scholarly journals Operator product expansion of the non-local gluon condensate

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
V. M. Braun ◽  
K. G. Chetyrkin ◽  
B. A. Kniehl
Keyword(s):  
Operator Product Expansion ◽  
Wilson Line ◽  
Gluon Condensate ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Distribution Functions ◽  
Operator Product ◽  
Nonlocal Operator ◽  
Expectation Value ◽  
Qcd Vacuum

Abstract We consider the short-distance expansion of the product of two gluon field strength tensors connected by a straight-line-ordered Wilson line. The vacuum expectation value of this nonlocal operator is a common object in studies of the QCD vacuum structure, whereas its nucleon expectation value is known as the gluon quasi-parton distribution and is receiving a lot of attention as a tool to extract gluon distribution functions from lattice calculations. Extending our previous study [1], we calculate the three-loop coefficient functions of the scalar operators in the operator product expansion up to dimension four. As a by-product, the three-loop anomalous dimension of the nonlocal two-gluon operator is obtained as well.

scholarly journals OPERATOR-PRODUCT EXPANSION AND ANALYTICITY

1999 ◽  
Vol 14 (30) ◽  
pp. 4819-4840
Author(s):  
JAN FISCHER ◽  
IVO VRKOČ
Keyword(s):  
Operator Product Expansion ◽  
Deflection Angle ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Operator Product ◽  
Coupling Constant ◽  
Expectation Value ◽  
Euclidean Region ◽  
The Deflection Angle ◽  
Class Of Functions

We discuss the current use of the operator-product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the Euclidean region, we observe how the bound varies with increasing deflection from the Euclidean ray down to the cut (Minkowski region). We argue that the assumption that the remainder is constant for all angles in the cut complex plane down to the Minkowski region is not justified. Making specific assumptions on the properties of the expanded function, we obtain bounds on the remainder in explicit form and show that they are very sensitive both to the deflection angle and to the class of functions considered. The results obtained are discussed in connection with calculations of the coupling constant αs from the τ decay.

CHIRAL CONDENSATE IN DENSE BARYONS

2013 ◽  
Vol 21 ◽  
pp. 126-131
Author(s):  
SHIGENORI SEKI
Keyword(s):  
Wilson Line ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Open String ◽  
Chiral Condensate ◽  
Baryon Density ◽  
World Sheet ◽  
Expectation Value ◽  
Holographic Qcd ◽  
Minimal Area

We study the chiral condensate in dense baryonic medium by the use of the generalized Sakai-Sugimoto model of holographic QCD. The chiral condensate is identified with the vacuum expectation value of the open Wilson line operator. We evaluate it by the minimal area of open string world-sheet whose boundary is the V-shape flavor D8-branes. As a result, we find that the chiral condensate decreases in low baryon density and increases in high density. This decreasing behavior is in agreement with the expectation from QCD.

COLOR CONFINEMENT AND FINITE TEMPERATURE QCD PHASE TRANSITION

2004 ◽  
Vol 19 (02) ◽  
pp. 271-285 ◽  
Author(s):  
H. C. PANDEY ◽  
H. C. CHANDOLA ◽  
H. DEHNEN
Keyword(s):  
Phase Transition ◽  
Critical Temperature ◽  
Effective Potential ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Zero Temperature ◽  
Expectation Value ◽  
Qcd Phase Transition ◽  
Qcd Vacuum ◽  
Color Confinement

We study an effective theory of QCD in which the fundamental variables are dual magnetic potentials coupled to the monopole field. Dual dynamics are then used to explain the properties of QCD vacuum at zero temperature as well as at finite temperatures. At zero temperature, the color confinement is realized through the dynamical breaking of magnetic symmetry, which leads to the magnetic condensation of QCD vacuum. The flux tube structure of SU(2) QCD vacuum is investigated by solving the field equations in the low energy regimes of the theory, which guarantees dual superconducting nature of the QCD vacuum. The QCD phase transition at finite temperature is studied by the functional diagrammatic evaluation of the effective potential on the one-loop level. We then obtained analytical expressions for the vacuum expectation value of the condensed monopoles as well as the masses of glueballs from the temperature dependent effective potential. These nonperturbative parameters are also evaluated numerically and used to determine the critical temperature of the QCD phase transition. Finally, it is shown that near the critical temperature (Tc≃0.195 GeV ), continuous reduction of vacuum expectation value (VEV) of the condensed monopoles caused the disappearance of vector and scalar glueball masses, which brings a second order phase transition in pure SU(2) gauge QCD.

A Study of Fermionic Three-Point Vertex with Gluon Condensate

1997 ◽  
Vol 12 (34) ◽  
pp. 2577-2583 ◽  
Author(s):  
J. J. Yang ◽  
H. Chen ◽  
G. L. Li ◽  
H. Q. Shen
Keyword(s):  
Fixed Point ◽  
Gluon Condensate ◽  
Zero Point ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Covariant Form ◽  
Expectation Value ◽  
Point Vertex

We derive the dimension-four gluon condensate contributions to the fermionic three-point vertex with different forms of the gluon condensate component of the nonlocal two-gluon vacuum expectation value (vev). We find that the result with the non-covariant form of nonlocal two-gluon vev in the fixed-point gauge depends on whether the zero-point is set on the fermionic- or gluonic-line. But this uncertainty can be avoided by using the covariant form of the nonlocal two-gluon vev.

Global symmetries and Noether’s theorem

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Global Symmetries ◽  
Symmetry Transformation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Quantum Field ◽  
Expectation Value ◽  
Minkowski Space Time ◽  
Integral Measure ◽  
Colour Charge ◽  
Internal Symmetries

Noethers theorem shows that continuous global symmetries lead classically to conservation laws. Such symmetries can be divided into spacetime and internal symmetries. The invariance of Minkowski space-time under global Poincaré transformations leads to the conservation of the four-momentum and the total angular momentum. Examples for conserved charges due to internal symmetries are electric and colour charge. The vacuum expectation value of a Noether current is shown to beconserved in a quantum field theory if the symmetry transformation keeps the path-integral measure invariant.

scholarly journals High-energy operator product expansion at sub-eikonal level

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Giovanni Antonio Chirilli
Keyword(s):  
Operator Product Expansion ◽  
Evolution Equations ◽  
Energy Operator ◽  
High Energy ◽  
Structure Functions ◽  
Distribution Functions ◽  
Impact Factors ◽  
Operator Product ◽  
The Impact ◽  
New Distribution

Abstract The high energy Operator Product Expansion for the product of two electromagnetic currents is extended to the sub-eikonal level in a rigorous way. I calculate the impact factors for polarized and unpolarized structure functions, define new distribution functions, and derive the evolution equations for unpolarized and polarized structure functions in the flavor singlet and non-singlet case.

scholarly journals THE TACHYON FIELD BELOW THE MASS BARRIER

1994 ◽  
Vol 09 (20) ◽  
pp. 3497-3502 ◽  
Author(s):  
D.G. BARCI ◽  
C.G. BOLLINI ◽  
M.C. ROCCA
Keyword(s):  
Green Function ◽  
Eigenvalue Problem ◽  
Plane Wave ◽  
Time Evolution ◽  
Mass Parameter ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Tachyon Field ◽  
Expectation Value ◽  
Wave Solutions

We consider a tachyon field whose Fourier components correspond to spatial momenta with modulus smaller than the mass parameter. The plane wave solutions have then a time evolution which is a real exponential. The field is quantized and the solution of the eigenvalue problem for the Hamiltonian leads to the evaluation of the vacuum expectation value of products of field operators. The propagator turns out to be half-advanced and half-retarded. This completes the proof4 that the total propagator is the Wheeler Green function.4,7

THE TWISTED EUCLIDEAN GREEN’S FUNCTION IN THE SPACETIME OF A COSMIC STRING

1992 ◽  
Vol 01 (02) ◽  
pp. 371-377 ◽  
Author(s):  
B. LINET
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Minkowski Spacetime ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Massive Scalar ◽  
Elementary Functions ◽  
Integral Expression ◽  
Massive Scalar Field ◽  
Expectation Value

In a conical spacetime, we determine the twisted Euclidean Green’s function for a massive scalar field. In particular, we give a convenient form for studying the vacuum averages. We then derive an integral expression of the vacuum expectation value <Φ2(x)>. In the Minkowski spacetime, we express <Φ2(x)> in terms of elementary functions.

Functional Solution Scheme for Relativistic Strong Coupling Theor

1964 ◽  
Vol 19 (7-8) ◽  
pp. 828-834
Author(s):  
G. Heber ◽  
H. J. Kaiser
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Functional Integral ◽  
The Self ◽  
Matrix Elements ◽  
Point Function ◽  
Expectation Value ◽  
Lattice Space ◽  
S Matrix ◽  
Functional Solution

The vacuum expectation value of the S-matrix is represented, following HORI, as a functional integral and separated according to Svac=exp( — i W) ∫ D φ exp( —i ∫ dx Lw). Now, the functional integral involves only the part Lw of the Lagrangian without derivatives and can be easily calculated in lattice space. We propose a graphical scheme which formalizes the action of the operator W = f dx dy δ (x—y) (δ/δ(y))⬜x(δ/δ(x)) . The scheme is worked out in some detail for the calculation of the two-point-function of neutral BOSE fields with the self-interaction λ φM for even M. A method is proposed which under certain convergence assumptions should yield in a finite number of steps the lowest mass eigenvalues and the related matrix elements. The method exhibits characteristic differences between renormalizable and nonrenormalizable theories.

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