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89 relations: Alexandroff extension, Boson, Canonical commutation relation, Canonical transformation, Classical electromagnetism, Classical limit, Classical mechanics, Classical physics, Commutator, Condensed matter physics, Constructive quantum field theory, Correspondence principle, Creation and annihilation operators, Dirac bracket, Electric charge, Electromagnetic field, Energy, Fermion, Field (physics), First quantization, Fock space, Foliation, Fourier transform, Functor, Gauge fixing, Gauge theory, Geometric quantization, Hamiltonian (quantum mechanics), Hamiltonian mechanics, Higgs mechanism, Hilbert space, Hilbrand J. Groenewold, Identical particles, Klein–Gordon equation, Lagrangian (field theory), Legendre transform, Linear combination, Local symmetry, Mass, Motion (physics), Moyal bracket, Normal mode, Normal order, Particle number, Particle number operator, Particle physics, Path integral formulation, Paul Dirac, Pauli exclusion principle, Phase space formulation, ..., Physics, Poincaré group, Poisson algebra, Poisson bracket, Poisson manifold, Poisson supermanifold, Position and momentum space, QCD vacuum, Quantization (physics), Quantum electrodynamics, Quantum field theory, Quantum harmonic oscillator, Quantum mechanics, Quantum number, Quantum state, Scalar field theory, Second quantization, Segal–Bargmann space, Silvan S. Schweber, Simple harmonic motion, Slater determinant, Spacetime, Special relativity, Spin (physics), Spontaneous symmetry breaking, Standard Model, Symmetry (physics), Symplectic geometry, Symplectic manifold, Symplectomorphism, Uncertainty principle, Unitary representation, Unitary transformation, Vacuum expectation value, Vacuum polarization, Vacuum state, Wave function, Werner Heisenberg, Wigner–Weyl transform. Expand index (39 more) »
Alexandroff extension
In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact.
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Boson
In quantum mechanics, a boson is a particle that follows Bose–Einstein statistics.
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Canonical commutation relation
In quantum mechanics (physics), the canonical commutation relation is the fundamental relation between canonical conjugate quantities (quantities which are related by definition such that one is the Fourier transform of another).
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Canonical transformation
In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates that preserves the form of Hamilton's equations.
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Classical electromagnetism
Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model.
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Classical limit
The classical limit or correspondence limit is the ability of a physical theory to approximate or "recover" classical mechanics when considered over special values of its parameters.
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Classical mechanics
Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.
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Classical physics
Classical physics refers to theories of physics that predate modern, more complete, or more widely applicable theories.
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Commutator
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.
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Condensed matter physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter.
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Constructive quantum field theory
In mathematical physics, constructive quantum field theory is the field devoted to showing that quantum theory is mathematically compatible with special relativity.
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Correspondence principle
In physics, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by the old quantum theory) reproduces classical physics in the limit of large quantum numbers.
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Creation and annihilation operators
Creation and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems.
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Dirac bracket
The Dirac bracket is a generalization of the Poisson bracket developed by Paul Dirac to treat classical systems with second class constraints in Hamiltonian mechanics, and to thus allow them to undergo canonical quantization.
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Electric charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
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Electromagnetic field
An electromagnetic field (also EMF or EM field) is a physical field produced by electrically charged objects.
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Energy
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.
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Fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics.
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Field (physics)
In physics, a field is a physical quantity, represented by a number or tensor, that has a value for each point in space and time.
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First quantization
A first quantization of a physical system is a semi-classical treatment of quantum mechanics, in which particles or physical objects are treated using quantum wave functions but the surrounding environment (for example a potential well or a bulk electromagnetic field or gravitational field) is treated classically.
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Fock space
The Fock space is an algebraic construction used in quantum mechanics to construct the quantum states space of a variable or unknown number of identical particles from a single particle Hilbert space.
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Foliation
In mathematics, a foliation is a geometric tool for understanding manifolds.
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Fourier transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
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Functor
In mathematics, a functor is a map between categories.
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Gauge fixing
In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables.
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Gauge theory
In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations.
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Geometric quantization
In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory.
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Hamiltonian (quantum mechanics)
In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases.
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Hamiltonian mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.
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Higgs mechanism
In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Hilbrand J. Groenewold
Hilbrand Johannes "Hip" Groenewold (1910–1996) was a Dutch theoretical physicist who pioneered the largely operator-free formulation of quantum mechanics in phase space known as phase-space quantization.
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Identical particles
Identical particles, also called indistinguishable or indiscernible particles, are particles that cannot be distinguished from one another, even in principle.
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Klein–Gordon equation
The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation.
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Lagrangian (field theory)
Lagrangian field theory is a formalism in classical field theory.
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Legendre transform
In mathematics, Legendre transform is an integral transform named after the mathematician Adrien-Marie Legendre, which uses Legendre polynomials P_n(x) as kernels of the transform.
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Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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Local symmetry
In physics, a local symmetry is symmetry of some physical quantity, which smoothly depends on the point of the base manifold.
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Mass
Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.
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Motion (physics)
In physics, motion is a change in position of an object over time.
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Moyal bracket
In physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase-space star product.
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Normal mode
A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation.
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Normal order
In quantum field theory a product of quantum fields, or equivalently their creation and annihilation operators, is usually said to be normal ordered (also called Wick order) when all creation operators are to the left of all annihilation operators in the product.
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Particle number
The particle number (or number of particles) of a thermodynamic system, conventionally indicated with the letter N, is the number of constituent particles in that system.
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Particle number operator
In quantum mechanics, for systems where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles.
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Particle physics
Particle physics (also high energy physics) is the branch of physics that studies the nature of the particles that constitute matter and radiation.
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Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics.
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Paul Dirac
Paul Adrien Maurice Dirac (8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.
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Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.
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Phase space formulation
The phase space formulation of quantum mechanics places the position and momentum variables on equal footing, in phase space.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Poincaré group
The Poincaré group, named after Henri Poincaré (1906), was first defined by Minkowski (1908) as the group of Minkowski spacetime isometries.
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Poisson algebra
In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also a derivation.
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Poisson bracket
In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system.
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Poisson manifold
In geometry, a Poisson structure on a smooth manifold M is a Lie bracket \ (called a Poisson bracket in this special case) on the algebra (M) of smooth functions on M, subject to the Leibniz rule Said in another manner, it is a Lie algebra structure on the vector space of smooth functions on M such that X_ \stackrel \: (M) \to (M) is a vector field for each smooth function f, which we call the Hamiltonian vector field associated to f. These vector fields span a completely integrable singular foliation, each of whose maximal integral sub-manifolds inherits a symplectic structure.
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Poisson supermanifold
In differential geometry a Poisson supermanifold is a differential supermanifold M such that the supercommutative algebra of smooth functions over it (to clarify this: M is not a point set space and so, doesn't "really" exist, and really, this algebra is all we have), C^\infty(M) is equipped with a bilinear map called the Poisson superbracket turning it into a Poisson superalgebra.
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Position and momentum space
In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general could be any finite number of dimensions.
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QCD vacuum
Th Quantum Chromodynamic Vacuum or QCD vacuum is the vacuum state of quantum chromodynamics (QCD).
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Quantization (physics)
In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.
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Quantum electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics.
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Quantum field theory
In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.
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Quantum harmonic oscillator
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of a quantum system.
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Quantum state
In quantum physics, quantum state refers to the state of an isolated quantum system.
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Scalar field theory
In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields.
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Second quantization
Second quantization, also referred to as occupation number representation, is a formalism used to describe and analyze quantum many-body systems.
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Segal–Bargmann space
In mathematics, the Segal–Bargmann space (for Irving Segal and Valentine Bargmann), also known as the Bargmann space or Bargmann–Fock space, is the space of holomorphic functions F in n complex variables satisfying the square-integrability condition: where here dz denotes the 2n-dimensional Lebesgue measure on Cn.
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Silvan S. Schweber
Silvan Samuel Schweber (10 April 1928 in Strasbourg – 14 May 2017) was a French-born American theoretical physicist and science historian.
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Simple harmonic motion
In mechanics and physics, simple harmonic motion is a special type of periodic motion or oscillation motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
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Slater determinant
In quantum mechanics, a Slater determinant is an expression that describes the wave function of a multi-fermionic system that satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two electrons (or other fermions).
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Spacetime
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.
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Special relativity
In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.
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Spin (physics)
In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.
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Spontaneous symmetry breaking
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state ends up in an asymmetric state.
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Standard Model
The Standard Model of particle physics is the theory describing three of the four known fundamental forces (the electromagnetic, weak, and strong interactions, and not including the gravitational force) in the universe, as well as classifying all known elementary particles.
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Symmetry (physics)
In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation.
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Symplectic geometry
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form.
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Symplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form.
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Symplectomorphism
In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds.
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Uncertainty principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.
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Unitary representation
In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every g ∈ G. The general theory is well-developed in case G is a locally compact (Hausdorff) topological group and the representations are strongly continuous.
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Unitary transformation
In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.
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Vacuum expectation value
In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average, expected value in the vacuum.
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Vacuum polarization
In quantum field theory, and specifically quantum electrodynamics, vacuum polarization describes a process in which a background electromagnetic field produces virtual electron–positron pairs that change the distribution of charges and currents that generated the original electromagnetic field.
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Vacuum state
In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy.
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Wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.
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Werner Heisenberg
Werner Karl Heisenberg (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the key pioneers of quantum mechanics.
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Wigner–Weyl transform
In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform is the invertible mapping between functions in the quantum phase space formulation and Hilbert space operators in the Schrödinger picture.
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Redirects here:
Canonical quantisation, Canonically quantised, Canonically quantized, Field operator, Field operators, Second-quantized.
References
[1] https://en.wikipedia.org/wiki/Canonical_quantization
