Operator regularization beyond lowest order

1988 ◽  
Vol 66 (3) ◽  
pp. 268-278 ◽  
Author(s):  
D. G. C. McKeon ◽  
S. S. Samant ◽  
T. N. Sherry
Keyword(s):  
Quantum Electrodynamics ◽  
Loop Order ◽  
Point Function ◽  
Scalar Theory ◽  
Final Model ◽  
Component Field ◽  
Field Formalism ◽  
Massless Quantum ◽  
Limiting Value ◽  
Zumino Model

We pursue operator regularization beyond lowest order. In lowest order, it is the determinants of operators that are regulated; beyond lowest order it is the inverses of operators. As in lowest order, operator regularization to two-loop order and beyond avoids explicit infinities both in the integrals that are evaluated and in the regulating parameter s as it approaches its limiting value of zero. Operator regularization also replaces the Feynman diagrammatic expansion with an expansion due to Schwinger. No explicit symmetry-breaking regulating parameter is inserted into the original Lagrangian. We illustrate our technique by examining the two-point function in [Formula: see text] scalar theory, the effective potential in [Formula: see text] scalar theory, the vacuum polarization in massless quantum electrodynamics, and the two-point function in the Wess–Zumino model using both the superfield and component-field formalism. In all cases we find expressions that are divergence free and remain finite as the regulating parameter approaches its limiting value. In the final model we explicitly show that the supersymmetry Ward identity for the two-point functions is satisfied to two-loop order.

OPERATOR REGULARIZATION AND THE COMPONENT WESS-ZUMINO MODEL

1990 ◽  
Vol 05 (10) ◽  
pp. 1919-1949 ◽  
Author(s):  
D.G.C. McKEON ◽  
S.S. SAMANT ◽  
T.N. SHERRY
Keyword(s):  
Symmetry Breaking ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Loop Order ◽  
Ward Identities ◽  
Model Calculations ◽  
Stress Energy ◽  
Component Field ◽  
Spinor Current ◽  
Zumino Model

Operator regularization has been shown to provide a method for computing Green’s functions without introducing any symmetry breaking regulating parameters, and without the occurrence of explicit infinities at any stage of the calculation. In this paper, we apply this technique to the component field Wess-Zumino model. Calculations to two-loop order of the two-point functions show that the supersymmetric Ward identities are satisfied, and that infinities do not arise. One-loop anomalous processes involving the chiral current, the spinor current and the stress-energy tensor are computed.

scholarly journals NONLOCAL REGULARISATION OF NONCOMMUTATIVE FIELD THEORIES

2006 ◽  
Vol 21 (24) ◽  
pp. 1851-1863 ◽  
Author(s):  
T. R. GOVINDARAJAN ◽  
SEÇKIN KÜRKÇÜOǦLU ◽  
MARCO PANERO
Keyword(s):  
Dimensionless Parameter ◽  
Nonlocal Theory ◽  
Field Theories ◽  
Loop Order ◽  
Scalar Theory ◽  
Noncommutative Spaces ◽  
Perturbative Corrections

We study noncommutative field theories, which are inherently nonlocal, using a Poincaré-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cutoff scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention on the particular case when the noncommutativity parameter is inversely proportional to the square of the cutoff, via a dimensionless parameter η. We work out the perturbative corrections at one-loop order for a scalar theory with quartic interactions, where the signature of noncommutativity appears in η-dependent terms. The implications of this approach, which avoids the problems related to uv–ir mixing, are discussed from the perspective of the Wilson renormalisation program. Finally, we remark about the generality of the method, arguing that it may lead to phenomenologically relevant predictions, when applied to realistic field theories.

Evaluation of loop diagrams using quantum mechanics

1992 ◽  
Vol 70 (8) ◽  
pp. 652-655 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Matrix Element ◽  
Proper Time ◽  
Quantum Field ◽  
Loop Momentum ◽  
Loop Order ◽  
Point Function ◽  
Integral Formalism ◽  
Time Formalism

In using the proper time formalism, Schwinger demonstrated that one-loop processes in quantum field theory can be expressed in terms of a matrix element whose form is encountered in quantum mechanics, and which can be evaluated using the Heisenberg formalism. We demonstrate how instead this matrix element can be computed using standard results in the path-integral formalism. The technique of operator regularization allows one to extend this approach to arbitrary loop order. No loop-momentum integrals are ever encountered. This technique is illustrated by computing the two-point function in [Formula: see text] theory to one-loop order.

New anomaly. Nonvanishing emission and scattering of longitudinal photons in massless quantum electrodynamics

1989 ◽  
Vol 227 (3-4) ◽  
pp. 474-478 ◽  
Author(s):  
A.S. Gorsky ◽  
B.L. Ioffe ◽  
A.Yu. Khodjamirian
Keyword(s):  
Quantum Electrodynamics ◽  
Massless Quantum

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 Precision Calculations in Supersymmetric Theories

2013 ◽  
Vol 2013 ◽  
pp. 1-64 ◽  
Author(s):  
L. Mihaila
Keyword(s):  
Theoretical Calculations ◽  
Gauge Coupling ◽  
Decay Rates ◽  
Boson Mass ◽  
Experimental Accuracy ◽  
The Standard Model ◽  
Component Field ◽  
Field Formalism ◽  
The One ◽  
Supersymmetric Theories

In this paper we report on the newest developments in precision calculations in supersymmetric theories. An important issue related to this topic is the construction of a regularization scheme preserving simultaneously gauge invariance and supersymmetry. In this context, we discuss in detail dimensional reduction in component field formalism as it is currently the preferred framework employed in the literature. Furthermore, we set special emphasis on the application of multi-loop calculations to the analysis of gauge coupling unification, the prediction of the lightest Higgs boson mass, and the computation of the hadronic Higgs production and decay rates in supersymmetric models. Such precise theoretical calculations up to the fourth order in perturbation theory are required in order to cope with the expected experimental accuracy on the one hand and to enable us to distinguish between the predictions of the Standard Model and those of supersymmetric theories on the other hand.

Sign in / Sign up

Export Citation Format

Share Document