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Euclidean Wightman distributions
^{d}} that are pairwise distinct. These functions are called the Schwinger functions (named after Julian Schwinger) and they are real-analytic, symmetric
Schwinger_function
American theoretical physicist (1918–1994)
Julian Seymour Schwinger (/ˈʃwɪŋər/; February 12, 1918 – July 16, 1994) was an American theoretical physicist. He shared the 1965 Nobel Prize in Physics
Julian_Schwinger
Schwinger include the following: Birman–Schwinger principle Schwinger effect (Schwinger pair production) Schwinger function Schwinger limit Schwinger
List of things named after Julian Schwinger
List_of_things_named_after_Julian_Schwinger
Equations for correlation functions in QFT
The Schwinger–Dyson equations (SDEs) or Dyson–Schwinger equations, named after Julian Schwinger and Freeman Dyson, are general relations between correlation
Schwinger–Dyson_equation
Equation used in quantum scattering problems
The Lippmann–Schwinger equation (named after Bernard Lippmann and Julian Schwinger) is one of the most used equations to describe particle collisions –
Lippmann–Schwinger_equation
View of quantum mechanics
Chapter 18 - for those who saw this being called the Schwinger-Tomonaga equation, this is not the Schwinger-Tomonaga equation. That is a generalization of the
Interaction_picture
Theoretical framework in physics
Julian Schwinger (Repr ed.). Oxford: Oxford University Press. ISBN 978-0-19-850658-4. Schwinger, Julian (July 1951). "On the Green's functions of quantized
Quantum_field_theory
Mathematical description of quantum state
theory. Higher spin analogues include the Proca equation (spin 1), Rarita–Schwinger equation (spin 3⁄2), and, more generally, the Bargmann–Wigner equations
Wave_function
Mathematical trick using imaginary numbers to simplify certain formulas in physics
infinity § Imaginary transformation Complex spacetime Imaginary time Schwinger function Zee, Anthony (2010). Quantum Field Theory in a Nutshell (2nd ed.)
Wick_rotation
Fundamental mechanical principles
transition clearly to classical equivalents. Both Richard Feynman and Julian Schwinger developed quantum action principles based on early work by Paul Dirac
Action_principles
Japanese physicist (1906-1979)
shared the 1965 Nobel Prize in Physics with Richard Feynman and Julian Schwinger "for their fundamental work in quantum electrodynamics (QED), with deep-ploughing
Shin'ichirō_Tomonaga
Pictorial representation of the behavior of subatomic particles
Ernst Stueckelberg and Hans Bethe and implemented by Dyson, Feynman, Schwinger, and Tomonaga compensates for this effect and eliminates the troublesome
Feynman_diagram
Quantum field theory of electromagnetism
electrodynamics Schrödinger equation Schwinger model Schwinger–Dyson equation Vacuum polarization Vertex function Wheeler–Feynman absorber theory R. P
Quantum_electrodynamics
Type of field appearing in the Lagrangian
theoretical physics, a source is an abstract concept, developed by Julian Schwinger, motivated by the physical effects of surrounding particles involved in
Source_field
Quantum field theory enjoying conformal symmetry
{\displaystyle \mathbb {R} ^{d}} . In this case, correlation functions are Schwinger functions. They are defined for x i ≠ x j {\displaystyle x_{i}\neq
Conformal_field_theory
Function in quantum field theory showing probability amplitudes of moving particles
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one
Propagator
Schwinger variational principle is a variational principle which expresses the scattering T-matrix as a functional depending on two unknown wave functions
Schwinger variational principle
Schwinger_variational_principle
Special function in mathematics
Julian Schwinger, giving an exact result for the pair production rate of a Dirac electron in a uniform electric field. The Hurwitz zeta function with a
Hurwitz_zeta_function
Topic in mathematical physics
components of the metric tensor.) The resulting functions are called Schwinger functions. For the Schwinger functions there is a list of conditions — analyticity
Axiomatic quantum field theory
Axiomatic_quantum_field_theory
Expectation value of time-ordered quantum operators
In quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products
Correlation function (quantum field theory)
Correlation_function_(quantum_field_theory)
Procedure of coping with redundant degrees of freedom in physical field theories
{r} ,t)du.} The gauge condition of the Fock–Schwinger gauge (named after Vladimir Fock and Julian Schwinger; sometimes also called the relativistic Poincaré
Gauge_fixing
Parametrization used for loop integrals
integration in areas of pure mathematics as well. It was introduced by Julian Schwinger and Richard Feynman in 1949 to perform calculations in quantum electrodynamics
Feynman_parametrization
Function that encodes the dependence of a coupling parameter on the energy scale
theoretical physics, specifically quantum field theory, a beta function or Gell-Mann–Low function, β(g), encodes the dependence of a coupling parameter, g,
Beta_function_(physics)
Approach to quantum theory
Schwinger's quantum action principle is a variational approach to quantum mechanics and quantum field theory. This theory was introduced by Julian Schwinger
Schwinger's quantum action principle
Schwinger's_quantum_action_principle
Spectral density of light emitted by a black body
1958, p. 14 Pauli 1973, p. 1 Feynman, Leighton & Sands 1963, p. 38-1 Schwinger 2001, p. 203 Bohren & Clothiaux 2006, p. 2 Schiff 1949, p. 2 Mihalas &
Planck's_law
Concept in non-equilibrium physics
In non-equilibrium physics, the Keldysh formalism or Keldysh–Schwinger formalism is a general framework for describing the quantum mechanical evolution
Keldysh_formalism
Generating function for quantum correlation functions
In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral
Partition function (quantum field theory)
Partition_function_(quantum_field_theory)
Summation method for divergent series
theory. In particular in 2-dimensional Euclidean field theory the Schwinger functions can often be recovered from their perturbation series using Borel
Borel_summation
Framework to describe phase transitions
equivalent.[citation needed] The correlation functions of a statistical field theory are called Schwinger functions, and their properties are described by the
Statistical_field_theory
Type of state in thermal systems
Kubo–Martin–Schwinger (KMS) state: a state satisfying the KMS condition. Ryogo Kubo introduced the condition in 1957, Paul C. Martin [de] and Julian Schwinger used
KMS_state
developed by Tomonaga and Schwinger, generalizing earlier efforts of Dirac, Fock and Boris Podolsky. Tomonaga and Schwinger invented a relativistically
History of quantum field theory
History_of_quantum_field_theory
Formulation of quantum mechanics
{(x-y)^{2}}{\mathrm {T} }}-\alpha \mathrm {T} }\,d\mathrm {T} .} This is the Schwinger representation. Taking a Fourier transform over the variable (x − y) can
Path-integral_formulation
Formulation of the quantum many-body problem
as canonical quantization, in which the fields (typically as the wave functions of matter) are thought of as field operators, in a manner similar to how
Second_quantization
Method in physics used to deal with infinities
divergences was discovered in 1947–49 by Hans Kramers, Hans Bethe, Julian Schwinger, Richard Feynman, and Shin'ichiro Tomonaga, and systematized by Freeman
Renormalization
Irreducible representation of the rotation group SO
theory of angular momentum. Dover. ISBN 0-486-68480-6. OCLC 31374243. Schwinger, J. (January 26, 1952). On Angular Momentum (Technical report). Harvard
Wigner_D-matrix
Scattering theory
{\displaystyle k=|\mathbf {k} _{f}-\mathbf {k} _{i}|.} The Lippmann–Schwinger equation for the scattering state | Ψ p ( ± ) ⟩ {\displaystyle \vert {\Psi
Born_approximation
Interpretation of quantum mechanics
mechanics that asserts that the universal wave function is objectively real, and that there is no wave function collapse. This implies that all possible outcomes
Many-worlds_interpretation
Quantum state with the lowest possible energy
1940s and early 1950s, it was reformulated by Feynman, Tomonaga, and Schwinger, who jointly received the Nobel prize for this work in 1965. Today, the
Quantum_vacuum_state
Theorem for reducing high-order derivatives
products of pairs of these operators. This allows for the use of Green's function methods, and consequently the use of Feynman diagrams in the field under
Wick's_theorem
Fringe hypothesis
features of the brain than cells, may play an important part in the brain's function and could explain critical aspects of consciousness. These scientific hypotheses
Quantum_mind
Axiomatization of quantum field theory
around this, the Wightman axioms introduce the idea of smearing over a test function to tame the UV divergences, which arise even in a free field theory. Because
Wightman_axioms
Force resulting from the quantisation of a field
original paper used this method to derive the Casimir–Polder force. In 1978, Schwinger, DeRadd, and Milton published a similar derivation for the Casimir effect
Casimir_effect
Lowest possible energy of a quantum system or field
derivation was first given by Schwinger (1975) for a scalar field, and then generalized to the electromagnetic case by Schwinger, DeRaad, and Milton (1978)
Zero-point_energy
Quantum field theory at non-zero temperatures
Matsubara formalism, based on evolving the system in imaginary time. Schwinger–Keldysh formalism, based on the real-time evolution, allowing the treatment
Thermal_quantum_field_theory
Schwarzschild radius Schwinger's quantum action principle Schwinger function Schwinger limit Schwinger model Schwinger parametrization Schwinger–Dyson equation
Index_of_physics_articles_(S)
Effective particle coupling beyond tree level
F 2 ( 0 ) {\displaystyle a={\frac {g-2}{2}}=F_{2}(0)} In 1948, Julian Schwinger calculated the first correction to anomalous magnetic moment, given by
Vertex_function
Functions that can't be described by perturbation theory
instantons are examples. A concrete, physical example is given by the Schwinger effect, whereby a strong electric field may spontaneously decay into electron-positron
Non-perturbative
American theoretical physicist (1918–1988)
theoretical physicist. He shared the 1965 Nobel Prize in Physics with Julian Schwinger and Shin'ichirō Tomonaga "for their fundamental work in quantum electrodynamics
Richard_Feynman
Expression for two-point correlation functions
representation, gives a general expression for the (time ordered) two-point function of an interacting quantum field theory as a sum of free propagators. It
Källén–Lehmann spectral representation
Källén–Lehmann_spectral_representation
Branch of mathematics
to a step function having infinitely many points of increase at the points qj..The jump at the point qj is qj. Calling this step function gq(t) gives
Quantum_calculus
Swiss mathematician and physicist (1939–2015)
theorem states that the Wightman functions of a relativistic QFT can be reconstructed from the Schwinger functions of a Euclidean theory satisfying the
Robert_Schrader
Surgical removal of the spleen
Pratl B, Benesch M, Lackner H, Portugaller HR, Pusswald B, Sovinz P, Schwinger W, Moser A, Urban C (January 2008). "Partial splenic embolization in children
Splenectomy
\rangle } with free particle wave function | ϕ ⟩ {\displaystyle |\phi \rangle } on the right hand side of the Lippmann-Schwinger equation and it gives the first
Born_series
Field equation from quantum gravity
|\psi \rangle } is no longer a spatial wave function in the traditional sense of a complex-valued function that is defined on a 3-dimensional space-like
Wheeler–DeWitt_equation
Quantum chromodynamics on a lattice
supercomputer. After Wick rotation, the path integral for the partition function of QCD takes the form Z = ∫ D U e − S [ U ] = ∫ ∏ x , μ d U μ ( x ) e −
Lattice_QCD
Relativistic wave equation in quantum mechanics
only a gauge choice of the Lorenz gauge for the Maxwell equation. Rarita–Schwinger equation This can be seen from the role that m {\displaystyle m} plays
Klein–Gordon_equation
Parameter describing the strength of a force
In this case, the non-zero beta function tells us that the classical scale-invariance is anomalous. If a beta function is positive, the corresponding coupling
Coupling_constant
Relativistic wave equation describing massless fermions
equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations Schwinger-Dyson equation Renormalization group equation Standard Model Quantum electrodynamics
Weyl_equation
Transformation in quantum mechanics
(non-Hermitian) Dyson–Maleev technique, and to a lesser extent the Jordan–Schwinger map. There is, furthermore, a close link to the theory of (generalized)
Holstein–Primakoff transformation
Holstein–Primakoff_transformation
Quantum version of the classical action
and the Standard Model, Cambridge University Press 2014 Toms, D.J.: The Schwinger Action Principle and Effective Action, Cambridge University Press 2007
Effective_action
Attempts to develop a quantum mechanical theory of cosmology
causal set theory. In quantum cosmology, the universe is treated as a wave function instead of classical spacetime. String cosmology Brane cosmology Loop quantum
Quantum_cosmology
Connection between correlation functions and the S-matrix
elements (the scattering amplitudes) from the time-ordered correlation functions of a quantum field theory. It is a step of the path that starts from the
LSZ_reduction_formula
Physical quantity of dimension energy × time
work with different forms of action until Richard Feynman and Julian Schwinger developed quantum action principles. Expressed in mathematical language
Action_(physics)
Hypothetical particle with one magnetic pole
equator, the phase φ of its wave function eiφ must be unchanged, which implies that the phase φ added to the wave function must be a multiple of 2π. This
Magnetic_monopole
British theoretical physicist and mathematician (1923–2020)
Richard Feynman's diagrams and the operator method developed by Julian Schwinger and Shin'ichirō Tomonaga. He was the first person after their creator
Freeman_Dyson
Theory of quantum gauge fields on a lattice
equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations Schwinger-Dyson equation Renormalization group equation Standard Model Quantum electrodynamics
Lattice_gauge_theory
Symmetry breaking through the vacuum state
"Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order". Phys. Rev. B. 82 (15) 155138.
Spontaneous_symmetry_breaking
Equation for two-body bound states
representation. ABINIT Araki–Sucher correction Breit equation Lippmann–Schwinger equation Schwinger–Dyson equation Two-body Dirac equations YAMBO code H. Bethe,
Bethe–Salpeter_equation
British mathematical physicist (1793–1841)
hands of Julian Schwinger and Freeman Dyson in the 1940s, Green's functions became standard tools of quantum electrodynamics (QED). Schwinger, who had previously
George_Green_(mathematician)
Japanese-born American theoretical physicist (1925–2023)
Dirac, Proc. Roy. Soc. Lond. A 117, 610 (1928). J. S. Schwinger, Phys. Rev. 73, 416 (1948); J. Schwinger, Phys. Rev. 75, 898 (1949). R. Karplus and N. M. Kroll
Toichiro_Kinoshita
Process in quantum mechanical theories
extend the single-particle state function ψ ( r ) {\displaystyle \psi (\mathbf {r} )} to the N-particle state function ψ ( r 1 , r 2 , … , r N ) {\displaystyle
Canonical_quantization
Quantum field that enables consistent quantization
equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations Schwinger-Dyson equation Renormalization group equation Standard Model Quantum electrodynamics
Ghost_(physics)
n-space and the Atiyah–Singer–Dirac operator on a spin manifold, Rarita–Schwinger/Stein–Weiss type operators, conformal Laplacians, spinorial Laplacians
Clifford_analysis
}},} in terms of new function | ψ 1 ⟩ {\displaystyle |\psi _{1}\rangle } . This function is solution of modified Lippmann–Schwinger equation | ψ 1 ⟩ = |
Method_of_continued_fractions
Dimensionless number that quantifies the strength of the electromagnetic interaction
α/2π is engraved on the tombstone of one of the pioneers of QED, Julian Schwinger, referring to his calculation of the anomalous magnetic dipole moment
Fine-structure_constant
Insertion device consisting of dipole magnets
in a 1947 paper. Julian Schwinger published a useful paper in 1949 that reduced the necessary calculations to Bessel functions, for which there were tables
Undulator
Maximally helicity violating amplitudes
equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations Schwinger-Dyson equation Renormalization group equation Standard Model Quantum electrodynamics
MHV_amplitudes
British physicist (1902–1984)
quantum mechanics by the next generation of theorists, in particular Julian Schwinger, Richard Feynman, Sin-Itiro Tomonaga and Freeman Dyson in their formulation
Paul_Dirac
Mechanism that explains the generation of mass for gauge bosons
W mesons in the Schwinger model, with a mass set by the mass scale Ã, and one massless U(1) gauge boson, similar to the photon. The Schwinger model predicts
Higgs_mechanism
Graduate textbook by J.D. Jackson
used with physical phenomena. Unlike Jackson, Schwinger employs variational methods and Green's functions extensively. Mehra took issue with the use of
Classical Electrodynamics (book)
Classical_Electrodynamics_(book)
Quantum field giving rise to gluons
gauge covariant derivative transforms similarly. The functions θn here are similar to the gauge function χ(r, t) when changing the electromagnetic four-potential
Gluon_field
American theoretical physicist (1904–1967)
expressions in the quantum electrodynamics of elementary particles. Julian Schwinger, Richard Feynman and Shin'ichiro Tomonaga tackled the problem of regularization
J._Robert_Oppenheimer
Technique in quantum field theory
\phi (x)=B(x)+\eta (x)} . After this is done, the Green's functions are evaluated as a function of the background. This approach has the advantage that
Background_field_method
Extension of quantum field theory to curved spacetime
equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations Schwinger-Dyson equation Renormalization group equation Standard Model Quantum electrodynamics
Quantum field theory in curved spacetime
Quantum_field_theory_in_curved_spacetime
Operator in quantum field theory
equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations Schwinger-Dyson equation Renormalization group equation Standard Model Quantum electrodynamics
Pauli–Lubanski_pseudovector
Evolutionary equation under renormalization group flow
n-point correlation functions under variation of the energy scale at which the theory is defined and involves the beta function of the theory and the
Callan–Symanzik_equation
Possible outcome of renormalization in physics
ability of charge screening, which makes the effective charge being a function of the length (or momentum) scale. Quantum triviality is referred to a
Quantum_triviality
Physical field theory with no forces/interactions
differentiate distributions by defining their derivatives via differentiated test functions. See Schwartz distribution for more details. Since we are dealing not
Free_field
Describing something mathematical with variables
model, the standard model of Big Bang cosmology Feynman parametrization Schwinger parametrization Solid modeling Dependency injection Hughes-Hallet, Deborah;
Parametrization_(geometry)
Action of a massive abelian gauge field
B^{\mu }-\partial ^{\mu }f} where f {\displaystyle f} is an arbitrary function. Electromagnetic field Photon Quantum electrodynamics Quantum gravity Vector
Proca_action
Introductory article
be local. That is, rather than adding a constant onto V, one can add a function that takes on different values at different points in space and time. If
Introduction_to_gauge_theory
Dirac equation for self-interacting fermions
resulting field equations, the torsion tensor is a homogeneous, linear function of the spin tensor. The minimal coupling between torsion and Dirac spinors
Nonlinear_Dirac_equation
Theorem in quantum mechanics
theory results with probabilities greater than one. A proof by Julian Schwinger in 1950 based on time-reversal invariance followed a proof by Frederik
Spin–statistics_theorem
Hypothetical superpartner to the graviton
exists, it is a fermion of spin 3/2 ħ and therefore obeys the Rarita–Schwinger equation. The gravitino field is conventionally written as ψμα with μ
Gravitino
American physicist (born 1935)
earned his Ph.D. from Harvard University in 1960, studying under Julian Schwinger. He joined the physics faculty of the University of Illinois at Urbana-Champaign
Gordon_Baym
Application of computational physics
scattering amplitude is evaluated recursively through a set of Dyson-Schwinger equations. The computational cost of this algorithm grows asymptotically
Automatic calculation of particle interaction or decay
Automatic_calculation_of_particle_interaction_or_decay
Cross-platform instant messaging service
from the original on 8 November 2020. Retrieved 21 March 2021. Robert A. Schwinger (26 May 2020). "Blockchain law. A "Telegram" to SAFTs: "Beware!"" (PDF)
Telegram_(software)
Type of operator expectation value
Casimir effect. This concept is important for working with correlation functions in quantum field theory. In the context of spontaneous symmetry breaking
Vacuum_expectation_value
Range of physical processes in physics
Schrödinger equation, although equivalent formulations, such as the Lippmann-Schwinger equation and the Faddeev equations, are also largely used. The solutions
Scattering
Protein domain
Kayser S, Wolff D, Tuve S, Kyzirakos C, Bethge W, Greil J, Albert MH, Schwinger W, Nathrath M, Schumm M, Stevanovic S, Handgretinger R, Lang P, Feuchtinger
Epstein–Barr virus nuclear antigen 1
Epstein–Barr_virus_nuclear_antigen_1
SCHWINGER FUNCTION
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