BRST and Anti-BRST Symmetry in Topological BF Theories

1997 ◽  
Vol 12 (18) ◽  
pp. 3153-3170 ◽  
Author(s):  
M. Tahiri
Keyword(s):  
Brst Symmetry ◽  
Point Of View ◽  
Ghost Number ◽  
Time Dimension ◽  
Direct Construction ◽  
Superspace Formalism ◽  
Structure Equations ◽  
Quantum Action ◽  
Full Quantum ◽  
Invariant Quantum

We realize the quantization of arbitrary-dimensional non-Abelian BF theories from the point of view of both the BRST symmetry and anti-BRST symmetry. The method relies on the possibility of enlarging the system of fields occurring in such theories by auxiliary fields introduced geometrically in terms of a superspace formalism. The off-shell nilpotency of the BRST and anti-BRST transformations of these fields is automatically guaranteed, thanks to the structure equations and the Bianchi identities. From this follows a direct construction of the BRST invariant full quantum action which leads, after the elimination of the auxiliary fields, to the same quantum action obtained in the context of the Batalin–Vilkovisky formalism. We also discuss how the constructed BRST invariant quantum action is anti-BRST invariant. In addition, we show that the non-Abelian BF theory in any space–time dimension possesses a vector supersymmetry of ghost number +1.

scholarly journals AN ALTERNATIVE CONSTRUCTION OF THE QUANTUM ACTION FOR SUPERGRAVITY

2000 ◽  
Vol 15 (20) ◽  
pp. 1307-1320 ◽  
Author(s):  
N. DJEGHLOUL ◽  
M. TAHIRI
Keyword(s):  
Classical Action ◽  
Invariant Extension ◽  
Alternative Construction ◽  
Simple Supergravity ◽  
Quantum Action ◽  
Full Quantum ◽  
Invariant Quantum

We develop a method to derive the on-shell invariant quantum action of the simple supergravity in such a way that the quartic ghost interactions term is explicity determined. First, we reinvestigate the simple supergravity in terms of a principal superfiber bundle. This gives rise to the closed geometrical BRST algebra. Therefore we determine the open BRST algebra, which realizes the invariance of the classical action. Then, given a prescription to build the full quantum action, we obtain the quantum BRST algebra. Together with the constructed quantum action this allows us to recover the auxiliary fields and the invariant extension of the classical action.

QUANTUM CLOSED STRINGS FROM MINIMAL AREA

1990 ◽  
Vol 05 (32) ◽  
pp. 2753-2762 ◽  
Author(s):  
BARTON ZWIEBACH
Keyword(s):  
Exact Solution ◽  
Quantum Theory ◽  
String Theory ◽  
Master Equation ◽  
Closed String ◽  
Feynman Rules ◽  
Higher Genus ◽  
Quantum Action ◽  
Full Quantum ◽  
Minimal Area

Canonical and factorizable off-shell amplitudes for covariant closed string theory can be obtained from string diagrams of minimal area. Evidence is given that all higher genus minimal area string diagrams can be built using vertices and propagators, implying that the off-shell amplitudes arise from the Feynman rules of a full quantum theory of closed strings. The quantum action gives an exact solution of the full master equation of Batalin and Vilkoviski.

scholarly journals Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

2014 ◽  
Vol 92 (9) ◽  
pp. 1033-1042 ◽  
Author(s):  
S. Gupta ◽  
R. Kumar ◽  
R.P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Point Of View ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

In the available literature, only the Becchi–Rouet–Stora–Tyutin (BRST) symmetries are known for the Jackiw–Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent [Formula: see text] and absolutely anticommuting (sbsab + sabsb = 0) (anti-)BRST transformations s(a)b corresponding to the usual Yang–Mills gauge transformations of this model by exploiting the “augmented” superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang–Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci–Ferrari restriction, which plays a key role in the proof of absolute anticommutativity of s(a)b. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field ρ from our superfield formalism, which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and (or) absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.

scholarly journals Field-dependent BRST–anti-BRST Lagrangian transformations

2015 ◽  
Vol 30 (04n05) ◽  
pp. 1550021 ◽  
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Symmetry Breaking ◽  
Ward Identity ◽  
Brst Symmetry ◽  
Lagrangian Formalism ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Change Of Variables ◽  
Field Dependent ◽  
Renormalization Group Approach ◽  
Quantum Action

We continue our study of finite BRST–anti-BRST transformations for general gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790 [hep-th] and arXiv:1406.0179 [hep-th]], with a doublet λa, a = 1, 2, of anticommuting Grassmann parameters, and prove the correctness of the explicit Jacobian in the partition function announced in [arXiv:1406.0179 [hep-th]], which corresponds to a change of variables with functionally dependent parameters λa = UaΛ induced by a finite Bosonic functional Λ(ϕ, π, λ) and by the anticommuting generators Ua of BRST–anti-BRST transformations in the space of fields ϕ and auxiliary variables πa, λ. We obtain a Ward identity depending on the field-dependent parameters λa and study the problem of gauge dependence, including the case of Yang–Mills theories. We examine a formulation with BRST–anti-BRST symmetry breaking terms, additively introduced into the quantum action constructed by the Sp(2)-covariant Lagrangian rules, obtain the Ward identity and investigate the gauge independence of the corresponding generating functional of Green's functions. A formulation with BRST symmetry breaking terms is developed. It is argued that the gauge independence of the above generating functionals is fulfilled in the BRST and BRST–anti-BRST settings. These concepts are applied to the average effective action in Yang–Mills theories within the functional renormalization group approach.

scholarly journals GAUGE MODELS IN MODIFIED TRIPLECTIC QUANTIZATION

2001 ◽  
Vol 16 (26) ◽  
pp. 4297-4319 ◽  
Author(s):  
B. GEYER ◽  
P. M. LAVROV ◽  
P. YU. MOSHIN
Keyword(s):  
2D Gravity ◽  
Brst Symmetry ◽  
Antisymmetric Tensor ◽  
Explicit Solutions ◽  
Tensor Fields ◽  
Gauge Models ◽  
Gauge Fixing ◽  
Quantum Action

The modified triplectic quantization is applied to several well-known gauge models: the Freedman–Townsend model of non-Abelian antisymmetric tensor fields, W2 gravity, and 2D gravity with dynamical torsion. For these models we obtain explicit solutions of those generating equations that determine the quantum action and the gauge-fixing functional. Using these solutions, we construct the vacuum functional, determine the Sp(2)-invariant effective actions and obtain the corresponding transformations of extended BRST symmetry.

scholarly journals Superconformal geometries and local twistors

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
P. S. Howe ◽  
U. Lindström
Keyword(s):  
Point Of View ◽  
Minimal Point ◽  
Conformal Supergravity ◽  
Dimension Zero ◽  
New Class ◽  
Superspace Formalism ◽  
Alternative Setting ◽  
The Subject ◽  
Superconformal Theories ◽  
Dimension One

Abstract Superconformal geometries in spacetime dimensions D = 3, 4, 5 and 6 are discussed in terms of local supertwistor bundles over standard superspace. These natually admit superconformal connections as matrix-valued one-forms. In order to make contact with the standard superspace formalism it is shown that one can always choose gauges in which the scale parts of the connection and curvature vanish, in which case the conformal and S-supersymmetry transformations become subsumed into super-Weyl transformations. The number of component fields can be reduced to those of the minimal off-shell conformal supergravity multiplets by imposing constraints which in most cases simply consists of taking the even covariant torsion two-form to vanish. This must be supplemented by further dimension-one constraints for the maximal cases in D = 3, 4. The subject is also discussed from a minimal point of view in which only the dimension-zero torsion is introduced. Finally, we introduce a new class of supermanifolds, local super Grassmannians, which provide an alternative setting for superconformal theories.

Modelling Fundamental Legal Change: The Paradox of Context and the Context of Paradox

2015 ◽  
Vol 28 (1) ◽  
pp. 77-96
Author(s):  
Fabien Gélinas
Keyword(s):  
Legal Reasoning ◽  
Point Of View ◽  
Constitutional Change ◽  
Legal Change ◽  
Time Dimension ◽  
Starting Point ◽  
Nuanced Understanding ◽  
The Relationship ◽  
Self Reference

The author takes the paradox of omnipotence faced by lawyers in the context of constitutional change as a starting point to explore the relationship between formal law, logic, and the “pragmatics” that inform legal reasoning. Self-reference in constitutions appears problematic because it has no representation in basic, first-order logic. But self-reference in the context of legal change effectively represents a time dimension that is essential to the practice of law. The dissolution of the paradox is then used to illuminate the relationship between formal law and the context in which it is embedded. The author concludes with a nuanced understanding of law as a semi-open system in which judges play the key role of translating fundamental constitutional change into the law’s “internal” point of view.

UNCONSTRAINED SUPERSPACE FORMALISM OF TOPOLOGICAL 2-D GRAVITY

1995 ◽  
Vol 10 (26) ◽  
pp. 1949-1958 ◽  
Author(s):  
M. TAHIRI
Keyword(s):  
Exact Quantum ◽  
Superspace Formalism ◽  
Quantum Action ◽  
Natural Way

An unconstrained superconnection formalism is used to derive in a natural way the fields and their BRST transformations in topological 2-D gravity. Anti-BRST transformations of the fields are also obtained. We also show how the usual BRST exact quantum action is anti-BRST exact.

scholarly journals Gravitational Dispersion Forces and Gravity Quantization

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 40
Author(s):  
Fabrizio Pinto
Keyword(s):  
Gravitational Field ◽  
Quantum Electrodynamics ◽  
Casimir Effect ◽  
Critical Role ◽  
Evolutionary Process ◽  
Point Of View ◽  
Dispersion Forces ◽  
Semiclassical Theory ◽  
Mixed Potentials ◽  
Full Quantum

The parallel development of the theories of electrodynamical and gravitational dispersion forces reveals important differences. The former arose earlier than the formulation of quantum electrodynamics so that expressions for the unretarded, van der Waals forces were obtained by treating the field as classical. Even after the derivation of quantum electrodynamics, semiclassical considerations continued to play a critical role in the interpretation of the full results, including in the retarded regime. On the other hand, recent predictions about the existence of gravitational dispersion forces were obtained without any consideration that the gravitational field might be fundamentally classical. This is an interesting contrast, as several semiclassical theories of electrodynamical dispersion forces exist although the electromagnetic field is well known to be quantized, whereas no semiclassical theory of gravitational dispersion forces was ever developed although a full quantum theory of gravity is lacking. In the first part of this paper, we explore this evolutionary process from a historical point of view, stressing that the existence of a Casimir effect is insufficient to demonstrate that a field is quantized. In the second part of the paper, we show that the recently published results about gravitational dispersion forces can be obtained without quantizing the gravitational field. This is done first in the unretarded regime by means of Margenau’s treatment of multipole dispersion forces, also obtaining mixed potentials. These results are extended to the retarded regime by generalizing to the gravitational field the approach originally proposed by McLachlan. The paper closes with a discussion of experimental challenges and philosophical implications connected to gravitational dispersion forces.

Conclusion

2017 ◽  
Author(s):  
Mara Marin
Keyword(s):  
Social Relations ◽  
Social World ◽  
Point Of View ◽  
Individual Responsibility ◽  
Social Injustice ◽  
Time Dimension ◽  
Transformative Potential ◽  
Social Structural ◽  
Lack Of Control ◽  
Structural Point

The conclusion reminds the reader of the significance of taking a social structural point of view to the issue of individual responsibility for social injustice. It underscores the advantages of the notion of commitment for making this point of view intuitively available. It points to the fact that calls for justice are calls for social change, which requires change of material structures and of interlocking structures of meaning. It reiterates the transformative potential of open-ended action, action that embraces its lack of control, invites the responses of others, and has a time dimension. It discusses the relevance of the book’s claim that the oppressive character of social relations is intrinsically connected to their social character. It suggests that this claim can be interpreted pessimistically, as showing that social relations always contain the possibility of oppression, or optimistically, as showing that the transformation of our social world is within our power.

Sign in / Sign up

Export Citation Format

Share Document