Quantum physics

Quantum mechanics

Introduction to... Mathematical formulation of...

Fundamental concepts

Decoherence Interference Uncertainty Exclusion Transformation theory Ehrenfest theorem Measurement

Experiments

Double-slit experiment Davisson-Germer experiment Stern–Gerlach experiment EPR paradox Popper's experiment Schrdinger's cat

Equations

Schrdinger equation Pauli equation Klein-Gordon equation Dirac equation

Advanced theories

Quantum field theory Wightman axioms Quantum electrodynamics Quantum chromodynamics Quantum gravity Feynman diagram

Interpretations

Copenhagen Ensemble Hidden variables Transactional Many-worlds Consistent histories Quantum logic Consciousness causes collapse

Scientists

Planck Schrdinger Heisenberg Bohr Pauli Dirac Bohm Born de Broglie von Neumann Einstein Feynman Everett Others

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Quantum electrodynamics (QED) is a relativistic quantum field theory of electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s.^[1] QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons. It has been called "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron, and the Lamb shift of the energy levels of hydrogen.

History

Main article: History of quantum mechanics

The word 'quantum' is Latin, meaning "how much," (neut. sing. of quantus "how great").^[2] The word 'electrodynamics' was coined by André-Marie Ampère in 1822.^[3] The word 'quantum', as used in physics, was first used by Max Planck, i.e. "energy elements", in 1900 and reinforced by Einstein in 1905 with his use of the term light quanta.

Quantum theory began in 1900, when Max Planck assumed that energy is quantized in order to derive a formula predicting the observed frequency dependence of the energy emitted by a black body. This dependence is completely at variance with classical physics. In 1905, Einstein explained the photoelectric effect by postulating that light energy comes in quanta later called photons. In 1913, Bohr invoked quantization in his proposed explanation of the spectral lines of the hydrogen atom. In 1924, Louis de Broglie proposed a quantum theory of the wave-like nature of subatomic particles. The phrase "quantum physics" was first employed in Johnston's Planck's Universe in Light of Modern Physics. These theories, while they fit the experimental facts to some extent, were strictly phenomenological: they provided no rigorous justification for the quantization they employed.

Modern quantum mechanics was born in 1925 with Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave mechanics and the Schrödinger equation, which was a non-relativistic generalization of de Broglie's(1925) relativistic approach. Schrödinger subsequently showed that these two approaches were equivalent. In 1927, Heisenberg formulated his uncertainty principle, and the Copenhagen interpretation of quantum mechanics began to take shape. Around this time, Paul Dirac, in work culminating in his 1930 monograph finally joined quantum mechanics and special relativity, pioneered the use of operator theory, and devised the bra-ket notation widely used since. In 1932, John von Neumann formulated the rigorous mathematical basis for quantum mechanics as the theory of linear operators on Hilbert spaces. This and other work from the founding period remains valid and widely used.

Quantum chemistry began with Walter Heitler and Fritz London's 1927 quantum account of the covalent bond of the hydrogen molecule. Linus Pauling and others contributed to the subsequent development of quantum chemistry.

The application of quantum mechanics to fields rather than single particles, resulting in what are known as quantum field theories, began in 1927. Early contributors included Dirac, Wolfgang Pauli, Weisskopf, and Jordan. This line of research culminated in the 1940s in the quantum electrodynamics (QED) of Richard Feynman, Freeman Dyson, Julian Schwinger, and Sin-Itiro Tomonaga, for which Feynman, Schwinger and Tomonaga received the 1965 Nobel Prize in Physics. QED, a quantum theory of electrons, positrons, and the electromagnetic field, was the first satisfactory quantum description of a physical field and of the creation and annihilation of quantum particles.

QED involves a covariant and gauge invariant prescription for the calculation of observable quantities. Feynman's mathematical technique, based on his diagrams, initially seemed very different from the field-theoretic, operator-based approach of Schwinger and Tomonaga, but Freeman Dyson later showed that the two approaches were equivalent. The renormalization procedure for eliminating the awkward infinite predictions of quantum field theory was first implemented in QED. Even though renormalization works very well in practice, Feynman was never entirely comfortable with its mathematical validity, even referring to renormalization as a "shell game" and "hocus pocus". (Feynman, 1985: 128)

QED has served as a role model and template for all subsequent quantum field theories. One such subsequent theory is quantum chromodynamics, which began in the early 1960s and attained its present form in the 1975 work by H. David Politzer, Sidney Coleman, David Gross and Frank Wilczek. Building on the pioneering work of Schwinger, Peter Higgs, Goldstone, and others, Sheldon Glashow, Steven Weinberg and Abdus Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into a single electroweak force.

Physical interpretation of QED

In classical optics light travels over all allowed paths, and their interference results in Fermat's principle. Similarly, in QED light (or any other particle like an electron or a proton) passes over every possible path allowed by apertures or lenses. The observer (at a particular location) simply detects the mathematical result of all wave functions added up, as a sum of all line integrals. For other interpretations, paths are viewed as non physical, mathematical constructs that are equivalent to other, possibly infinite, sets of mathematical expansions. According to QED, light can go slower or faster than c, but will travel at speed c on average^[4].

Physically, QED describes charged particles (and their antiparticles) interacting with each other by the exchange of photons. The magnitude of these interactions can be computed using perturbation theory; these rather complex formulas have a remarkable pictorial representation as Feynman diagrams [1]. QED was the theory to which Feynman diagrams were first applied. These diagrams were invented on the basis of Lagrangian mechanics. Using a Feynman diagram, one decides every possible path between the start and end points. Each path is assigned a complex-valued probability amplitude, and the actual amplitude we observe is the sum of all amplitudes over all possible paths. Obviously, among all possible paths the ones with stationary phase contribute most (due to lack of destructive interference with some neighboring counter-phase paths) — this results in the stationary classical path between the two points.

QED doesn't predict what will happen in an experiment, but it can predict the probability of what will happen in an experiment, which is how it is experimentally verified. Predictions of QED agree with experiments to an extremely high degree of accuracy: currently about 10⁻¹² (and limited by experimental errors); for details see precision tests of QED. This makes QED the most accurate physical theory constructed thus far.

Near the end of his life, Richard P. Feynman gave a series of lectures on QED intended for the lay public. These lectures were transcribed and published as Feynman (1985), QED: The strange theory of light and matter, a classic non-mathematical exposition of QED from the point of view articulated above.

Mathematics

Mathematically, QED has the structure of an abelian gauge theory with a symmetry group being U(1) gauge group. The gauge field which mediates the interaction between the charged spin-1/2 fields is the electromagnetic field. The QED Lagrangian for the interaction of electrons and positrons through photons is

:

where

: are Dirac matrices.

: and its Dirac adjoint are the fields representing electrically charged particles, specifically electron and positron fields represented as Dirac spinors.

: is the gauge covariant derivative, with the coupling strength (equal to the elementary charge),

: the covariant vector potential of the electromagnetic field and

: the electromagnetic field tensor.

Euler-Lagrange equations

To begin, plug in the definition of D into the Lagrangian to see that L is

:

One can plug this Lagrangian into the Euler-Lagrange equation of motion for a field

:

to find the field equations for QED.

The two terms from this lagrangian are then

:

:

Plugging these two back into the Euler-Lagrange equation (2) results in

:

and the complex conjugate

:

If you bring the middle term to the right-hand side looks like:

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

One more important equation can be found by plugging in the lagrangian into one more Euler-lagrange equation, but now for the field, :

:

The two terms this time are

:

:

And these two terms, when plugged back into (3) give

:

In pictures

The part of the Lagrangian containing the electromagnetic field tensor describes the free evolution of the electromagnetic field, whereas the Dirac-like equation with the gauge covariant derivative describes the free evolution of the electron and positron fields as well as their interaction with the electromagnetic field.

The one-loop contribution to the vacuum polarization function

The one-loop contribution to the electron self-energy function

The one-loop contribution to the vertex function

See also

Abraham-Lorentz force Anomalous magnetic moment Basics of quantum mechanics Bhabha scattering Cavity quantum electrodynamics (Cavity QED) Compton scattering Gauge theory Gupta-Bleuler formalism Lamb shift Landau pole Moeller scattering Photon dynamics in the double-slit experiment Photon polarization Positronium

Quantum chromodynamics Quantum field theory Quantum gauge theory Renormalization Scalar electrodynamics Schrödinger equation Schwinger model Schwinger-Dyson equation Self-energy Standard Model Theoretical and experimental justification for the Schrödinger equation Vacuum polarization Vertex function

References

1. ^ Richard Feynman, 1985. QED: The strange theory of light and matter (chapter 1, page 6, first paragraph). Princeton Univ. Press.
2. ^ Online Etymology Dictionary
3. ^ Grandy, W.T. (2001). Relativistic Quantum Mechanics of Leptons and Fields, Springer.
4. ^ Richard P. Feynman QED:(QED (book)) p89-90 "the light has an amplitude to go faster or slower than the speed c, but these amplitudes cancel each other out over long distances"; see also accompanying text

Further reading

Books

• Feynman, Richard Phillips (1998). Quantum Electrodynamics. Westview Press; New Ed edition. ISBN 978-0201360752. 
• Tannoudji-Cohen, Claude; Dupont-Roc, Jacques, and Grynberg, Gilbert (1997). Photons and Atoms: Introduction to Quantum Electrodynamics. Wiley-Interscience. ISBN 978-0471184331. 
• De Broglie, Louis (1925). Recherches sur la theorie des quanta [Research on quantum theory]. France: Wiley-Interscience. 
• Jauch, J.M.; Rohrlich, F. (1980). The Theory of Photons and Electrons. Springer-Verlag. ISBN 978-0387072951. 
• Miller, Arthur I. (1995). Early Quantum Electrodynamics : A Sourcebook. Cambridge University Press. ISBN 978-0521568913. 
• Schweber, Silvian,S. (1994). QED and the Men Who Made It. Princeton University Press. ISBN 978-0691033273. 
• Schwinger, Julian (1958). Selected Papers on Quantum Electrodynamics. Dover Publications. ISBN 978-0486604442. 
• Greiner, Walter; Bromley, D.A.,Müller, Berndt. (2000). Gauge Theory of Weak Interactions. Springer. ISBN 978-3540676720. 
• Kane, Gordon, L. (1993). Modern Elementary Particle Physics. Westview Press. ISBN 978-0201624601. 

Journals

• J.M. Dudley and A.M. Kwan, "Richard Feynman's popular lectures on quantum electrodynamics: The 1979 Robb Lectures at Auckland University," American Journal of Physics Vol. 64 (June 1996) 694-698.

External links

• Feynman's Nobel Prize lecture describing the evolution of QED and his role in it
• Feynman's New Zealand lectures on QED for non-physicists

•  • [ e] Quantum Electrodynamics
electron • positron • photon • self-energy • vacuum polarization • vertex function • Gupta-Bleuler formalism • ξ gauge • Ward-Takahashi identity • Compton scattering • Bhabha scattering • Mller scattering • anomalous magnetic dipole moment • bremsstrahlung • positronium

quantum mechanics is the study of the relationship between energy quanta (radiation) and matter, in particular that between valence shell electrons and photons. Quantum mechanics is a fundamental branch of physics with wide applications in both experimental and theoretical physics.
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Quantum mechanics (QM, or quantum theory) is a physical science dealing with the behaviour of matter and energy on the scale of atoms and subatomic particles / waves.^[1]
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The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. It is distinguished from mathematical formalisms for theories developed prior to the early 1900s by the use of abstract mathematical
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Please [improve the article] or discuss this issue on the talk page. This article has been tagged since April 2007.
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Interference is the addition (superposition) of two or more waves that results in a new wave pattern.

As most commonly used, the term interference usually refers to the interaction of waves which are correlated or coherent with each other, either because they
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Heisenberg uncertainty principle, or HUP, gives a lower bound on the product of the standard deviations of position and momentum for a system, implying that it is impossible to have a particle that has an arbitrarily well-defined position and momentum simultaneously.
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The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. This principle is significant, because it explains why matter occupies space exclusively for itself and does not allow other material objects to pass through it, while at the same
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The term transformation theory refers to a procedure used by P. A. M. Dirac in his early formulation of quantum theory, from around 1927.

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The Ehrenfest theorem, named after Paul Ehrenfest, relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system.
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The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications.

Measurement from a practical point of view

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π due to reflection at the interface of a denser medium)

Quantum version of experiment

By the 1920s, various other experiments (such as the photoelectric effect) had demonstrated that light interacts with matter only in discrete, "quantum"-sized packets called photons.
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In quantum mechanics, the EPR paradox is a thought experiment which challenged long-held ideas about the relation between the observed values of physical quantities and the values that can be accounted for by a physical theory.
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action at a distance.

The debate

Many viewed Popper's experiment as a crucial test of quantum mechanics, and there was a debate on what result an actual realization of the experiment would yield.
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In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the
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Quantum field theory (QFT) is a theoretical framework for constructing quantum mechanical models of field-like systems, or, equivalently, of many-body systems. It is widely used in particle physics and condensed matter physics.
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In physics the Wightman axioms are an attempt at a mathematically rigorous formulation of quantum field theory. Arthur Wightman formulated the axioms in the early 1950s but they were first published only in 1964, after Haag-Ruelle scattering theory affirmed their significance.
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Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion).
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Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity.
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radiates a gluon. (Time goes left to right, and one space dimension runs from top to bottom.)]]

A Feynman diagram is a tool invented by American physicist Richard Feynman for performing scattering calculations in quantum field theory.
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An interpretation of quantum mechanics is a statement which attempts to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has been extensively tested in very fine experiments, some believe the fundamentals of the theory are yet to be
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The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. Bohr and Heisenberg extended the probabilistic interpretation of the wave function, proposed by Max Born.
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''Hidden variable redirects here. For hidden variables in economics, see latent variable.

In physics, hidden variable theories are espoused by a minority of physicists who argue that the statistical nature of quantum mechanics indicates that quantum
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The transactional interpretation of quantum mechanics (TIQM) is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward-in-time) and advanced (backward-in-time) waves.
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The many-worlds interpretation or MWI (also known as relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics.
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In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology.
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In mathematical physics and quantum mechanics, quantum logic is a formalism for reasoning about propositions which takes the principles of quantum theory into account. This research area and its name originated in the 1936 paper by Garrett Birkhoff and John von Neumann, who were
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Further information: quantum mind

"Consciousness causes collapse" is the name given to the claim that observation by a conscious observer is responsible for the wavefunction collapse in quantum mechanics.
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