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Branch of mathematics
Quantum calculus, sometimes called calculus without limits, is equivalent to traditional infinitesimal calculus without the notion of limits. The two
Quantum_calculus
Form of calculus
Quantum stochastic calculus is a generalization of stochastic calculus to noncommuting variables. The tools provided by quantum stochastic calculus are
Quantum_stochastic_calculus
In quantum geometry or noncommutative geometry a quantum differential calculus or noncommutative differential structure on an algebra A {\displaystyle
Quantum_differential_calculus
Graphical language for quantum processes
spin systems. The ZX-calculus was first introduced by Bob Coecke and Ross Duncan in 2008 as an extension of the categorical quantum mechanics school of
ZX-calculus
Computer programming for quantum computers
Quantum programming refers to the process of designing and implementing algorithms that operate on quantum systems, typically using quantum circuits composed
Quantum_programming
Q-analog of the ordinary derivative
In mathematics, in the area of combinatorics and quantum calculus, the q-derivative, or Jackson derivative, is a q-analog of the ordinary derivative, introduced
Q-derivative
Branch of mathematics
infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus studies
Calculus
Quantum mechanics posed in terms of category theory
resulting in a much more compact calculus. In particular, the ZX-calculus has sprung forth from categorical quantum mechanics as a diagrammatic counterpart
Categorical_quantum_mechanics
Formalism in general relativity
Regge calculus has motivated the construction of further generalizations of this idea. In particular, Regge calculus has been adapted to study quantum gravity
Regge_calculus
This is a list of notable textbooks on classical mechanics and quantum mechanics arranged according to level and surnames of the authors in alphabetical
List of textbooks on classical mechanics and quantum mechanics
List_of_textbooks_on_classical_mechanics_and_quantum_mechanics
Theory of logic to account for observations from quantum theory
analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The formal
Quantum_logic
Branch of mathematical analysis
Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number
Fractional_calculus
Unification of discrete and continuous theories of calculus
three most popular examples of calculus on time scales are differential calculus, difference calculus, and quantum calculus. Dynamic equations on a time
Time-scale_calculus
Calculus of functions of several variables
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to functions of several variables: the differentiation
Multivariable_calculus
Calculus of vector-valued functions
The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial
Vector_calculus
Study of rates of change
differential calculus is a subfield of calculus that studies the rates at which quantities change. The primary objects of study in differential calculus are the
Differential_calculus
Fringe hypothesis
The quantum mind or quantum consciousness is a group of hypotheses proposing that local physical laws and interactions from classical mechanics or connections
Quantum_mind
R S T U V W X Y Z See also References Quantum calculus a form of calculus without the notion of limits. Quantum geometry the generalization of concepts
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Calculus of stochastic differential equations
Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important
Itô_calculus
algebra Quantum affine algebra Quantum enveloping algebra Quantum group Jackson integral q-derivative q-difference polynomial Quantum calculus LLT polynomial
List_of_q-analogs
Branch of functional analysis
functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras
Borel_functional_calculus
Calculus on stochastic processes
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals
Stochastic_calculus
Theory allowing one to apply mathematical functions to mathematical operators
functional calculus. The C*-algebras were originally developed to explore and formalize the operator equations being developed for quantum mechanics,
Functional_calculus
Interpretation of quantum mechanics
The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that
Many-worlds_interpretation
Probability distribution
2307/2041858. JSTOR 2041858. "Updates to the Cauchy Central Limit". Quantum Calculus. 13 November 2022. Retrieved 21 June 2023. Frederic, Chyzak; Nielsen
Cauchy_distribution
Scientific field of study
with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas
Physics
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
Infinitesimal calculus on functions defined on a geometric algebra
In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to
Geometric_calculus
Public dispute between Isaac Newton and Gottfried Leibniz (beginning 1699)
In the history of calculus, the calculus controversy (German: Prioritätsstreit, lit. 'priority dispute') was an argument between mathematicians Isaac Newton
Leibniz–Newton calculus controversy
Leibniz–Newton_calculus_controversy
Physical quantities taking values at each point in space and time
spacetime, or as a single rank-2 tensor field. In the modern framework of the quantum field theory, even without referring to a test particle, a field occupies
Field_(physics)
Description of gravity using discrete values
of quantum cosmology Quadratic gravity Regge calculus Shape Dynamics String-nets and quantum graphity Supergravity Twistor theory Canonical quantum gravity
Quantum_gravity
Branch of applied mathematics
mathematics proper, the theory of partial differential equation, variational calculus, Fourier analysis, potential theory, and vector analysis are perhaps most
Mathematical_physics
Branch of physics seeking to explain chaotic dynamical systems in terms of quantum theory
Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question
Quantum_chaos
Type of differential equation
S2CID 1200900. Griebel, Thomas (2017-01-01). "The pantograph equation in quantum calculus". Masters Theses. Ockendon, John Richard; Tayler, A. B.; Temple, George
Delay_differential_equation
Quantum operator for the sum of energies of a system
In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential
Hamiltonian (quantum mechanics)
Hamiltonian_(quantum_mechanics)
S2CID 16930694. Kac-Cheung, Theorem 19.1. Victor Kac, Pokman Cheung, Quantum Calculus, Universitext, Springer-Verlag, 2002. ISBN 0-387-95341-8 Jackson F
Jackson_integral
Cryptography based on quantum mechanical phenomena
Quantum cryptography is the exploiting of quantum-mechanical properties such as quantum entanglement, measurement disturbance, no-cloning theorem, and
Quantum_cryptography
Graphical notation for multilinear algebra calculations
quantum theory, particularly in matrix product states and quantum circuits. In particular, categorical quantum mechanics (which includes ZX-calculus)
Penrose_graphical_notation
Russian mathematician
Society. ISBN 0-8218-0643-2. Kac, Victor G.; Cheung, Pokman (2002). Quantum calculus. New York: Springer. ISBN 0387953418. OCLC 47243954. Kac, Victor G
Victor_Kac
Differential calculus on function spaces
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and
Calculus_of_variations
Concept in theoretical mathematical physics
There might be a notion of quantum differential calculus on the quantum spacetime algebra, compatible with the (quantum) symmetry and preferably reducing
Quantum_spacetime
Branch of mathematics
quantitative methods of approximation and convergence. It grew out of calculus, especially the use of derivatives and integrals to study variable quantities
Mathematical_analysis
Physical theory with fields invariant under the action of local "gauge" Lie groups
of gauge symmetries appeared first in the relativistic quantum mechanics of electrons – quantum electrodynamics, elaborated-on below. Today, gauge theories
Gauge_theory
Field theory involving topological effects in physics
and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory that computes topological
Topological quantum field theory
Topological_quantum_field_theory
Indian statistician (1936–2023)
emeritus at the Indian Statistical Institute and a pioneer of quantum stochastic calculus. Parthasarathy was the recipient of the Shanti Swarup Bhatnagar
K. R. Parthasarathy (probabilist)
K._R._Parthasarathy_(probabilist)
Mathematical structures that allow quantum mechanics to be explained
mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Interpretation of quantum mechanics
philosophy of physics, QBism (pronounced "cubism") is an interpretation of quantum mechanics that takes an agent's actions and experiences as the central
QBism
Hypothetical approach to quantum gravity with emergent spacetime
Asymptotic safety in quantum gravity Causal sets Fractal cosmology Loop quantum gravity 5-cell Planck scale Quantum gravity Regge calculus Simplex Simplicial
Causal dynamical triangulation
Causal_dynamical_triangulation
Inverse of a finite difference
In the calculus of finite differences, the indefinite sum (or antidifference operator), denoted by ∑ x {\textstyle \sum _{x}} or Δ − 1 {\displaystyle \Delta
Indefinite_sum
Scientific principles enabling the use of the calculus of variations
Gibbons–Hawking–York boundary term Variational quantum eigensolver Goldstine, Herman H. (1980). A History of the Calculus of Variations from the 17th through the
Variational_principle
Quantum mechanics with supersymmetry
supersymmetric quantum mechanics is an area of research where supersymmetry are applied to the simpler setting of plain quantum mechanics, rather than quantum field
Supersymmetric quantum mechanics
Supersymmetric_quantum_mechanics
Mathematical approach to quantum physics
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated
Perturbation theory (quantum mechanics)
Perturbation_theory_(quantum_mechanics)
Mathematical description of quantum state
In quantum mechanics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common
Wave_function
Relativistic wave equation in quantum mechanics
named. Within relativistic quantum mechanics, it suffers from numerous conceptual problems that are only resolved in quantum field theory, where the equation
Klein–Gordon_equation
Branch of mathematics concerning probability
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations
Probability_theory
Interdisciplinary research area
Quantum machine learning (QML) is the study of quantum algorithms for machine learning. It often refers to quantum algorithms for machine learning tasks
Quantum_machine_learning
Quantum field theory enjoying conformal symmetry
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional
Conformal_field_theory
Belgian theoretical physicist and logician
pioneered categorical quantum mechanics (entry 18M40 in Mathematics Subject Classification 2020), Quantum Picturalism, ZX-calculus, DisCoCat model for natural
Bob_Coecke
Tensor index notation for tensor-based calculations
mathematics of general relativity), quantum field theory, and machine learning. Working with a main proponent of the exterior calculus Élie Cartan, the influential
Ricci_calculus
Theory of a quantum origin of consciousness
originates at the quantum level inside neurons (rather than being a product of neural connections). The mechanism is held to be a quantum process called
Orchestrated objective reduction
Orchestrated_objective_reduction
Q-analog of hypergeometric series
und angewandte Mathematik, 32: 210–212 Victor Kac, Pokman Cheung, Quantum calculus, Universitext, Springer-Verlag, 2002. ISBN 0-387-95341-8 Koekoek, Roelof;
Basic_hypergeometric_series
Modern discipline
In mathematics, secondary calculus is a proposed expansion of classical differential calculus on manifolds, to the "space" of solutions of a (nonlinear)
Secondary calculus and cohomological physics
Secondary_calculus_and_cohomological_physics
Fundamental mechanical principles
principles are fundamental to physics, from classical mechanics through quantum mechanics, particle physics, and general relativity. Action principles
Action_principles
Theory of subatomic structure
corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity. String theory
String_theory
Set of mathematical concepts in quantum gravity
In quantum gravity, quantum geometry is the set of mathematical concepts that generalize geometry to describe physical phenomena at distance scales comparable
Quantum_geometry
British computer scientist
lazy lambda calculus, strictness analysis, concurrency theory, interaction categories and geometry of interaction, game semantics and quantum computing
Samson_Abramsky
Physical quantity of dimension energy × time
Feynman and Julian Schwinger developed quantum action principles. Expressed in mathematical language, using the calculus of variations, the evolution of a
Action_(physics)
Force resulting from the quantisation of a field
In quantum field theory, the Casimir effect (or Casimir force) is a physical force acting on the macroscopic boundaries of a confined space which arises
Casimir_effect
Q-analog in combinatorial mathematics
1142/S0217732394000447. ISSN 0217-7323. S2CID 119124642. Kac, V.; Cheung, P. (2011). Quantum Calculus. Springer. p. 31. ISBN 978-1461300724. Cieśliński, Jan L. (2011). "Improved
Q-exponential
Collection of random variables
Stochastic Calculus. Springer. ISBN 978-1-4612-0949-2. Applebaum, David (2004). "Lévy processes: From probability to finance and quantum groups". Notices
Stochastic_process
Theory of quantum gravity merging quantum mechanics and general relativity
Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic
Loop_quantum_gravity
Discrete analog of a derivative
of umbral calculus. Newton series expansions can be superior to Taylor series expansions when applied to discrete quantities like quantum spins (see
Finite_difference
Description of a quantum-mechanical system
function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after
Schrödinger_equation
Computer scientist and quantum computing researcher
publications include; Universal blind quantum computation Demonstration of Blind Quantum Computing The measurement calculus Elham Kashefi publications indexed
Elham_Kashefi
Textbook by Paul Dirac
1073/pnas.12.7.473. Eckart, Carl (1926). "Operator Calculus and the Solution of the Equations of Quantum Dynamics". Physical Review. 28: 711–26. doi:10.1103/PhysRev
The Principles of Quantum Mechanics
The_Principles_of_Quantum_Mechanics
Formula for spectral line wavelengths in alkali metals
then theoretically by Niels Bohr in 1913, who used a primitive form of quantum mechanics. The formula directly generalizes the equations used to calculate
Rydberg_formula
Phenomenon resulting from the superposition of two waves
addition to the classical wave model for understanding optical interference, quantum matter waves also demonstrate interference. The above can be demonstrated
Wave_interference
Topics referred to by the same term
dictionary. Calculus of variations, a field of mathematical analysis that deals with maximizing or minimizing functionals Variational method (quantum mechanics)
Variational
Study of discrete mathematical structures
mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers;
Discrete_mathematics
Branch of logic
classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes zeroth-order logic. Sometimes
Propositional_logic
Symmetry between bosons and fermions
Supersymmetric quantum mechanics adds the SUSY superalgebra to quantum mechanics as opposed to quantum field theory. Supersymmetric quantum mechanics often
Supersymmetry
Sequence of operations for a task
algorithms that seem inherently quantum or use some essential feature of Quantum computing such as quantum superposition or quantum entanglement. Another way
Algorithm
cardinal numbers) Cantor's theorem (set theory) Church–Rosser theorem (lambda calculus) Compactness theorem (mathematical logic) Conservativity theorem (mathematical
List_of_theorems
timeline of quantum computing and communication. Erwin Schrödinger publishes a theorem setting the basis for quantum steering and the limits of quantum state
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
Quantum mechanics taking into account particles near or at the speed of light
In physics, relativistic quantum mechanics (RQM) is any Poincaré-covariant formulation of quantum mechanics (QM). This theory is applicable to massive
Relativistic quantum mechanics
Relativistic_quantum_mechanics
Methods of mathematical approximation
and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The field in
Perturbation_theory
2011 book by Brian Cox
The Quantum Universe: Everything That Can Happen Does Happen is a 2011 book by the theoretical physicists Brian Cox and Jeff Forshaw. The book aims to
The_Quantum_Universe
Formulation of classical mechanics
crucial influence on other branches of physics, including relativity and quantum field theory. Lagrangian mechanics describes a mechanical system as a pair
Lagrangian_mechanics
Mathematical concept applicable to physics
surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications in physics. For transport phenomena, flux is
Flux
American theoretical physicist (1918–1988)
Formulation of the Quantum Theory of Electromagnetic Interaction" in 1950 and "An Operator Calculus Having Applications in Quantum Electrodynamics" in
Richard_Feynman
Formulation of classical mechanics using momenta
geometry and Poisson structures) and serves as a link between classical and quantum mechanics. Let ( M , L ) {\displaystyle (M,{\mathcal {L}})} be a mechanical
Hamiltonian_mechanics
Concept in theoretical physics
in a quantum field theory that is renormalizable) as the energy or mass scale at which physical processes occur varies. For example, in quantum electrodynamics
Renormalization_group
Class of mathematical software
Calculus is a Mathematica package for doing tensor and exterior calculus on differentiable manifolds. EDC and RGTC, "Exterior Differential Calculus"
Tensor_software
Range of physical processes in physics
subatomic particles (e.g. Ernest Rutherford in 1911) and the development of quantum theory in the 20th century, the sense of the term became broader as it
Scattering
Type of vector space in math
notion of Euclidean space. It extends the methods of Euclidean geometry and calculus from the two-dimensional Euclidean plane and three-dimensional space to
Hilbert_space
Integration over the space of functions
partial differential equations, and in the path integral formulation to the quantum mechanics of particles and fields. While the term suggests an extension
Functional_integration
Physical theory describing classical fields
considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory'
Classical_field_theory
Differential equations involving stochastic processes
rules of calculus. There are two dominating versions of stochastic calculus, the Itô stochastic calculus and the Stratonovich stochastic calculus. Each of
Stochastic differential equation
Stochastic_differential_equation
Framework to describe phase transitions
through field configurations. It is closely related to quantum field theory, which describes the quantum mechanics of fields, and shares with it many techniques
Statistical_field_theory
Pakistani theoretical physicist and professor (1937–2000)
faculty at the Institute of Physics, and co-authored papers on variation calculus and fission isomer. He was one of the notable theoretical physicists at
Ghulam_Dastagir_Alam
QUANTUM CALCULUS
QUANTUM CALCULUS
Male
English
English surname transferred to forename use, derived from the Norman baronial name Cuinchy, a derivative of Roman Quintus, QUINCY means "fifth."
Surname or Lastname
South German
South German : occupational name for an official in charge of the legal auction of property confiscated in default of a fine; such a sale was known in Middle High German as a gant (from Italian incanto, a derivative of Late Latin inquantare ‘to auction’, from the phrase In quantum? ‘To how much (is the price raised)?’).German : metonymic occupational name for a cooper, from Middle High German ganter, kanter ‘barrel rack’.German : variant of Gander 3.English : occupational name for a glover, from Old French gantier, an agent derivative of gant ‘glove’ (see Gant).
Surname or Lastname
English
English : from the personal name Horace, Latin Horatius, a Roman family name of unknown origin, associated chiefly with the name of the poet Quintus Horatius Flaccus (65–8 bc).
Girl/Female
Biblical
Fourth.
Boy/Male
Danish, Finnish, French, German, Latin, Shakespearean, Swedish
Born Fifth
Biblical
fourth
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from any of several places in France deriving their names from the Gallo-Roman personal name Quintus, meaning ‘fifth(-born)’ + the locative suffix -acum. The earliest bearers of the name in England were from Cuinchy in Pas-de-Calais, but other stocks may be from Quincy-sous-Sénard in Seine-et-Oise or Quincy-Voisins in Seine-et-Marne.The American Quincy family were established in MA by Edmund Quincy in 1633. Fifth in descent was Josiah Quincy (1744–75), a leading patriot, who was sent to England to argue the colonists’ case in 1774. His son Josiah (1772–1864) was a powerful opponent of slavery, president of Harvard, and mayor of Boston, a post also held by several of his descendants. The traditional pronunciation is “Quinzyâ€.
Boy/Male
Latin Biblical
Born fourth.
Boy/Male
Hindu, Indian
Calm
Surname or Lastname
English
English : nickname from Middle English cointe, quointe ‘known’ (via Old French, from Latin cognitus ‘known’). The Middle English word was used in various senses, any of which could have given rise to the surname: ‘cunning’, ‘crafty’, ‘knowledgeable’ (especially about dress, hence ‘elegant’), ‘attractive’. The sense development continued with ‘odd’ or ‘unusual’, the normal meaning of the modern English word ‘quaint’.German and Dutch : variant of Quandt.
QUANTUM CALCULUS
QUANTUM CALCULUS
Boy/Male
Hindu
Brave one with a bell around his neck
Boy/Male
Indian
Lord Brahma
Girl/Female
Hindu
Expert in Vedas
Girl/Female
Tamil
Adornment
Boy/Male
Hindu, Indian
Divine
Girl/Female
Arabic, Kurdish, Muslim, Parsi
Garden; Rose Garden
Girl/Female
French Italian
From Gaete.
Surname or Lastname
English
English :
Boy/Male
Arabic, Muslim
Profitable
Girl/Female
Hindu
QUANTUM CALCULUS
QUANTUM CALCULUS
QUANTUM CALCULUS
QUANTUM CALCULUS
QUANTUM CALCULUS
a.
Pertaining to, or proceeding by, integration; as, the integral calculus.
n.
A definite portion of a manifoldness, limited by a mark or by a boundary.
n.
Part or proportion; quota.
n.
A quantic of the second degree. See Quantic.
n.
A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation.
n.
A punting pole with a broad flange near the end to prevent it from sinking into the mud; a setting pole.
n.
A fanciful, odd, or extravagant notion; a quant fancy; an unnatural or affected conception; a witty thought or turn of expression; a fanciful device; a whim; a quip.
pl.
of Quantum
n.
A function involving the coefficients and the variables of a quantic, and such that when the quantic is lineally transformed the same function of the new variables and coefficients shall be equal to the old function multiplied by a factor. An invariant is a like function involving only the coefficients of the quantic.
n.
A quantic of the fourth degree. See Quantic.
n.
A quantic of the seventh degree.
n.
A homogeneous algebraic function of two or more variables, in general containing only positive integral powers of the variables, and called quadric, cubic, quartic, etc., according as it is of the second, third, fourth, fifth, or a higher degree. These are further called binary, ternary, quaternary, etc., according as they contain two, three, four, or more variables; thus, the quantic / is a binary cubic.
n.
A calculous concretion, especially one in the kidneys or bladder; the disease arising from a calculus.
n.
A quantic of the fifth degree. See Quantic.
n.
A quantic of the sixth degree.
n.
One of the variables of a quantic as distinguished from a coefficient.
n.
The calculus; fluxions.
a.
Of, pertaining to, or in the manner of, the Roman general, Quintus Fabius Maximus Verrucosus; cautious; dilatory; avoiding a decisive contest.
n.
A quantic of the eighth degree.
n.
Quantity; amount.