scholarly journals ON THE β-FUNCTION AND CONFORMAL ANOMALY OF NONCOMMUTATIVE QED WITH ADJOINT MATTER FIELDS

2003 ◽  
Vol 18 (15) ◽  
pp. 2591-2607 ◽  
Author(s):  
NÉDA SADOOGHI ◽  
MOJTABA MOHAMMADI
Keyword(s):  
Gauge Theory ◽  
Integral Method ◽  
Degrees Of Freedom ◽  
Adjoint Representation ◽  
Conformal Anomaly ◽  
Loop Order ◽  
Path Integral Method ◽  
Β Function ◽  
The One ◽  
Matter Fields

In the first part of this work, a perturbative analysis up to one-loop order is carried out to determine the one-loop β-function of noncommutative U(1) gauge theory with matter fields in the adjoint representation. In the second part, the conformal anomaly of the same theory is calculated using Fujikawa's path integral method. The value of the one-loop β-function calculated in both methods coincides. As it turns out, noncommutative QED with matter fields in the adjoint representation is asymptotically free for the number of flavor degrees of freedom Nf < 3.

scholarly journals NONCOMMUTATIVE DIPOLE QED

2003 ◽  
Vol 18 (01) ◽  
pp. 97-126 ◽  
Author(s):  
NÉDA SADOOGHI ◽  
MASOUD SOROUSH
Keyword(s):  
Semiclassical Approximation ◽  
Form Factors ◽  
Adjoint Representation ◽  
Four Dimensions ◽  
Path Integral Method ◽  
Β Function ◽  
The One ◽  
Definition Of ◽  
Matter Fields ◽  
Dipole Length

The noncommutative dipole QED is studied in detail for the matter fields in the adjoint representation. The axial anomaly of this theory is calculated in two and four dimensions using various regularization methods. The Ward–Takahashi identity is proved by making use of a nonperturbative path integral method. The one-loop β-function of the theory is calculated explicitly. It turns out that the value of the β-function depends on the direction of the dipole length L, which defines the noncommutativity. Finally using a semiclassical approximation a nonperturbative definition of the form factors is presented and the anomalous magnetic moment of this theory at one-loop order is computed.

Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Mario Di Paola ◽  
Gioacchino Alotta
Keyword(s):  
Path Integral ◽  
Path Integration ◽  
Integral Method ◽  
Degrees Of Freedom ◽  
Kolmogorov Equation ◽  
Integral Methods ◽  
Alternative Approach ◽  
Path Integration Method ◽  
Path Integral Method ◽  
Barrier Problems

Abstract In this paper, the widely known path integral method, derived from the application of the Chapman–Kolmogorov equation, is described in details and discussed with reference to the main results available in literature in several decades of contributions. The most simple application of the method is related to the solution of Fokker–Planck type equations. In this paper, the solution in the presence of normal, α-stable, and Poissonian white noises is first discussed. Then, application to barrier problems, such as first passage problems and vibroimpact problems is described. Further, the extension of the path integral method to problems involving multi-degrees-of-freedom systems is analyzed. Lastly, an alternative approach to the path integration method, that is the Wiener Path integration (WPI), also based on the Chapman–Komogorov equation, is discussed. The main advantages and the drawbacks in using these two methods are deeply analyzed and the main results available in literature are highlighted.

PATH-INTEGRAL DERIVATION OF ONE-PARAMETER DEPENDENT NONMINIMAL ANOMALIES AND EFFECTIVE ACTIONS IN SCHWINGER MODEL AND ITS VARIANTS

1988 ◽  
Vol 03 (02) ◽  
pp. 201-214 ◽  
Author(s):  
S.H. YI ◽  
D.K. PARK ◽  
B.H. CHO
Keyword(s):  
Path Integral ◽  
Integral Method ◽  
Parameter Family ◽  
Schwinger Model ◽  
Physical Role ◽  
Regularization Operator ◽  
Path Integral Method ◽  
The One ◽  
Parameter Dependent

The one-parameter dependent nonminimal anomalies and effective actions are derived by the path-integral method using the one-parameter family of Euclidean regularization operator in Schwinger model with vector, chiral, and chirally asymmetric couplings. We also investigate the factorizability of fermion determinant and the physical role of regularization ambiguity in chiral Schwinger model.

scholarly journals AN EXACT RG FORMULATION OF QUANTUM GAUGE THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 1899-1911 ◽  
Author(s):  
T. R. MORRIS
Keyword(s):  
Gauge Theory ◽  
Flow Equation ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Quantum Gauge Theory ◽  
Supergauge Theory ◽  
Gauge Fixing ◽  
Β Function ◽  
The One ◽  
First Time

A gauge invariant Wilsonian effective action is constructed for pure SU(N) Yang-Mills theory by formulating the corresponding flow equation. Manifestly gauge invariant calculations can be performed i.e. without gauge fixing or ghosts. Regularisation is implemented in a novel way which realises a spontaneously broken SU(N|N) supergauge theory. As an example we sketch the computation of the one-loop β function, performed for the first time without any gauge fixing.

scholarly journals EQUIVALENCE OF THE β-FUNCTION OF THE VARIATIONAL APPROACH TO THAT OF QCD

1998 ◽  
Vol 13 (30) ◽  
pp. 5219-5243 ◽  
Author(s):  
WILLIAM E. BROWN
Keyword(s):  
Gauge Theory ◽  
Coulomb Interaction ◽  
Ground State ◽  
Variational Approach ◽  
Degrees Of Freedom ◽  
Hamiltonian Formalism ◽  
Asymptotic Freedom ◽  
Coupling Constant ◽  
Transverse Gluon ◽  
Β Function

The variational ansatz for the ground state wavefunctional of QCD is found to capture the antiscreening behaviour that contributes the dominant "-4" to the β-function and leads to asymptotic freedom. By considering an SU (N) purely gauge theory in the Hamiltonian formalism and choosing the Coulomb gauge, the origins of all screening and antiscreening contributions in gluon processes are found in terms of the physical degrees of freedom. The overwhelming antiscreening contribution of "-4" is seen to originate in the renormalisation of a Coulomb interaction by a transverse gluon. The lesser screening contribution of " [Formula: see text]" is seen to originate in processes involving transverse gluon interactions. It is thus apparent how the variational ansatz must be developed to capture the full running of the QCD coupling constant.

THE GENERALIZED ANOMALY AND EFFECTIVE ACTION IN THE CHIRAL SCHWINGER MODEL

1987 ◽  
Vol 02 (08) ◽  
pp. 579-584 ◽  
Author(s):  
S. H. YI ◽  
D. K. PARK ◽  
B. H. CHO
Keyword(s):  
Path Integral ◽  
Effective Action ◽  
Integral Method ◽  
Parameter Family ◽  
Schwinger Model ◽  
Regularization Operator ◽  
Path Integral Method ◽  
The One

The one-parameter class of the non-minimal anomaly and effective action are derived by the path integral method using the one-parameter family of the Euclidean regularization operator in the Chiral Schwinger model. We show that the regularization dependence is related to the choice of the chiral operator in the calculation of the non-vanishing Jacobian.

Gauge Interactions

2021 ◽  
pp. 273-286
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Quantum Electrodynamics ◽  
Integral Method ◽  
Equations Of Motion ◽  
Internal Symmetry ◽  
Symmetry Groups ◽  
Yang Mills ◽  
Path Integral Method ◽  
Popov Ghost ◽  
Mills Field ◽  
Matter Fields

The principle of gauge symmetry is introduced as a consequence of the invariance of the equations of motion under local transformations. We apply it to Abelian, as well as non-Abelian, internal symmetry groups. We derive in this way the Lagrangian of quantum electrodynamics and that of Yang–Mills theories. We quantise the latter using the path integral method and show the need for unphysical Faddeev–Popov ghost fields. We exhibit the geometric properties of the theory by formulating it on a discrete space-time lattice. We show that matter fields live on lattice sites and gauge fields on oriented lattice links. The Yang–Mills field strength is related to the curvature in field space.

scholarly journals ONE-LOOP VACUUM ENERGY IN NON-PARALLEL D1-BRANES: A PATH INTEGRAL FORMULATION

2010 ◽  
Vol 25 (08) ◽  
pp. 619-625 ◽  
Author(s):  
A. JAHAN
Keyword(s):  
String Theory ◽  
Path Integral ◽  
Integral Method ◽  
Vacuum Energy ◽  
Bosonic String ◽  
Integral Formulation ◽  
Path Integral Formulation ◽  
Bosonic String Theory ◽  
Path Integral Method ◽  
The One

We derive the one-loop vacuum energy of the bosonic string theory in a system of non-parallel D1-branes using the path integral method.

scholarly journals TRANSVERSE WARD–TAKAHASHI RELATION FOR THE FERMION–BOSON VERTEX TO ONE-LOOP ORDER

2006 ◽  
Vol 21 (12) ◽  
pp. 2541-2551 ◽  
Author(s):  
HAN-XIN HE ◽  
F. C. KHANNA
Keyword(s):  
Perturbation Theory ◽  
Gauge Theory ◽  
Loop Order ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Transverse Part ◽  
Feynman Rules ◽  
Covariant Gauge ◽  
The One ◽  
Massless Fermions

In this paper, the transverse Ward–Takahashi relation for the fermion–boson vertex in momentum space is derived in four-dimensional Abelian gauge theory. We show that, by a formal derivation, the transverse Ward–Takahashi relation to one-loop order is satisfied. We also calculate the transverse Ward–Takahashi relation to one-loop order in an arbitrary covariant gauge in the case of massless fermions and find that the result is exactly the same as we obtain in terms of the one-loop fermion–boson vertex calculated in perturbation theory by using Feynman rules. This provides an approach to determine the transverse part of the vertex.

Sign in / Sign up

Export Citation Format

Share Document