scholarly journals LOOP EQUATIONS IN ABELIAN GAUGE THEORIES

2005 ◽  
Vol 20 (35) ◽  
pp. 2735-2743
Author(s):  
CAYETANO DI BARTOLO ◽  
LORENZO LEAL ◽  
FRANCISCO PEÑA
Keyword(s):  
Gauge Theories ◽  
Mean Field ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Point Of View ◽  
Maxwell Theory ◽  
Abelian Gauge ◽  
Partial Difference ◽  
Expectation Value ◽  
The Mean

The equations obeyed by the vacuum expectation value of the Wilson loop of Abelian gauge theories are considered from the point of view of the loop-space. An approximative scheme for studying these loop-equations for lattice Maxwell theory is presented. The approximation leads to a partial difference equation in the area and length variables of the loop, and certain physically motivated ansatz is seen to reproduce the mean field results from a geometrical perspective.

RELATION BETWEEN THE ALGEBRA OF CURRENTS AND THEIR DEFINITION IN CHIRAL GAUGE THEORIES

1992 ◽  
Vol 07 (04) ◽  
pp. 765-776
Author(s):  
C. FOSCO ◽  
R. C. TRINCHERO
Keyword(s):  
Charge Density ◽  
Gauge Field ◽  
Gauge Theories ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Simple Relation ◽  
Expectation Value ◽  
Covariant Gauge ◽  
The Difference ◽  
Definition Of

We consider anomalous commutators between the charge density and any component of the gauge current in chiral gauge theories. This is done using the BJL definition of commutators, and without quantizing the gauge field. We study the relation between the vacuum expectation value (VEV) of these commutators for the case of consistent and covariant gauge currents. We obtain a simple relation valid for any dimension and gauge group. This relation shows that the difference between the VEV's of the commutators for the consistent and covariant gauge currents depends only on the difference between the VEV's of the corresponding currents.

Mass hierarchies and scalar field self-couplings

1983 ◽  
Vol 61 (3) ◽  
pp. 415-427
Author(s):  
V. Elias ◽  
T. N. Sherry
Keyword(s):  
Scalar Field ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Large Mass ◽  
Mass Ratio ◽  
Abelian Gauge ◽  
Expectation Value ◽  
Tree Approximation ◽  
First Order ◽  
Large Mass Ratio

One (internal gauge boson) loop corrections to the scalar field self-couplings of a spontaneously broken Abelian gauge theory are shown to be independent of one loop shifts in mass (and vacuum expectation value) from tree approximation values, suggesting that stability of arbitrarily large mass ratios under perturbation theory may be possible under an appropriately chosen set of renormalization conditions. However, imposition of a large mass ratio is shown to lead to overly large first order corrections to scalar field self-couplings, independent of the choice of renormalization conditions.

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 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

scholarly journals GRIBOV PROBLEM FOR GAUGE THEORIES: A PEDAGOGICAL INTRODUCTION

2004 ◽  
Vol 01 (04) ◽  
pp. 423-441 ◽  
Author(s):  
GIAMPIERO ESPOSITO ◽  
DIEGO N. PELLICCIA ◽  
FRANCESCO ZACCARIA
Keyword(s):  
Cross Sections ◽  
Gauge Theories ◽  
Functional Integral ◽  
Point Of View ◽  
Spherically Symmetric ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Recent Developments ◽  
Gribov Ambiguity ◽  
Gribov Copies

The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov problem at non-perturbative level: the requirement of preserving the supplementary conditions under gauge transformations leads to a nonlinear differential equation, and the various solutions of such a nonlinear equation represent different gauge configurations known as Gribov copies. Their occurrence (lack of global cross-sections from the point of view of differential geometry) is called Gribov ambiguity, and is here presented within the framework of a global approach to quantum field theory. We first give a simple (standard) example for the SU(2) group and spherically symmetric potentials, then we discuss this phenomenon in general relativity, and recent developments, including lattice calculations.

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.

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.

THE AFFINE N = 4 YANG–MILLS THEORY

1992 ◽  
Vol 07 (11) ◽  
pp. 2469-2485
Author(s):  
A. C. CADAVID ◽  
R. J. FINKELSTEIN
Keyword(s):  
Mass Spectrum ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Effective Theory ◽  
Affine Algebra ◽  
Linear Mass ◽  
Expectation Value ◽  
Yang Mills ◽  
Exotic States ◽  
Affine Symmetry

An affine field theory may be constructed by gauging an affine algebra. The momentum integrals of the affine N = 4 Yang–Mills theory are ultraviolet finite but diverge because the sum over states is infinite. If the affine symmetry is broken by postulating a nonvanishing vacuum expectation value for that component of the scalar field lying in the L0 direction, then the theory acquires a linear mass spectrum. This broken theory is ultraviolet finite too, but the mass spectrum is unbounded. If it is also postulated that the mass spectrum has an upper bound (say, the Planck mass), then the resulting theory appears to be altogether finite. The influence of the exotic states has been estimated and, according to the proposed scenario, is negligible below energies at which gravitational interactions become important. The final effective theory has the symmetry of a compact Lie algebra augmented by the operator L0.

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