by the IAU.

In relativistic terms, the SI second is defined as the proper time on the rotating geoid.

In relativistic terms, TT is described as the proper time of a clock located on the geoid ( essentially mean sea level ).

Ernst Neef defines landscapes as sections within the uninterrupted earth-wide interconnection of geofactors which are defined as such on the basis of their uniformity in terms of a specific land use, and are thus defined in an anthropocentric and relativistic way.

; beamed, beaming: shorter terms for ‘ relativistic beaming ’

Since they constitute a very simple and natural class of Lorentzian manifolds, defined in terms of a null congruence, it is not very surprising that they are also important in other relativistic classical field theories of gravitation.

After first attempts by Jakob Laub ( 1907 ) to create a relativistic " optics of moving bodies ", it was Max von Laue ( 1907 ) who derived the coefficient for terms of all orders by using the colinear case of the relativistic velocity addition law.

It turns out that such inconsistencies arise from relativistic wavefunctions having a probabilistic interpretation in position space, as probability conservation is not a relativistically covariant concept.

It is also possible that a rule which defines instantaneousness is contingent, by emerging dynamically from relativistic covariant laws combined with particular initial conditions.

Consequently, the jet bundle is now recognized as the correct domain for a geometrical covariant field theory and much work is done in general relativistic formulations of fields using this approach.

This could be conveniently done under the formalism of relativistic ( or covariant ) classical field theory.

Because of this, the Coulomb gauge is not used in covariant perturbation theory, which has become standard for the treatment of relativistic quantum field theories such as quantum electrodynamics.

Einstein published his first paper on relativistic cosmology in 1917, in which he added this cosmological constant to his field equations in order to force them to model a static universe.

Provided the theory is linear with respect to the wavefunction, the exact form of the quantum dynamics modelled, be it the non-relativistic Schrödinger equation, relativistic quantum field theory or some form of quantum gravity or string theory, does not alter the validity of MWI since MWI is a metatheory applicable to all linear quantum theories, and there is no experimental evidence for any non-linearity of the wavefunction in physics.

Charged particles can move at relativistic speeds nearing field propagation speeds, but, as Einstein showed, this requires enormous field energies, which are not present in our everyday experiences with electricity, magnetism, matter, and time.

The spin-statistics theorem holds that, in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.

In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology.

Variations on this basic formula describe the magnetic force on a current-carrying wire ( sometimes called Laplace force ), the electromotive force in a wire loop moving through a magnetic field ( an aspect of Faraday's law of induction ), and the force on a particle which might be traveling near the speed of light ( relativistic form of the Lorentz force ).

He is the third, and possibly most important, pillar of that field ( he soon was the only one to have discovered a relativistic generalization of the theory ).

Note that that while bound orbits around a point mass or around a spherical body with an Newtonian gravitational field are closed ellipses, which repeat the same path exactly and indefinitely, any non-spherical or non-Newtonian effects ( as caused, for example, by the slight oblateness of the Earth, or by relativistic effects, changing the gravitational field's behavior with distance ) will cause the orbit's shape to depart from the closed ellipses characteristic of Newtonian two-body motion.

In relativistic quantum field theory, the Pauli principle follows from applying a rotation operator in imaginary time to particles of half-integer spin.

A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field ( rather than a fixed set of particles ).

Most theories in modern particle physics, including the Standard Model of elementary particles and their interactions, are formulated as relativistic quantum field theories.

Quantum electrodynamics ( QED ) is the relativistic quantum field theory of electrodynamics.

In relativistic quantum field theory, just as in classical field theory, Minkowski spacetime is the fixed background of the theory.

* Quantum field theory, a generic type of relativistic quantum theory, which includes:

In quantum field theory, spinors describe the state of relativistic many-particle systems.

Likewise using the 4 × 4 Dirac gamma matrices gives rise to the 4 component Dirac spinors used in 3 + 1 dimensional relativistic quantum field theory.

Although it is not a successful relativistic generalization of the Schrödinger equation, this equation is resurrected in the context of quantum field theory, where it is known as the Klein – Gordon equation, and describes a spinless particle field ( e. g. pi meson ).

* In particle accelerators an isochronous cyclotron is a cyclotron where the field strength increases with radius to compensate for relativistic increase in mass with speed

In contrast to this approximation, as particles approach the speed of light, their relativistic mass increases, requiring either modifications to the frequency, leading to the synchrocyclotron, or modifications to the magnetic field during the acceleration, which leads to the isochronous cyclotron.

A synchrocyclotron is a cyclotron in which the frequency of the driving RF electric field is varied to compensate for relativistic effects as the particles ' velocity begins to approach the speed of light.

In the language of four-vectors and tensors the angular momentum of a particle in relativistic mechanics is expressed as an antisymmetric tensor of second order

As it is constructed using tensors, general relativity exhibits general covariance: its laws — and further laws formulated within the general relativistic framework — take on the same form in all coordinate systems.

The Dirac equation for the relativistic quantum electron caused Eddington to rethink his previous conviction that fundamental physical theory had to be based on tensors.