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Relevant bibliographies by topics / Wightman axioms

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Academic literature on the topic 'Wightman axioms'

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Published: 25 May 2024

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Journal articles on the topic "Wightman axioms"

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Maharana, Jnanadeva. "PCT theorem, Wightman axioms and conformal bootstrap." Modern Physics Letters A 36, no. 11 (March 17, 2021): 2150072. http://dx.doi.org/10.1142/s0217732321500723.

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The axiomatic Wightman formulation for nonderivative conformal field theory is adopted to derive conformal bootstrap equation for the four-point function. The equivalence between PCT theorem and weak local commutativity, due to Jost plays a very crucial role in axiomatic field theory. The theorem is suitably adopted for conformal field theory to derive the desired equations in CFT. We demonstrate that the two Wightman functions are analytic continuation of each other.

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Mendoza-Martínez, M. L., J. A. Vallejo, and W. A. Zúñiga-Galindo. "Acausal quantum theory for non-Archimedean scalar fields." Reviews in Mathematical Physics 31, no. 04 (April 17, 2019): 1950011. http://dx.doi.org/10.1142/s0129055x19500119.

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We construct a family of quantum scalar fields over a [Formula: see text]-adic spacetime which satisfy [Formula: see text]-adic analogues of the Gårding–Wightman axioms. Most of the axioms can be formulated in the same way for both the Archimedean and non-Archimedean frameworks; however, the axioms depending on the ordering of the background field must be reformulated, reflecting the acausality of [Formula: see text]-adic spacetime. The [Formula: see text]-adic scalar fields satisfy certain [Formula: see text]-adic Klein–Gordon pseudo-differential equations. The second quantization of the solutions of these Klein–Gordon equations corresponds exactly to the scalar fields introduced here. The main conclusion is that there seems to be no obstruction to the existence of a mathematically rigorous quantum field theory (QFT) for free fields in the [Formula: see text]-adic framework, based on an acausal spacetime.

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GIELERAK, R., and P. ŁUGIEWICZ. "4D LOCAL QUANTUM FIELD THEORY MODELS FROM COVARIANT STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS I: GENERALITIES." Reviews in Mathematical Physics 13, no. 03 (March 2001): 335–408. http://dx.doi.org/10.1142/s0129055x01000685.

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A general class of covariant stochastic partial differential equations in Euclidean space-time dimension D=4 is selected and solutions of them are discussed. In particular we demonstrate a possibility of an analytic continuation of the moments of the constructed solutions to the Minkowski space-time. That gives rise to systems of tempered distributions obeying a substantial part of Wightman axioms. Specific models appropriate for vector, Higgs-like and Maxwell-like fields are described in detail. Covariant schemes for solving rectangular systems of equations are presented. Those ideas lead in particular to clarification of the concept of gauge-invariance in the present context. The explicit forms of Wightman distributions are obtained and used to prove the Hilbert Space Structure Condition. Some explicitly computable covariant models of extended random objects like loops, membranes and bags are presented.

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NIKOLOV, N. M., and I. T. TODOROV. "CONFORMAL INVARIANCE AND RATIONALITY IN AN EVEN DIMENSIONAL QUANTUM FIELD THEORY." International Journal of Modern Physics A 19, no. 22 (September 10, 2004): 3605–36. http://dx.doi.org/10.1142/s0217751x04019342.

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Invariance under finite conformal transformations in Minkowski space and the Wightman axioms imply strong locality (Huygens principle) and rationality of correlation functions, thus providing an extension of the concept of vertex algebra to higher dimensions. Gibbs (finite temperature) expectation values appear as elliptic functions in the conformal time. We survey and further pursue our program of constructing a globally conformal invariant model of a Hermitian scalar field ℒ of scale dimension four in Minkowski space–time which can be interpreted as the Lagrangian density of a gauge field theory.

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Bostelmann, Henning, and Daniela Cadamuro. "Towards an Explicit Construction of Local Observables in Integrable Quantum Field Theories." Annales Henri Poincaré 20, no. 12 (September 20, 2019): 3889–926. http://dx.doi.org/10.1007/s00023-019-00847-7.

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Abstract We present a new viewpoint on the construction of pointlike local fields in integrable models of quantum field theory. As usual, we define these local observables by their form factors; but rather than exhibiting their n-point functions and verifying the Wightman axioms, we aim to establish them as closed operators affiliated with a net of local von Neumann algebras, which is defined indirectly via wedge-local quantities. We also investigate whether these fields have the Reeh–Schlieder property, and in which sense they generate the net of algebras. Our investigation focuses on scalar models without bound states. We establish sufficient criteria for the existence of averaged fields as closable operators, and complete the construction in the specific case of the massive Ising model.

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Wreszinski, Walter Felipe. "Perturbative versus Non-Perturbative Quantum Field Theory: Tao’s Method, the Casimir Effect, and Interacting Wightman Theories." Universe 7, no. 7 (July 5, 2021): 229. http://dx.doi.org/10.3390/universe7070229.

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We dwell upon certain points concerning the meaning of quantum field theory: the problems with the perturbative approach, and the question raised by ’t Hooft of the existence of the theory in a well-defined (rigorous) mathematical sense, as well as some of the few existent mathematically precise results on fully quantized field theories. Emphasis is brought on how the mathematical contributions help to elucidate or illuminate certain conceptual aspects of the theory when applied to real physical phenomena, in particular, the singular nature of quantum fields. In a first part, we present a comprehensive review of divergent versus asymptotic series, with qed as background example, as well as a method due to Terence Tao which conveys mathematical sense to divergent series. In a second part, we apply Tao’s method to the Casimir effect in its simplest form, consisting of perfectly conducting parallel plates, arguing that the usual theory, which makes use of the Euler-MacLaurin formula, still contains a residual infinity, which is eliminated in our approach. In the third part, we revisit the general theory of nonperturbative quantum fields, in the form of newly proposed (with Christian Jaekel) Wightman axioms for interacting field theories, with applications to “dressed” electrons in a theory with massless particles (such as qed), as well as unstable particles. Various problems (mostly open) are finally discussed in connection with concrete models.

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7

Rehren, Karl-Henning. "Comments on a recent solution to Wightman's axioms." Communications in Mathematical Physics 178, no. 2 (May 1996): 453–65. http://dx.doi.org/10.1007/bf02099457.

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8

Maharana, Jnanadeva. "Causality, crossing and analyticity in conformal field theories." International Journal of Modern Physics A, September 3, 2021, 2150177. http://dx.doi.org/10.1142/s0217751x21501773.

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Analyticity and crossing properties of four-point function are investigated in conformal field theories in the frameworks of Wightman axioms. A Hermitian scalar conformal field, satisfying the Wightman axioms, is considered. The crucial role of microcausality in deriving analyticity domains is discussed and domains of analyticity are presented. A pair of permuted Wightman functions are envisaged. The crossing property is derived by appealing to the technique of analytic completion for the pair of permuted Wightman functions. The operator product expansion of a pair of scalar fields is studied and analyticity property of the matrix elements of composite fields, appearing in the operator product expansion, is investigated. An integral representation is presented for the commutator of composite fields where microcausality is a key ingredient. Three fundamental theorems of axiomatic local field theories; namely, PCT theorem, the theorem proving equivalence between PCT theorem and weak local commutativity and the edge-of-the-wedge theorem are invoked to derive a conformal bootstrap equation rigorously.

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Raymond, Christopher, Yoh Tanimoto, and James E. Tener. "Unitary Vertex Algebras and Wightman Conformal Field Theories." Communications in Mathematical Physics, August 3, 2022. http://dx.doi.org/10.1007/s00220-022-04431-9.

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AbstractWe prove an equivalence between the following notions: (i) unitary Möbius vertex algebras, and (ii) Wightman conformal field theories on the circle (with finite-dimensional conformal weight spaces) satisfying an additional condition that we call uniformly bounded order. Reading this equivalence in one direction, we obtain new analytic and operator-theoretic information about vertex operators. In the other direction we characterize OPEs of Wightman fields and show they satisfy the axioms of a vertex algebra. As an application we establish new results linking unitary vertex operator algebras with conformal nets.

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Kravchuk, Petr, Jiaxin Qiao, and Slava Rychkov. "Distributions in CFT. Part II. Minkowski space." Journal of High Energy Physics 2021, no. 8 (August 2021). http://dx.doi.org/10.1007/jhep08(2021)094.

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Abstract CFTs in Euclidean signature satisfy well-accepted rules, such as the convergent Euclidean OPE. It is nowadays common to assume that CFT correlators exist and have various properties also in Lorentzian signature. Some of these properties may represent extra assumptions, and it is an open question if they hold for familiar statistical-physics CFTs such as the critical 3d Ising model. Here we consider Wightman 4-point functions of scalar primaries in Lorentzian signature. We derive a minimal set of their properties solely from the Euclidean unitary CFT axioms, without using extra assumptions. We establish all Wightman axioms (temperedness, spectral property, local commutativity, clustering), Lorentzian conformal invariance, and distributional convergence of the s-channel Lorentzian OPE. This is done constructively, by analytically continuing the 4-point functions using the s-channel OPE expansion in the radial cross-ratios ρ, $$ \overline{\rho} $$ ρ ¯ . We prove a key fact that |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ < 1 inside the forward tube, and set bounds on how fast |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ may tend to 1 when approaching the Minkowski space.We also provide a guide to the axiomatic QFT literature for the modern CFT audience. We review the Wightman and Osterwalder-Schrader (OS) axioms for Lorentzian and Euclidean QFTs, and the celebrated OS theorem connecting them. We also review a classic result of Mack about the distributional OPE convergence. Some of the classic arguments turn out useful in our setup. Others fall short of our needs due to Lorentzian assumptions (Mack) or unverifiable Euclidean assumptions (OS theorem).

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Dissertations / Theses on the topic "Wightman axioms"

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Qiao, Jiaxin. "On the Wick rotation of the four-point function in conformal field theories." Electronic Thesis or Diss., Université Paris sciences et lettres, 2022. http://www.theses.fr/2022UPSLE041.

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Les théories des champs conformes (CFTs) en signature euclidienne satisfont plusieurs règles bien acceptées, telles que l'invariance conforme et la convergence de l'expansion du produit d'opérateurs (OPE) en signature euclidienne. De nos jours, il est courant de supposer l'existence des fonctions de corrélation d'une CFT et d'assumer diverses propriétés en signature lorentzienne. Certaines de ces propriétés peuvent représenter des hypothèses supplémentaires, et leur validité reste incertaine dans les CFT de physique statistique familières telles que le modèle d'Ising critique en trois dimensions. Dans cette thèse, nous clarifions qu'au niveau des fonctions de corrélation à quatre points, les axiomes CFT euclidiens impliquent les axiomes standards de la théorie quantique des champs tels que les axiomes d'Osterwalder-Schrader (en signature euclidienne) et les axiomes de Wightman (en signature lorentzienne)
Conformal field theories (CFTs) in Euclidean signature satisfy well-accepted rules, such as conformal invariance and the convergent Euclidean operator product expansion (OPE). Nowadays, it is common to assume that CFT correlators exist and have various properties in the Lorentzian signature. Some of these properties may represent extra assumptions, and it is an open question if they hold for familiar statistical-physics CFTs such as the critical 3d Ising model. In this thesis, we clarify that at the level of four-point functions, the Euclidean CFT axioms imply the standard quantum field theory axioms such as Osterwalder-Schrader axioms (in Euclidean) and Wightman axioms (in Lorentzian)

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Books on the topic "Wightman axioms"

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Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. Relativistic Quantum Fields. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0012.

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The general formulation of quantum field theory. The Wightman axioms. The PCT and spin-statistics theorems. The assumption for the existence of asymptotic states. The reduction formulae and scattering theory. The Feynman rules for the S-matrix. Discussion for spin-12 and spin-1 particles. Applications to quantum electrodynamics. A formal expression for the S-matrix.

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Book chapters on the topic "Wightman axioms"

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Gieres, François, Fang Li, Peter Trotter, Anatoly Nikitin, Barak Kol, Sven Blåbjörn, Jürgen Fuchs, et al. "Wightman Axioms." In Concise Encyclopedia of Supersymmetry, 507. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_693.

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2

Kac, Victor. "Wightman axioms and vertex algebras." In University Lecture Series, 5–16. Providence, Rhode Island: American Mathematical Society, 1998. http://dx.doi.org/10.1090/ulect/010/03.

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3

Glimm, James, Arthur Jaffe, and Thomas Spencer. "The Wightman axioms and particle structure in the ℘(φ)2 quantum field model." In Collected Papers, 118–65. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5421-8_5.

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Glimm, James, Arthur Jaffe, and Thomas Spencer. "The Wightman axioms and particle structure in the P (ϕ)2 quantum field model." In Collected Papers, 118–65. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5418-8_6.

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5

Iliopoulos, J., and T. N. Tomaras. "Interacting Fields." In Elementary Particle Physics, 237–52. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192844200.003.0011.

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We present a simple form of the Wightman axioms in a four-dimensional Minkowski space-time which are supposed to define a physically interesting interacting quantum field theory. Two important consequences follow from these axioms. The first is the invariance under CPT which implies, in particular, the equality of masses and lifetimes for particles and anti-particles. The second is the connection between spin and statistics. We give examples of interacting field theories and develop the perturbation expansion for Green functions. We derive the Feynman rules, both in configuration and in momentum space, for some simple interacting theories. The rules are unambiguous and allow, in principle, to compute any Green function at any order in perturbation.

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