Conformally invariant operator-product expansions of any number of operators of arbitrary spin

1985 ◽  
Vol 63 (11) ◽  
pp. 1427-1437 ◽  
Author(s):  
C. S. Lam ◽  
M. V. Tratnik
Keyword(s):  
Invariant Operator ◽  
Arbitrary Spin ◽  
Conformal Group ◽  
Wave Functions ◽  
Operator Product ◽  
Conformally Invariant

We derive operator-product expansions of any number of operators of arbitrary spin that are invariant under the collinear conformal group. The corresponding parton wave functions of hadrons are calculated. The result can be expressed in terms of the conformal polynomials or the dual-conformal polynomials, the properties of which are also discussed.

scholarly journals Instability of complex CFTs with operators in the principal series

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Dario Benedetti
Keyword(s):  
Principal Series ◽  
Conformal Group ◽  
Point Of View ◽  
Field Theories ◽  
Operator Product ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Primary Operator ◽  
Tensor Models

Abstract We prove the instability of d-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension h = $$ \frac{d}{2} $$ d 2 + i r, with non-vanishing r ∈ ℝ. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdSd+1; we derive it here directly for generic d-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

scholarly journals Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Salim Medjber ◽  
Hacene Bekkar ◽  
Salah Menouar ◽  
Jeong Ryeol Choi
Keyword(s):  
Separation Of Variables ◽  
Type Equation ◽  
Invariant Operator ◽  
Wave Functions ◽  
Time Dependent ◽  
Harmonic Potential ◽  
Uncertainty Relations ◽  
Mathematical Methods ◽  
Potential System ◽  
Uvarov Method

The Schrödinger solutions for a three-dimensional central potential system whose Hamiltonian is composed of a time-dependent harmonic plus an inverse harmonic potential are investigated. Because of the time-dependence of parameters, we cannot solve the Schrödinger solutions relying only on the conventional method of separation of variables. To overcome this difficulty, special mathematical methods, which are the invariant operator method, the unitary transformation method, and the Nikiforov-Uvarov method, are used when we derive solutions of the Schrödinger equation for the system. In particular, the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat. Through this procedure, we derived exact Schrödinger solutions (wave functions) of the system. It is confirmed that the wave functions are represented in terms of time-dependent radial functions, spherical harmonics, and general time-varying global phases. Such wave functions are useful for studying various quantum properties of the system. As an example, the uncertainty relations for position and momentum are derived by taking advantage of the wave functions.

TOWARDS A CONFORMAL QED4 WITH A NONVANISHING CURRENT 2-POINT FUNCTION

1988 ◽  
Vol 03 (04) ◽  
pp. 1023-1049 ◽  
Author(s):  
YASSEN S. STANEV ◽  
IVAN T. TODOROV
Keyword(s):  
Quantum Electrodynamics ◽  
Anomalous Dimension ◽  
Operator Product ◽  
Indefinite Metric ◽  
Conformal Invariant ◽  
Point Function ◽  
Four Dimensions ◽  
Conformally Invariant ◽  
Longitudinal Correlation ◽  
Electron Field

The possibility of constructing a conformally invariant model of spinor quantum electrodynamics (QED) in four dimensions involving an anomalous dimension of the electron field and a general indecomposable conformal law for the Maxwell field Fµν is studied within the local indefinite metric framework making systematic use of conformal operator product expansions (OPEs). It is demonstrated that the standard elementary conformal law for Fµν, which is known to yield a vanishing current-current 2-point function leads to a trivial theory. On the other hand, the conformal invariant 2-point function <Jμ(x1)Jν(x2)> (proportional to the second order perturbation theory expression in a massless QED) gives rise to a soluble conformal model involving [Formula: see text] and a vector field Vµ with longitudinal correlation function. The question whether the model can be extended to include Fµν (rather than its divergence) remains unresolved.

scholarly journals Conformal group theory of tensor structures

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Ilija Burić ◽  
Volker Schomerus ◽  
Mikhail Isachenkov
Keyword(s):  
Correlation Functions ◽  
Conformal Group ◽  
Wave Functions ◽  
Dimensional Euclidean Space ◽  
Theoretic Approach ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Local Operators ◽  
Indispensable Tool ◽  
Systematic Derivation

Abstract The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are functions of cross ratios only, and the correlation functions that depend on insertion points in the d-dimensional Euclidean space. Here we develop an entirely group theoretic approach to tensor structures, based on the Cartan decomposition of the conformal group. It provides us with a new universal formula for tensor structures and thereby a systematic derivation of crossing equations. Our approach applies to a ‘gauge’ in which the conformal blocks are wave functions of Calogero-Sutherland models rather than solutions of the more standard Casimir equations. Through this ab initio construction of tensor structures we complete the Calogero-Sutherland approach to conformal correlators, at least for four-point functions of local operators in non-supersymmetric models. An extension to defects and superconformal symmetry is possible.

scholarly journals QUANTUM DYNAMICS FOR DE SITTER RADIATION

2012 ◽  
Vol 10 ◽  
pp. 43-54 ◽  
Author(s):  
SANG PYO KIM
Keyword(s):  
Quantum Dynamics ◽  
Particle Production ◽  
Hamiltonian Formalism ◽  
Classical Equation ◽  
Invariant Operator ◽  
Wave Functions ◽  
De Sitter ◽  
Massive Scalar Field ◽  
Gaussian Wave Function ◽  
Creation Operators

We revisit the Hamiltonian formalism for a massive scalar field and study the particle production in a de Sitter space. In the invariant-operator picture the time-dependent annihilation and creation operators are constructed in terms of a complex solution to the classical equation of motion for the field and the Gaussian wave function for each Fourier mode is found which is an exact solution to the Schrödinger equation. The in-out formalism is reformulated by the annihilation and creation operators and the Gaussian wave functions. The de Sitter radiation from the in-out formalism differs from the Gibbons-Hawking radiation in the planar coordinates, and we discuss the discrepancy of the particle production by the two methods.

Bethe-Salpeter wave functions for mesons of arbitrary spin and the covariant instantaneous approximation

1995 ◽  
Vol 51 (5) ◽  
pp. 2347-2352 ◽  
Author(s):  
Chao-Shang Huang ◽  
Hong-Ying Jin ◽  
Yuan-Ben Dai
Keyword(s):  
Arbitrary Spin ◽  
Wave Functions ◽  
Instantaneous Approximation
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