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Conjugate variables

Index Conjugate variables

Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. [1]

35 relations: Action (physics), Ambiguity function, Angular momentum, Canonical coordinates, Density, Doppler effect, Duality (mathematics), Electric charge, Electric current, Electric field, Electric potential, Energy, Event (relativity), Fourier transform, Frequency, Gravitational potential, Hamiltonian fluid mechanics, Magnetic field, Magnetic potential, Magnetization, Momentum, Orientation (geometry), Physics, Polarization density, Pontryagin duality, Position (vector), Probability density function, Quantum hydrodynamics, Radar, Surface tension, Symplectic vector space, Time, Uncertainty principle, Velocity potential, Voltage.

Action (physics)

In physics, action is an attribute of the dynamics of a physical system from which the equations of motion of the system can be derived.

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Ambiguity function

In pulsed radar and sonar signal processing, an ambiguity function is a two-dimensional function of time delay and Doppler frequency \chi(\tau,f) showing the distortion of a returned pulse due to the receiver matched filter (commonly, but not exclusively, used in pulse compression radar) due to the Doppler shift of the return from a moving target.

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Angular momentum

In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum.

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Canonical coordinates

In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time.

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Density

The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume.

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Doppler effect

The Doppler effect (or the Doppler shift) is the change in frequency or wavelength of a wave in relation to observer who is moving relative to the wave source.

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Duality (mathematics)

In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself.

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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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Electric current

An electric current is a flow of electric charge.

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Electric field

An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.

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Electric potential

An electric potential (also called the electric field potential, potential drop or the electrostatic potential) is the amount of work needed to move a unit positive charge from a reference point to a specific point inside the field without producing any acceleration.

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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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Event (relativity)

In physics, and in particular relativity, an event is the instantaneous physical situation or occurrence associated with a point in spacetime (that is, a specific place and time).

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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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Frequency

Frequency is the number of occurrences of a repeating event per unit of time.

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Gravitational potential

In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move the object from a fixed reference location to the location of the object.

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Hamiltonian fluid mechanics

Hamiltonian fluid mechanics is the application of Hamiltonian methods to fluid mechanics.

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Magnetic field

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials.

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Magnetic potential

The term magnetic potential can be used for either of two quantities in classical electromagnetism: the magnetic vector potential, or simply vector potential, A; and the magnetic scalar potential ψ. Both quantities can be used in certain circumstances to calculate the magnetic field B. The more frequently used magnetic vector potential is defined so that its curl is equal to the magnetic field: curl A.

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Magnetization

In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material.

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Momentum

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.

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Orientation (geometry)

In geometry the orientation, angular position, or attitude of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it occupies.

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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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Polarization density

In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material.

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Pontryagin duality

In mathematics, specifically in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform on locally compact abelian groups, such as \R, the circle, or finite cyclic groups.

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Position (vector)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line from O to P. The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.

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Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

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Quantum hydrodynamics

Quantum hydrodynamics is most generally the study of hydrodynamic systems which demonstrate behavior implicit in quantum subsystems (usually quantum tunnelling).

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Radar

Radar is an object-detection system that uses radio waves to determine the range, angle, or velocity of objects.

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Surface tension

Surface tension is the elastic tendency of a fluid surface which makes it acquire the least surface area possible.

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Symplectic vector space

In mathematics, a symplectic vector space is a vector space V over a field F (for example the real numbers R) equipped with a symplectic bilinear form.

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Time

Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.

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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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Velocity potential

A velocity potential is a scalar potential used in potential flow theory.

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Voltage

Voltage, electric potential difference, electric pressure or electric tension (formally denoted or, but more often simply as V or U, for instance in the context of Ohm's or Kirchhoff's circuit laws) is the difference in electric potential between two points.

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Cannonical conjugate variables, Canonical conjugate, Canonical conjugate variables, Canonical variables, Canonically conjugate variable, Canonically conjugate variables, Conjugate quantities, Conjugate variable, Fourier dual, Fourier duals, Fourier pair.

References

[1] https://en.wikipedia.org/wiki/Conjugate_variables

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