Explicit classical construction of the Faddeev-Popov ghost field

1980 ◽  
Vol 56 (4) ◽  
pp. 396-404 ◽  
Author(s):  
J. Thierry-Mieg
Keyword(s):  
Popov Ghost ◽  
Ghost Field ◽  
Classical Construction

scholarly journals Faddeev-Popov Ghost and BRST Symmetry in Yang-Mills Theory

2020 ◽  
Vol 31 (1) ◽  
pp. 30-34
Author(s):  
Edyharto Yanuwar ◽  
Jusak Sali Kosasih
Keyword(s):  
Gauge Field ◽  
Gauge Transformation ◽  
Brst Symmetry ◽  
Brst Transformation ◽  
Least Action Principle ◽  
Yang Mills ◽  
Least Action ◽  
Gauge Fixing ◽  
Popov Ghost ◽  
Ghost Field

Ghost fields arise from the quantization of the gauge field with constraints (gauge fixing) through the path integral method. By substituting a form of identity, an effective propagator will be obtained from the gauge field with constraints and this is called the Faddeev-Popov method. The Grassmann odd properties of the ghost field cause the gauge transformation parameter to be Grassmann odd, so a BRST transformation is defined. Ghost field emergence with Grassmann odd properties can also be obtained through the least action principle with gauge transformation, and thus the relations between the BRST transformation parameters and the ghost field is obtained.

PERTURBATIVE EXPANSION FOR THE t-J MODEL CONSTRUCTED FROM THE GENERATORS OF THE SUPERSYMMETRIC HUBBARD ALGEBRA

2009 ◽  
Vol 23 (14) ◽  
pp. 3159-3177
Author(s):  
CARLOS E. REPETTO ◽  
OSCAR P. ZANDRON
Keyword(s):  
Perturbative Expansion ◽  
Lagrangian Formalism ◽  
Graded Algebra ◽  
Integral Formalism ◽  
Generating Functional ◽  
First Order ◽  
Effective Lagrangian ◽  
Supersymmetric Version ◽  
Present Formalism ◽  
Ghost Field

By using the Hubbard [Formula: see text]-operators as field variables along with the supersymmetric version of the Faddeev–Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In order to satisfy the Hubbard [Formula: see text]-operator commutation rules satisfying the graded algebra spl(2,1), the number and kind of constraints that must be included in a classical first-order Lagrangian formalism for this model are presented. The model is also analyzed via path-integral formalism, where the correlation-generating functional and the effective Lagrangian are constructed. In this context, the introduction of a proper ghost field is needed to render the model renormalizable. The perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator arising in the present formalism is discussed. As an example, the thermal softening of the magnon frequency is computed.

THE ROLE OF THE GHOST FIELDS IN THE RENORMALIZED t–J LAGRANGIAN MODEL

2009 ◽  
Vol 23 (04) ◽  
pp. 493-519
Author(s):  
O. S. ZANDRON
Keyword(s):  
Thermal Softening ◽  
Lagrangian Model ◽  
Lagrangian Formalism ◽  
Spin Polaron ◽  
Renormalization Procedure ◽  
Ghost Field

The present work treats the role of ghost fields in the renormalization procedure of the Lagrangian perturbative formalism of the t–J model. We show that by introducing proper ghost field variables, the propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator coming from our previous Lagrangian formalism is studied in detail, and it is shown how the thermal softening of the magnon frequency is predicted by the model. The antiferromagnetic case is also analyzed, and the results are confronted with the previous one obtained by means of the spin-polaron theories.

Ghost Field Gauging Used in Electrodynamic Simulation

2004 ◽  
pp. 213-218
Author(s):  
Peter Meuris ◽  
Wim Schoenmaker ◽  
Wim Magnus ◽  
Bert Maleszka
Keyword(s):  
Ghost Field

From BRST symmetry to the Zinn-Justin equation

2019 ◽  
pp. 237-252
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Quadratic Equation ◽  
Local Action ◽  
Local Form ◽  
Abelian Gauge ◽  
Brst Cohomology ◽  
Gauge Fixing ◽  
Non Local ◽  
Popov Ghost

Chapter 14 contains a general discussion of the quantization and renormalization of non–Abelian gauge theories. The quantization necessitates gauge fixing and introduces the Faddeev–Popov determinant. Slavnov–Taylor identities for vertex (one–particle–irreducible (1PI)) functions, the basis of a first proof of renormalizability, follow. The Faddeev–Popov determinant leads to a non–local action. A local form is generated by introducing Faddeev–Popov ghost fields. The new local action has an important new symmetry, the BRST symmetry. However, the explicit realization of the symmetry is not stable under renormalization. By contrast, a quadratic equation that is satisfied by the action and generating functional of 1PI functions, the Zinn–Justin equation, is stable and at the basis of a general proof of the renormalizability of non–Abelian gauge theories. The proof involves some simple elements of BRST cohomology. The renormalized form of BRST symmetry then makes it possible to prove gauge independence and unitarity.

Gauge invariance and gauge fixing

2019 ◽  
pp. 177-194
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Gauge Invariance ◽  
Brst Symmetry ◽  
Parallel Transport ◽  
Abelian Gauge ◽  
The Standard Model ◽  
Gauge Fixing ◽  
Popov Ghost ◽  
Important Notion ◽  
Gribov Copies

Chapter 11 is the first of four chapters that discuss various issues connected with the Standard Model of fundamental interactions at the microscopic scale. It discusses the important notion of gauge invariance, first Abelian and then non–Abelian, the basic geometric structure that generates interactions. It relates it to the concept of parallel transport. Due to gauge invariance, not all components of the gauge field are dynamical and gauge fixing is required (with the problem of Gribov copies in non–Abelian theories). The quantization of non–Abelian gauge theories is briefly discussed, with the introduction of Faddeev–Popov ghost fields and the appearance of BRST symmetry.

scholarly journals Does emergent scenario in Hořava–Lifshitz gravity demand a ghost field?

2020 ◽  
Vol 30 ◽  
pp. 100740
Author(s):  
Akash Bose ◽  
Subenoy Chakraborty
Keyword(s):  
Emergent Scenario ◽  
Ghost Field

scholarly journals Progress in the development of the cutting assemblies’ construction of working machines due to the reduction in power consumption

2019 ◽  
Vol 287 ◽  
pp. 01023
Author(s):  
Andrzej Bochat ◽  
Marcin Zastempowski
Keyword(s):  
Power Consumption ◽  
Patent Protection ◽  
Life Sciences ◽  
Experimental Tests ◽  
Lower Power ◽  
University Of Technology ◽  
New Construction ◽  
The University ◽  
Classical Construction

New construction of the cutting assembly developed at the Institute of Mechatronics and Working Machines of the University of Technology and Life Sciences in Bydgoszcz. That new construction is covered by the patent protection. The conducted and presented results of the experimental tests have shown, that it is characterised by lower power consumption as compared to the classical construction, which is commonly used in working machines.

scholarly journals A CLASS OF QUASITRIANGULAR GROUP-COGRADED MULTIPLIER HOPF ALGEBRAS

2018 ◽  
Vol 62 (1) ◽  
pp. 43-57
Author(s):  
TAO YANG ◽  
XUAN ZHOU ◽  
HAIXING ZHU
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Finite Dimensional ◽  
Special Cases ◽  
Multiplier Hopf Algebras ◽  
Multiplier Hopf Algebra ◽  
Classical Construction

AbstractFor a multiplier Hopf algebra pairing 〈A,B〉, we construct a class of group-cograded multiplier Hopf algebras D(A,B), generalizing the classical construction of finite dimensional Hopf algebras introduced by Panaite and Staic Mihai [Isr. J. Math. 158 (2007), 349–365]. Furthermore, if the multiplier Hopf algebra pairing admits a canonical multiplier in M(B⊗A) we show the existence of quasitriangular structure on D(A,B). As an application, some special cases and examples are provided.

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