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Class of integrals appearing in quantum field theory
statistical mechanics, loop integrals are the integrals which appear when evaluating the Feynman diagrams with one or more loops by integrating over the
Loop_integral
Control loop feedback mechanism
A proportional–integral–derivative (PID) controller, or three-term controller, is a feedback-based control loop mechanism commonly used to manage machines
PID_controller
Loop integral parametrization
parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. It is named after Julian Schwinger, who
Schwinger_parametrization
Feedback controller
A closed-loop controller or feedback controller is a control loop which incorporates feedback, in contrast to an open-loop controller or non-feedback
Closed-loop_controller
Method in evaluating divergent integrals
x^{-1}} , as it should. Suppose one wishes to dimensionally regularize a loop integral which is logarithmically divergent in four dimensions, like I = ∫ d
Dimensional_regularization
Parametrization used for loop integrals
parametrization is a technique for evaluating loop integrals which arise from Feynman diagrams with one or more loops. However, it is sometimes useful in integration
Feynman_parametrization
function, integrals of loop diagrams, etc. The following Gaussian integrals are useful in calculating path integrals appearing in path integral formulation
Common integrals in quantum field theory
Common_integrals_in_quantum_field_theory
Type of Feynman diagram
dimensional analysis and the absence of any inherent mass scale in the loop integral). Tadpole corrections are needed if the corresponding external field
Tadpole_(physics)
Regularization technique in quantum field theory
and Dominique Rivier. In this treatment, a divergence arising from a loop integral (such as vacuum polarization or electron self-energy) is modulated by
Pauli–Villars_regularization
Error condition in a proportional–integral–derivative controller
feeding back the selected output to the integral circuit of all controllers in the selection scheme so that a closed loop is maintained. "Microchip Application
Integral_windup
Study of the strong force by perturbative methods
freedom. Showing that QCD is renormalizable at one-loop order requires the evaluation of loop integrals, which can be derived from Feynman rules and evaluated
Perturbative quantum chromodynamics
Perturbative_quantum_chromodynamics
Theory of quantum gravity merging quantum mechanics and general relativity
to obtain a Feynman's path integral (functional integration) description of quantum gravity. It is closely related to loop quantum gravity. The Hamiltonian
Loop_quantum_gravity
Theorem in quantum mechanics
the infrared divergences coming from loop integrals are canceled by IR divergences coming from phase space integrals. It was introduced independently by
Kinoshita–Lee–Nauenberg theorem
Kinoshita–Lee–Nauenberg_theorem
Pictorial representation of the behavior of subatomic particles
no external lines at all. The reason loop diagrams are called loop diagrams is because the number of k-integrals that are left undetermined by momentum
Feynman_diagram
Formulation of quantum mechanics
The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics. It replaces
Path_integral_formulation
Feynman diagram with only one cycle
In physics, a one-loop Feynman diagram is a connected Feynman diagram with only one cycle (unicyclic). Such a diagram can be obtained from a connected
One-loop_Feynman_diagram
Special function defined by an integral
The Fresnel integrals S(x) and C(x), and their auxiliary functions F(x) and G(x) are transcendental functions named after Augustin-Jean Fresnel that are
Fresnel_integral
Process where information about current status is used to influence future status
common general-purpose controller using a control-loop feedback mechanism is a proportional-integral-derivative (PID) controller. Heuristically, the terms
Feedback
Basic law of electromagnetism
is defined as the surface integral of the magnetic field B over a time-dependent surface Σ(t), whose boundary is the wire loop: Φ B = ∬ Σ ( t ) B ( t )
Faraday's_law_of_induction
Theorem in vector calculus
can be stated in one sentence: The line integral of a vector field over a loop is equal to the surface integral of its curl over the enclosed surface.
Stokes'_theorem
Type of textile fastener
notebooks often make use of hook-and-loop fasteners. Cloth diapers often make use of hook-and-loop fasteners. It is an integral part of games such as tag rugby
Velcro
Theorem in complex analysis
rectifiable simple loop in U ¯ {\displaystyle \textstyle {\overline {U}}} . The Cauchy integral theorem leads to Cauchy's integral formula and the residue
Cauchy's_integral_theorem
Commutative ring with no zero divisors other than zero
mathematics, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. In an integral domain, every
Integral_domain
Special mathematical function
closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the Bose–Einstein
Polylogarithm
Nuclear reactor design principle
nuclear power field, an integral reactor is a nuclear reactor design principle where the reactor core, primary cooling loop, steam generators and any
Integral_reactor
Electrical signalling scheme
In electrical signalling an analog current loop is used where a device must be monitored or controlled remotely over a pair of conductors. Only one current
Current_loop
Surface integral of the magnetic field
specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is
Magnetic_flux
Property of space that quantifies the magnetic influence at a given location
}}=I_{\mathrm {b} }\,,} where the integral is a line integral over any closed loop and Ib is the bound current enclosed by that closed loop. Unlike the magnetic B
Magnetic_field
American theoretical physicist (1941–2025)
maintains the conservation of the vector current in the definition of the loop integral, and places the anomaly in the axial current. This is known as the "covariant
William_A._Bardeen
Integral using products instead of sums
A product integral is any product-based counterpart of the usual sum-based integral of calculus. The product integral was developed by the mathematician
Product_integral
Phase of a cycle
}} . The nonadiabatic coupling can be used to define a loop integral, analogous to a Wilson loop (1974) in field theory, developed independently for molecular
Geometric_phase
Electronic control system
attenuation), an integral (low-pass filter) or derivative (high-pass filter). Loop parameters commonly examined for this are the loop's gain margin and
Phase-locked_loop
Field theory of scalar fields
make the Minkowski-space Gaussian integral converge. The integrals over unconstrained momenta, called "loop integrals", in the Feynman graphs typically
Scalar_field_theory
Type of membrane protein that is permanently attached to the biological membrane
An integral, or intrinsic, membrane protein (IMP) is a type of membrane protein that is permanently attached to the biological membrane. All transmembrane
Integral_membrane_protein
Quantum field theory with four-point interactions
make the Minkowski-space Gaussian integral converge. The integrals over unconstrained momenta, called "loop integrals", in the Feynman graphs typically
Quartic_interaction
Line integral of the fluid velocity around a closed curve
In physics, circulation is the line integral of a vector field around a closed curve embedded in the field. In fluid dynamics, the field is the fluid velocity
Circulation_(physics)
Topics referred to by the same term
effects of a feedback control loop on the input signal to the plant under control Electronic feedback loop Proportional–integral–derivative controller (PID)
Closed_loop
Graphical method of determining the stability of a dynamical system
plot of the open loop systems, it can be applied without explicitly computing the poles and zeros of either the closed-loop or open-loop system (although
Nyquist_stability_criterion
Magnetic analogue of the electric dipole
electric current density and the integral is a volume integral. When the current density in the integral is replaced by a loop of current I in a plane enclosing
Magnetic_dipole
Topological structure in loop quantum gravity
integration to obtain a Feynman's path integral description of quantum gravity. These structures are employed in loop quantum gravity as a version of quantum
Spin_foam
Control concept
are studied in control systems engineering. Negative feedback loops also play an integral role in maintaining the atmospheric balance in various climate
Negative_feedback
Pseudo-digital circuit
the integral of frequency, so a second integration is unavoidably performed by the oscillator itself. In the Control Systems jargon, the DLL is a loop one
Delay-locked_loop
Theoretical paradox resulting from time travel
exemplified by the Newcomb paradox. A causal loop, also known as a bootstrap paradox, information loop, information paradox, or ontological paradox,
Temporal_paradox
Bode's sensitivity integral, discovered by Hendrik Wade Bode, is a formula that quantifies some of the limitations in feedback control of linear parameter-invariant
Bode's_sensitivity_integral
Spiral shape of an unfurling fern frond
The koru (Māori for 'loop or coil') is a spiral shape evoking a newly unfurling frond from a silver fern frond. It is an integral symbol in Māori art,
Koru
Topological quantum field theory
action integral (path integral) of the field theory in physics is viewed as the Lagrangian integral of the Chern–Simons form and Wilson loop, holonomy
Chern–Simons_theory
How many times curves wind around each other
field. To get the path integral for the Wilson loops, we substitute for a source describing two particles moving in closed loops, i.e. J = J 1 + J 2 {\displaystyle
Linking_number
analysis, and semiclassical analysis. It is associated most classically with a loop or path of Lagrangian subspaces in a symplectic vector space, and measures
Maslov_index
Operation on formal power series
given immediately below in this section. The last integral formula is compared to Hankel's loop integral for the reciprocal gamma function applied termwise
Generating function transformation
Generating_function_transformation
Control system whose input is independent of output
In control theory, an open-loop controller, also called a non-feedback controller, is a control loop part of a control system in which the control action
Open-loop_controller
Concept in classical electromagnetism
these terms are associated with sign ambiguities: the line integral ∮C could go around the loop in either direction (clockwise or counterclockwise); the
Ampère's_circuital_law
Maximally helicity violating amplitudes
other drawback is the reliance on cut-constructibility to compute the loop integrals. This therefore cannot recover the rational parts of amplitudes (i.e
MHV_amplitudes
Equations describing classical electromagnetism
of an electric field. In integral form, it states that the work per unit charge required to move a charge around a closed loop equals the rate of change
Maxwell's_equations
American science fiction drama TV series
Tales from the Loop is an American science fiction drama television series developed and written by Nathaniel Halpern based on the art book of the same
Tales_from_the_Loop
American theoretical physicist (1941–2005)
3543-62 Corrigan, E; Hasslacher, B "Functional-Equation for Exponential Loop Integrals In Gauge Theories" Physics Letters B; 1979; v.81, no.2, p. 181-184 Feigenbaum
Brosl_Hasslacher
Transcendental single-variable function
definite integral, a trigonometric series, and various other forms. It is intimately connected with the polylogarithm, inverse tangent integral, polygamma
Clausen_function
Method of tuning a PID controller
G. Ziegler and Nathaniel B. Nichols. It is performed by setting the I (integral) and D (derivative) gains to zero. The "P" (proportional) gain, K p {\displaystyle
Ziegler–Nichols_method
Method in physics used to deal with infinities
for the loop process requires integration over all possible combinations of energy and momentum that could travel around the loop.These integrals are often
Renormalization
Attempt to find a consistent theory of quantum gravity
counterterms that should cancel divergent expressions appearing in loop integrals. Applying this method to gravity, however, the counterterms required
Asymptotic_safety
Aspect of loop quantum gravity
Lorentz invariance measures the universal features in the hypothetical loop quantum gravity universes; which is a hypothetical theory that explains the
Lorentz invariance in loop quantum gravity
Lorentz_invariance_in_loop_quantum_gravity
Loop that increases an initial effect
feedback, self-reinforcing feedback) is a process that occurs in a feedback loop where the outcome of a process reinforces the inciting process to build momentum
Positive_feedback
Algebraic structure
In commutative algebra, an integrally closed domain A is an integral domain whose integral closure in its field of fractions is A itself. Spelled out
Integrally_closed_domain
Description of gravity using discrete values
approaches to the problem of quantum gravity, the most popular being M-theory and loop quantum gravity. All of these approaches aim to describe the quantum behavior
Quantum_gravity
Metro line in Thane, India
The Thane Metro or Thane Integral Ring Metro is an under-construction rapid transit line serving Thane, Maharashtra. This metro line will be the third
Thane_Metro
Type of integral domain
the fundamental theorem of arithmetic holds. Specifically, a UFD is an integral domain (a nontrivial commutative ring in which the product of any two non-zero
Unique_factorization_domain
Algebraic ring without a multiplicative identity
chain of class inclusions: rngs ⊃ rings ⊃ commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains
Rng_(algebra)
Integral criterion for holomorphy
if the domain is simply connected; this is Cauchy's integral theorem, stating that the line integral of a holomorphic function along a closed curve is zero
Morera's_theorem
Type of electromagnet formed by a coil of wire
horizontal portions of loop c do not contribute anything to the integral. Thus the integral of the up side 1 is equal to the integral of the down side 2.
Solenoid
Magma obeying the Latin square property
x) for each x, y and z in Q (a right Bol loop). A loop that is both a left and right Bol loop is a Moufang loop. This is equivalent to any one of the following
Quasigroup
Hypercomplex number system
orders, forming a Moufang loop of order 240. The integral octonions have a "division with remainder" property: given integral octonions a and b ≠ 0, we
Octonion
Diagram showing the relationship between pressure and volume in a system
A pressure–volume diagram (or PV diagram, or volume–pressure loop) is used to describe corresponding changes in volume and pressure in a system. It is
Pressure–volume_diagram
Control systems and control theory based on negative feedback
complex than an on–off control system but simpler than a proportional-integral-derivative (PID) control system used, for instance, in an automobile cruise
Linear_control
Type of bolt
An eye bolt is a bolt with a loop at one end. They are used to firmly attach a securing eye to a structure, so that ropes or cables may then be tied to
Eye_bolt
Phase-locked loop-based demodulator circuit
A Costas loop is a phase-locked loop (PLL) based circuit which is used for carrier frequency recovery from suppressed-carrier modulation signals (e.g
Costas_loop
Type of unphysical field in quantum field theory which provides mathematical consistency
into gauge quantum field theories to maintain the consistency of the path integral formulation. They are named after Ludvig Faddeev and Victor Popov. A more
Faddeev–Popov_ghost
Random change in the energy inside a volume
propagator (to the right, above). These loop diagrams are initially problematic; they introduce an integral over the loop momentum (in this case k {\displaystyle
Quantum_fluctuation
Type of nuclear reactor cooled by molten sodium
cancellation of the CRBRP, the US program was refocused on the concept of an Integral Fast Reactor (IFR), an inherently safe SFR that would incorporate on-site
Sodium-cooled_fast_reactor
Unsolved problem in geometry
, ∫ Z i ∗ α . {\displaystyle \int _{Z}i^{*}\alpha .} To evaluate this integral, choose a point of Z and call it z = ( z 1 , … , z k ) {\displaystyle z=(z_{1}
Hodge_conjecture
Fur-lined cold weather overgarment
is very light and warm, the M-48 has a thicker wool pile liner with an integral hood liner made of wool. Both are distinguishable from any other type of
Parka
Nuclear reactor design
The integral fast reactor (IFR), originally the advanced liquid-metal reactor (ALMR), is a design for a nuclear reactor using fast neutrons and no neutron
Integral_fast_reactor
Evaluates a line integral through a gradient field using the original scalar field
also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the
Gradient_theorem
Algebraic structure
multiplication and therefore forms a Moufang loop. The subset of unit norm integral octonions is a finite Moufang loop of order 240. The basis octonions and
Moufang_loop
Principle suggesting that time travel paradoxes are inherently impossible
quantum mechanics, performing a quantum-mechanical sum over histories (path integral) using only the consistent extensions, and found that this resulted in
Novikov self-consistency principle
Novikov_self-consistency_principle
times of maximum solar activity, the solar maximum. Transequatorial loops play an integral role in the Babcock Model of solar dynamics and are therefore important
Transequatorial_loop
H-infinity loop-shaping is a design methodology in modern control theory. It combines the traditional intuition of classical control methods, such as Bode's
H-infinity_loop-shaping
Type of nuclear reactor
are: coolant loop separation from the steam system and pressure inside the primary coolant loop. In a PWR, there are two coolant loops (primary and secondary)
Pressurized_water_reactor
Compact luxury crossover SUV by Jaguar
stunt driver Terry Grant, performed a world-record-breaking 360 degree loop-the-loop. The F-Pace was offered with the Jaguar Land Rover's Ingenium 2.0L turbocharged
Jaguar_F-Pace
Mathematical concept applicable to physics
In vector calculus, flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. The word
Flux
Looming and similar refraction phenomena Loop braid group Loop entropy Loop integral Loop quantum cosmology Loop quantum gravity LOPES (telescope) Loránd
Index_of_physics_articles_(L)
Production of voltage by a varying magnetic field
ΦB through a region of space enclosed by a wire loop. The magnetic flux is defined by a surface integral: Φ B = ∫ Σ B ⋅ d A , {\displaystyle \Phi _{\mathrm
Electromagnetic_induction
Dependence of the state of a system on its history
called hysteretic. Plots of a single component of the moment often form a loop or hysteresis curve, where there are different values of one variable depending
Hysteresis
Magnetic loop operator dual to the Wilson loop
field theory, the 't Hooft loop is a magnetic analogue of the Wilson loop whose spatial loop operator give rise to thin loops of magnetic flux associated
't_Hooft_loop
Geometric model of the physical space
subtype of line integral found in physics is the plane closed loop, which determines the circulation of the function around the loop ∮ C F ( r ) ⋅ d r
Three-dimensional_space
the future. The variants of the scalar control include open-loop control and closed-loop control. The most common approach makes the voltage V proportional
Scalar_control
Deformation mechanism in crystallines
segment and different sizes of dipolar loops scattered between the walls and channels. One type of dislocation loop forms the boundary of a completely enclosed
Slip_bands_in_metals
Use of various control systems for operating equipment
example of sequence control. A proportional–integral–derivative controller (PID controller) is a control loop feedback mechanism (controller) widely used
Automation
Postulate in particle physics
points, half the lines will be directed forward in time and half will have looped round and be directed backwards. Wheeler suggested that these backwards
One-electron_universe
Strip of flexible material
shoulder strap. A strap differs from a belt mainly in that a strap is usually integral to the item of clothing; either can be used in combination with buckles
Strap
Cooking utensil
whisks consist of a long, narrow handle with a series of wire loops joined at the end. The loops can have different shapes depending on a whisk's intended
Whisk
Algebraic structure with an associative operation and an identity element
Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring Rng Semiring Near-ring Commutative ring Domain Integral domain Field Division
Monoid
LOOP INTEGRAL
LOOP INTEGRAL
Girl/Female
Gujarati, Hindu, Indian
Look
Surname or Lastname
North German
North German : habitational name from any of several places called Loose or Loosey.North German : from a short form of Nikolaus, German form of Nicholas.Dutch : nickname from the adjective loos ‘cunning’, ‘artful’, ‘guileful’.English : variant spelling of Loose.
Girl/Female
Arabic, Muslim
Look
Boy/Male
Hindu, Indian, Rajasthani, Sindhi, Traditional
Look; Beauty; Appearance
Boy/Male
Hindu
Flower
Boy/Male
Bengali, Indian
Loop; Autumn
Surname or Lastname
English (Somerset)
English (Somerset) : habitational name from Look in Puncknowle, Dorset, named in Old English with lūce ‘enclosure’.English : possibly a variant of Luck 3.Northern English and Scottish : from a vernacular pet form of Lucas.Dutch (van Look) : topographic name from look ‘enclosure’ or habitational name from a place named with this word.Thomas Look (b. c. 1622) was in Lynn, MA, by 1646. His son, also called Thomas (b. 1646), moved to Martha’s Vineyard about 1670.
Girl/Female
Tamil
Look, Blessed with beauty, Shape, Beauty
Boy/Male
Hindu, Indian
Look
Male
Dutch
, Jehovah's gift (or grace).
Surname or Lastname
English
English : possibly from the Old Norse personal name Tópi, Túpi, a short form of a personal name formed with þórr, name of the Norse god of thunder (see Thor) + a second element with initial b-, for example björn ‘bear’, ‘warrior’. On the other hand, the name is found mainly in Dorset and Devon, which are far from areas of Scandinavian settlement.
Male
French
French form of Latin Lupus, LOUP means "wolf."
Boy/Male
British, English
Barrel Maker
Boy/Male
Hebrew
God will multiply.
Surname or Lastname
English
English : metonymic occupational name for a cooper, from Middle English coupe ‘tub’, ‘container’ (see Cooper). In some cases the surname may have been derived from a pub or house sign.Dutch : from koop ‘purchase’, ‘bargain’, hence a nickname for a haggler or a metonymic occupational name for a merchant.
Boy/Male
Indian, Sanskrit
Natural; Original; Innate; Simply; Loop
Boy/Male
Arabic
The Biblical Lot is the English Language Equivalent
Girl/Female
Hindu
Look, Blessed with beauty, Shape, Beauty
Boy/Male
Dutch, German, Hebrew
God will Multiply; God will Add
Surname or Lastname
Dutch
Dutch : from a short form of the Germanic personal name Robrecht.Altered spelling of German Rupp.English : variant spelling of Roope.
LOOP INTEGRAL
LOOP INTEGRAL
Girl/Female
Gujarati, Hindu, Indian, Modern, Muslim, Punjabi, Sikh
Place to Live; Habitat
Girl/Female
Bengali, Hindu, Indian, Sindhi, Tamil
Intelligent Girl
Surname or Lastname
Dutch
Dutch : from a personal name based on Middle Dutch bruun ‘brown’, or a nickname referring to the color of the hair or complexion. See also Braun.English : of uncertain origin. Reaney suggests that the name may simply reflect a pronunciation of French Brun.Altered spelling of Swiss Bruhin.
Boy/Male
Shakespearean
The Tragedy of Titus Andronicus' Son to Tamora.
Girl/Female
French
Cape.
Male
English
Variant spelling of English Hughie, HUEY means "heart," "mind," or "spirit."
Girl/Female
Arthurian Legend
Mother of Arthur.
Boy/Male
Hindu, Indian
Son of Lord Shiva
Girl/Female
Indian
Sweet
Girl/Female
Spanish Latin
Fire.
LOOP INTEGRAL
LOOP INTEGRAL
LOOP INTEGRAL
LOOP INTEGRAL
LOOP INTEGRAL
v. t.
To influence, overawe, or subdue by looks or presence as, to look down opposition.
v. t.
To confine in a coop; hence, to shut up or confine in a narrow compass; to cramp; -- usually followed by up, sometimes by in.
n.
Any one of several aquatic, wed-footed, northern birds of the genus Urinator (formerly Colymbus), noted for their expertness in diving and swimming under water. The common loon, or great northern diver (Urinator imber, or Colymbus torquatus), and the red-throated loon or diver (U. septentrionalis), are the best known species. See Diver.
n.
See Loon, the bird.
pl.
of Trou-de-loup
v. t.
To let hang down; as, to lop the head.
v. t.
To look at; to turn the eyes toward.
n.
Hence; Appearance; aspect; as, the house has a gloomy look; the affair has a bad look.
v. t.
To express or manifest by a look.
v. i.
To seem; to appear; to have a particular appearance; as, the patient looks better; the clouds look rainy.
v. t.
To break over the poop or stern, as a wave.
n.
See 1st Loop.
v. t.
To beat in the game of loo by winning every trick.
n.
Expression of the eyes and face; manner; as, a proud or defiant look.
n.
The act of looking; a glance; a sight; a view; -- often in certain phrases; as, to have, get, take, throw, or cast, a look.
v. t.
To bind or fasten with hoops; as, to hoop a barrel or puncheon.
n.
A curve of any kind in the form of a loop.
v. t.
To make a loop of or in; to fasten with a loop or loops; -- often with up; as, to loop a string; to loop up a curtain.
n.
A ring; a circular band; anything resembling a hoop, as the cylinder (cheese hoop) in which the curd is pressed in making cheese.
v. i.
To direct the attention (to something); to consider; to examine; as, to look at an action.