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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
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)
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
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
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
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
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
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
Formulation of quantum mechanics
The path-integral formulation of quantum mechanics generalizes the action principle of classical mechanics. It replaces the classical notion of a single
Path-integral_formulation
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Property of space that quantifies the magnetic influence at a given location
∮𝐌⋅dℓ=Ib, 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
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
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
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
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
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
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
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)
How many times curves wind around each other
convention for the integral. In quantum field theory, Gauss's integral definition arises when computing the expectation value of the Wilson loop observable in
Linking_number
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
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
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
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
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
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
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
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
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
Theorem in vector calculus
the left side is the line integral of the vector field around the boundary curve, while the right side is the surface integral of its curl over the surface
Stokes'_theorem
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
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
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
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
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
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
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
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
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
Foundational law of classical magnetism
for magnetism can be written in two forms, a differential form and an integral form. These forms are equivalent due to the divergence theorem. The name
Gauss's_law_for_magnetism
Transcendental single-variable function
Lu, Hung Jung; Perez, Christopher A. (1992). "Massless one-loop scalar three-point integral and associated Clausen, Glaisher, and L-functions" (PDF). Archived
Clausen_function
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
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
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
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
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
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
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
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 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)
Unsolved problem in geometry
Z} , ∫ 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
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
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
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
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
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
Algebraic structure
In mathematics, a principal ideal domain, or PID, is an integral domain (that is, a non-zero commutative ring without nonzero zero divisors) in which every
Principal_ideal_domain
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
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)
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
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
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
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
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
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
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
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
Railway station in Falkirk, Scotland
Manuel. The adjacent Birkhill Fireclay Mine is in the Bo'ness area and an integral part of the town's history but the Fireclay mine closed in 2013. There
Birkhill_railway_station
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
Ring without nonzero zero divisors
equivalently, the only right zero divisor). A commutative domain is called an integral domain. Mathematical literature contains multiple variants of the definition
Domain_(ring_theory)
Field of automation which studies how to precisely move parts of machines
more prime movers or actuators. Motion control may be open loop or closed loop. In open loop systems, the controller sends a command through the amplifier
Motion_control
Production of voltage by a varying magnetic field
a wire loop. The magnetic flux is defined by a surface integral: ΦB=∫Σ𝐁⋅d𝐀, where dA is an element of the surface Σ enclosed by the wire loop, B is the
Electromagnetic_induction
Tool used in marine ropework
Farmer's loop Figure-eight Figure-eight loop Figure-of-nine loop Friction hitch Klemheist Munter hitch Noose Overhand loop Prusik Trident loop Yosemite
Marlinspike
Topics referred to by the same term
function of a random variable Integral kernel or kernel function, a function of two variables that defines an integral transform Heat kernel, the fundamental
Kernel
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
Commutative ring with a Euclidean division
in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable
Euclidean_domain
Contour in the complex plane
complex plane (or Riemann sphere) of the two points looped. When it comes to taking contour integrals, moving basepoint from P to another choice Q makes
Pochhammer_contour
concept of cumulative quantities (CCQ) uses the feedback mechanism of a closed loop, which can be found in industrial, engineering and electronic systems. The
Cumulative quantities (logistics)
Cumulative_quantities_(logistics)
monkeys on Madagascar; Colin Tudge believed that mass extinctions were integral to evolution; Lystrosaurus lasted for ten million years. Narrated by Roger
List_of_Equinox_episodes
Technique in computational quantum field theory
it is not sufficient to construct a theory using regularization of loop integrals order-by-order and correspondingly redefining the masses, coupling constants
Light-front computational methods
Light-front_computational_methods
Mathematical structure with greatest common divisors
In mathematics, a GCD domain is an integral domain R with the property that any two elements have a greatest common divisor (GCD); i.e., there is a minimum
GCD_domain
Geometric model of the physical space
integral found in physics is the plane closed loop, which determines the circulation of the function around the loop ∮C𝐅(𝐫)⋅d𝐫. A surface integral
Three-dimensional_space
Vector field that is the gradient of some function
property that its line integral is path independent; the choice of path between two points does not change the value of the line integral. Path independence
Conservative_vector_field
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
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