scholarly journals CONNECTING GREEN FUNCTIONS IN AN ARBITRARY PAIR OF GAUGES AND AN APPLICATION TO PLANAR GAUGES

2001 ◽  
Vol 16 (31) ◽  
pp. 5043-5059 ◽  
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Green Function ◽  
Finite Field ◽  
Path Integrals ◽  
Green Functions ◽  
Expectation Values ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Field Dependent ◽  
Gauge Connection ◽  
Arbitrary Gauge

We establish a finite field-dependent BRS transformation that connects the Yang–Mills path integrals with the Faddeev–Popov effective actions for an arbitrary pair of gauges F and F'. We establish a result that relates an arbitrary Green function (either a primary one or that of an operator) in an arbitrary gauge F' to those in gauge F that are compatible to the ones in gauge Fby its construction. This is because the construction preserves expectation values of gauge-invariant observables. We establish parallel results also for the planar gauge-Lorentz gauge connection.

NON-PERTURBAITVE GREEN FUNCTIONS IN QUANTUM GAUGE THEORIES

1991 ◽  
Vol 06 (10) ◽  
pp. 909-921 ◽  
Author(s):  
S.V. SHABANOV
Keyword(s):  
Configuration Space ◽  
Gauge Theories ◽  
Gauge Condition ◽  
Green Functions ◽  
Spatial Infinity ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Global Gauge

Non-perturbative Green functions for gauge invariant variables are considered. The Green functions are found to be modified as compared with the usual ones in a definite gauge because of a physical configuration space (PCS) reduction. In the Yang-Mills theory with fermions, this phenomenon follows from the Singer theorem about the absence of a global gauge condition for the fields tending to zero at spatial infinity.

GREEN'S FUNCTIONS IN AXIAL- AND LORENTZ-TYPE GAUGES AND BRS TRANSFORMATIONS

2000 ◽  
Vol 15 (04) ◽  
pp. 245-252 ◽  
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Finite Field ◽  
Green's Functions ◽  
Green’S Functions ◽  
Green Functions ◽  
Field Dependent

A formula that relates the Green functions in axial-type gauges and Lorentz type gauges is established in a simpler manner. This result sheds further light on some of our earlier results using field transformations (a finite field-dependent BRS transformation) that relates these gauges. An indirect way of looking at these field transformations is presented. An example of such results is given and applications are indicated.

scholarly journals On the BRST and finite field-dependent BRST of a model where vector and axial vector interactions get mixed up with different weights

2016 ◽  
Vol 31 (32) ◽  
pp. 1650171 ◽  
Author(s):  
Safia Yasmin ◽  
Anisur Rahaman
Keyword(s):  
Gauge Symmetry ◽  
Finite Field ◽  
Axial Vector ◽  
Dimensional Model ◽  
Brst Transformation ◽  
Gauge Invariant ◽  
Local Gauge Symmetry ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Lower Dimensional

The generalized version of a lower dimensional model where vector and axial vector interactions get mixed up with different weights is considered. The bosonized version of which does not possess the local gauge symmetry. An attempt has been made here to construct the BRST invariant reformulation of this model using Batalin–Fradlin and Vilkovisky formalism. It is found that the extra field needed to make it gauge invariant turns into Wess–Zumino scalar with appropriate choice of gauge fixing. An application of finite field-dependent BRST and anti-BRST transformation is also made here in order to show the transmutation between the BRST symmetric and the usual nonsymmetric version of the model.

scholarly journals n-Point Functions of 2d Yang–Mills Theories on Riemann Surfaces

1997 ◽  
Vol 12 (11) ◽  
pp. 1959-1965 ◽  
Author(s):  
M. Alimohammadi ◽  
M. Khorrami
Keyword(s):  
Field Theory ◽  
Riemann Surfaces ◽  
Integral Method ◽  
Free Field ◽  
Green Functions ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Gauge Groups ◽  
Yang Mills ◽  
Path Integral Method

Using the simple path integral method we calculate the n-point functions of field strength of Yang–Mills theories on arbitrary two-dimensional Riemann surfaces. In U(1) case we show that the correlators consist of two parts, a free and an x-independent part. In the case of non-Abelian semisimple compact gauge groups we find the nongauge-invariant correlators in Schwinger–Fock gauge and show that it is also divided to a free and an almost x-independent part. We also find the gauge-invariant Green functions and show that they correspond to a free field theory.

scholarly journals WILSON LOOP AND THE TREATMENT OF AXIAL GAUGE POLES

2000 ◽  
Vol 15 (08) ◽  
pp. 541-546 ◽  
Author(s):  
SATISH. D. JOGLEKAR ◽  
A. MISRA
Keyword(s):  
Finite Field ◽  
Wilson Loop ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Gauge Invariant ◽  
Expectation Value ◽  
Direct Verification ◽  
Axial Gauge ◽  
Field Dependent ◽  
New Treatment

We consider the question of gauge invariance of the Wilson loop in the light of a new treatment of axial gauge propagator proposed recently based on a finite field-dependent BRS (FFBRS) transformation. We remark that under the FFBRS transformation as the vacuum expectation value of a gauge-invariant observable remains unchanged, our prescription automatically satisfies the Wilson loop criterion. Furthermore, we give an argument for direct verification of the invariance of Wilson loop to O(g4) using the earlier work by Cheng and Tsai. We also note that our prescription preserves the thermal Wilson loop to O(g2).

scholarly journals Gauge invariant target space entanglement in D-brane holography

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sumit R. Das ◽  
Anurag Kaushal ◽  
Sinong Liu ◽  
Gautam Mandal ◽  
Sandip P. Trivedi
Keyword(s):  
Path Integrals ◽  
Region Of Interest ◽  
Low Energy ◽  
Target Space ◽  
Space Region ◽  
Bulk Region ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Invariant Characterization

Abstract It has been suggested in arXiv:2004.00613 that in Dp-brane holography, entanglement in the target space of the D-brane Yang-Mills theory provides a precise notion of bulk entanglement in the gravity dual. We expand on this discussion by providing a gauge invariant characterization of operator sub-algebras corresponding to such entanglement. This is achieved by finding a projection operator which imposes a constraint characterizing the target space region of interest. By considering probe branes in the Coloumb branch we provide motivation for why the operator sub-algebras we consider are appropriate for describing a class of measurements carried out with low-energy probes in the corresponding bulk region of interest. We derive expressions for the corresponding Renyi entropies in terms of path integrals which can be directly used in numerical calculations.

scholarly journals Finite BRST–anti-BRST transformations in generalized Hamiltonian formalism

2014 ◽  
Vol 29 (27) ◽  
pp. 1450159 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Dynamical Systems ◽  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Lagrangian Formalism ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Field Dependent ◽  
Gauge Fixing ◽  
Constrained Dynamical Systems

We introduce the notion of finite BRST–anti-BRST transformations for constrained dynamical systems in the generalized Hamiltonian formalism, both global and field-dependent, with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of variables in the path integral. It turns out that the finite transformations are quadratic in their parameters. Exactly as in the case of finite field-dependent BRST–anti-BRST transformations for the Yang–Mills vacuum functional in the Lagrangian formalism examined in our previous paper [arXiv:1405.0790 [hep-th]], special field-dependent BRST–anti-BRST transformations with functionally-dependent parameters λa= ∫ dt(saΛ), generated by a finite even-valued function Λ(t) and by the anticommuting generators saof BRST–anti-BRST transformations, amount to a precise change of the gauge-fixing function for arbitrary constrained dynamical systems. This proves the independence of the vacuum functional under such transformations. We derive a new form of the Ward identities, depending on the parameters λaand study the problem of gauge dependence. We present the form of transformation parameters which generates a change of the gauge in the Hamiltonian path integral, evaluate it explicitly for connecting two arbitrary Rξ-like gauges in the Yang–Mills theory and establish, after integration over momenta, a coincidence with the Lagrangian path integral [arXiv:1405.0790 [hep-th]], which justifies the unitarity of the S-matrix in the Lagrangian approach.

scholarly journals Study of the gauge invariant, nonlocal mass operatorTr∫d4xFμν(D2)−1Fμνin Yang-Mills theories

2005 ◽  
Vol 72 (10) ◽  
Author(s):  
M. A. L. Capri ◽  
D. Dudal ◽  
J. A. Gracey ◽  
V. E. R. Lemes ◽  
R. F. Sobreiro ◽  
...  
Keyword(s):  
Gauge Invariant ◽  
Yang Mills

On modified Green functions in exterior problems for the Helmholtz equation

1982 ◽  
Vol 383 (1785) ◽  
pp. 313-332 ◽  
Keyword(s):  
Integral Equation ◽  
Green Function ◽  
Helmholtz Equation ◽  
Least Squares ◽  
Present Note ◽  
Boundary Integral ◽  
Green Functions ◽  
Exterior Problems ◽  
The Green Function ◽  
Definition Of

The question of non-uniqueness in boundary integral equation formu­lations of exterior problems for the Helmholtz equation has recently been resolved with the use of additional radiating multipoles in the definition of the Green function. The present note shows how this modification may be included in a rigorous formalism and presents an explicit choice of co­efficients of the added terms that is optimal in the sense of minimizing the least-squares difference between the modified and exact Green functions.

Green function formulation of the Dirac field in curved space

1966 ◽  
Vol 294 (1439) ◽  
pp. 437-448 ◽  
Keyword(s):  
Green Function ◽  
Dirac Field ◽  
Green Functions ◽  
Field Equations ◽  
Curved Space ◽  
Particle Field ◽  
Function Formulation ◽  
Essential Idea ◽  
Mass Field

A Green function formulation of the Dirac field in curved space is considered in the cases where the mass is constant and where it is regarded as a direct particle field in the manner of Hoyle & Narlikar (1964 c ). This description is equivalent to, and in some ways more satisfactory than, that given in terms of a suitable Lagrangian, in which the Dirac or the mass field is regarded as independent of the geometry. The essential idea is to define the Dirac or the mass field in terms of certain Green functions and sources so that the field equations are satisfied identically, and then to obtain the contribution of these fields to the metric field equations from the variation of a suitable action that is defined in terms of the Green functions and sources.

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