BRST SYMMETRY TOWARDS THE GAUSS CONSTRAINT FOR GENERAL RELATIVITY

2008 ◽  
Vol 23 (08) ◽  
pp. 1218-1221
Author(s):  
MICHELE CASTELLANA ◽  
GIOVANNI MONTANI
Keyword(s):  
General Relativity ◽  
Physical State ◽  
Brst Symmetry ◽  
Spin Connection ◽  
Brst Transformation ◽  
Gauge Transformations ◽  
Integral Methods ◽  
Gauge Fixing ◽  
The One ◽  
Brst Invariance

Quantization of systems with constraints can be carried on with several methods. In the Dirac's formulation the classical generators of gauge transformations are required to annihilate physical quantum states to ensure their gauge invariance. Carrying on BRST symmetry it is possible to get a condition on physical states which, differently from the Dirac's method, requires them to be invariant under the BRST transformation. Employing this method for the action of general relativity expressed in terms of the spin connection and tetrad fields with path integral methods, we construct the generator of BRST transformation associated with the underlying local Lorentz symmetry of the theory and write a physical state condition following from BRST invariance. The condition we gain differs form the one obtained within Ashtekar's canonical formulation, showing how we recover the latter only by a suitable choice of the gauge fixing functionals. We finally discuss how it should be possible to obtain all the requested physical state conditions associated with all the underlying gauge symmetries of the classical theory using our approach.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

scholarly journals Radiative corrections in 2 + 1 dimensional supergravity

2018 ◽  
Vol 96 (12) ◽  
pp. 1409-1412 ◽  
Author(s):  
D.G.C. McKeon
Keyword(s):  
Gauge Theory ◽  
Radiative Correction ◽  
Effective Action ◽  
Spin Connection ◽  
Dynamical Generation ◽  
Effective Lagrangian ◽  
Majorana Spinor ◽  
The One ◽  
Brst Invariance ◽  
Topological Mass

Supergravity in 2 + 1 dimensions has a set of first-class constraints that result in two bosonic and one fermionic gauge invariances. When one uses Faddeev–Popov quantization, these gauge invariances result in four fermionic scalar ghosts and two bosonic Majorana spinor ghosts. The BRST invariance of the effective Lagrangian is found. As an example of a radiative correction, we compute the phase of the one-loop effective action in the presence of a background spin connection, and show that it vanishes. This indicates that unlike a spinor coupled to a gauge field in 2 + 1 dimensions, there is no dynamical generation of a topological mass in this model. An additional example of how a BRST invariant effective action can arise in a gauge theory is provided in Appendix B where the BRST effective action for the classical Palatini action in 1 + 1 dimensions is examined.

scholarly journals TOPOLOGICALLY MASSIVE NON-ABELIAN THEORY: SUPERFIELD APPROACH

2011 ◽  
Vol 26 (25) ◽  
pp. 4419-4450 ◽  
Author(s):  
S. KRISHNA ◽  
A. SHUKLA ◽  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Brst Symmetry ◽  
Gauge Transformations ◽  
Abelian Theory ◽  
Gauge Symmetries ◽  
Vector Gauge ◽  
Symmetry Transformations ◽  
Brst Invariance ◽  
Lagrangian Densities

We apply the well-established techniques of geometrical superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism in the context of four (3+1)-dimensional (4D) dynamical non-Abelian 2-form gauge theory by exploiting its inherent "scalar" and "vector" gauge symmetry transformations and derive the corresponding off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetry transformations. Our approach leads to the derivation of three (anti-)BRST invariant Curci–Ferrari (CF)-type restrictions that are found to be responsible for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations. We derive the coupled Lagrangian densities that respect the (anti-)BRST symmetry transformations corresponding to the "vector" gauge transformations. We also capture the (anti-)BRST invariance of the CF-type restrictions and coupled Lagrangian densities within the framework of our superfield approach. We obtain, furthermore, the off-shell nilpotent (anti-)BRST symmetry transformations when the (anti-)BRST symmetry transformations corresponding to the "scalar" and "vector" gauge symmetries are merged together. These off-shell nilpotent "merged" (anti-)BRST symmetry transformations are, however, found to be non-anticommuting in nature.

scholarly journals BV AND BFV FORMULATION OF A GAUGE THEORY OF QUADRATIC LIE ALGEBRAS IN 2D AND A CONSTRUCTION OF W3 TOPOLOGICAL GRAVITY

1994 ◽  
Vol 09 (23) ◽  
pp. 2157-2165 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
Gauge Theory ◽  
Phase Space ◽  
Lie Algebras ◽  
Brst Symmetry ◽  
Field Method ◽  
Continuous Variable ◽  
Two Dimensions ◽  
Gauge Fixing ◽  
Topological Gravity ◽  
The One

The recently proposed generalized field method for solving the master equation of Batalin and Vilkovisky is applied to a gauge theory of quadratic Lie algebras in two dimensions. The charge corresponding to BRST symmetry derived from this solution in terms of the phase space variables by using the Noether procedure, and the one found due to the BFV-method are compared and found to coincide. W3-algebra, formulated in terms of a continuous variable is exploit in the mentioned gauge theory to construct a W3 topological gravity. Moreover, its gauge fixing is briefly discussed.

scholarly journals Gauge fixing invariance and anti-BRST symmetry

2017 ◽  
Vol 14 (11) ◽  
pp. 1750168 ◽  
Author(s):  
Amir Abbass Varshovi
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Gauge Fixing ◽  
Brst Invariance

It is shown that anti-BRST invariance in quantum gauge theories can be considered as the quantized version of the symmetry of classical gauge theories with respect to different gauge fixing mechanisms.

scholarly journals SIGNIFICANCE OF ZERO MODES IN PATH INTEGRAL QUANTIZATION OF SOLITONIC THEORIES WITH BRST INVARIANCE

1996 ◽  
Vol 11 (28) ◽  
pp. 4985-4998
Author(s):  
J.-G. ZHOU ◽  
F. ZIMMERSCHIED ◽  
H. J. W. MÜLLER-KIRSTEN ◽  
J.-Q. LIANG ◽  
D. H. TCHRAKIAN
Keyword(s):  
Path Integral ◽  
Transition Amplitude ◽  
Functional Integral ◽  
Field Equations ◽  
Path Integral Quantization ◽  
Zero Modes ◽  
Loop Approximation ◽  
Gauge Fixing ◽  
The One ◽  
Brst Invariance

The significance of zero modes in the path integral quantization of some solitonic models is investigated. In particular a Skyrme-like theory with topological vortices in 1 + 2 dimensions is studied, and with a BRST-invariant gauge fixing a well-defined transition amplitude is obtained in the one-loop approximation. We also present an alternative method which does not necessitate evoking the time dependence in the functional integral, but is equivalent to the original one in dealing with the quantization in the background of the static classical solution of the nonlinear field equations. The considerations given here are particularly useful in — but also limited to — the one-loop approximation.

scholarly journals Generalization of Faddeev–Popov rules in Yang–Mills theories: N = 3,4 BRST symmetries

2018 ◽  
Vol 33 (03) ◽  
pp. 1850006 ◽  
Author(s):  
Alexander Reshetnyak
Keyword(s):  
Irreducible Representation ◽  
Classical Model ◽  
Brst Symmetry ◽  
Classical Action ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Change Of Variables ◽  
Gauge Fixing ◽  
Quantum Action

The Faddeev–Popov rules for a local and Poincaré-covariant Lagrangian quantization of a gauge theory with gauge group are generalized to the case of an invariance of the respective quantum actions, [Formula: see text], with respect to [Formula: see text]-parametric Abelian SUSY transformations with odd-valued parameters [Formula: see text], [Formula: see text] and generators [Formula: see text]: [Formula: see text], for [Formula: see text], implying the substitution of an [Formula: see text]-plet of ghost fields, [Formula: see text], instead of the parameter, [Formula: see text], of infinitesimal gauge transformations: [Formula: see text]. The total configuration spaces of fields for a quantum theory of the same classical model coincide in the [Formula: see text] and [Formula: see text] symmetric cases. The superspace of [Formula: see text] SUSY irreducible representation includes, in addition to Yang–Mills fields [Formula: see text], [Formula: see text] ghost odd-valued fields [Formula: see text], [Formula: see text] and [Formula: see text] even-valued [Formula: see text] for [Formula: see text], [Formula: see text]. To construct the quantum action, [Formula: see text], by adding to the classical action, [Formula: see text], of an [Formula: see text]-exact gauge-fixing term (with gauge fermion), a gauge-fixing procedure requires [Formula: see text] additional fields, [Formula: see text]: antighost [Formula: see text], [Formula: see text] even-valued [Formula: see text], 3 odd-valued [Formula: see text] and Nakanishi–Lautrup [Formula: see text] fields. The action of [Formula: see text] transformations on new fields as [Formula: see text]-irreducible representation space is realized. These transformations are the [Formula: see text] BRST symmetry transformations for the vacuum functional, [Formula: see text]. The space of all fields [Formula: see text] proves to be the space of an irreducible representation of the fields [Formula: see text] for [Formula: see text]-parametric SUSY transformations, which contains, in addition to [Formula: see text] the [Formula: see text] ghost–antighost, [Formula: see text], even-valued, [Formula: see text], odd-valued [Formula: see text] and [Formula: see text] fields. The quantum action is constructed by adding to [Formula: see text] an [Formula: see text]-exact gauge-fixing term with a gauge boson, [Formula: see text]. The [Formula: see text] SUSY transformations are by [Formula: see text] BRST transformations for the vacuum functional, [Formula: see text]. The procedures are valid for any admissible gauge. The equivalence with [Formula: see text] BRST-invariant quantization method is explicitly found. The finite [Formula: see text] BRST transformations are derived and the Jacobians for a change of variables related to them but with field-dependent parameters in the respective path integral are calculated. They imply the presence of a corresponding modified Ward identity related to a new form of the standard Ward identities and describe the problem of a gauge-dependence. An introduction into diagrammatic Feynman techniques for [Formula: see text] BRST invariant quantum actions for Yang–Mills theory is suggested.

COSET SPACE DIMENSIONAL REDUCTION AND GAUGE FIXING OVER THE SUPERCIRCLE

1989 ◽  
Vol 04 (02) ◽  
pp. 401-409 ◽  
Author(s):  
P. D. JARVIS
Keyword(s):  
Scalar Field ◽  
Dimensional Reduction ◽  
Gauge Fields ◽  
Coset Space ◽  
Gauge Transformations ◽  
Abelian Case ◽  
Gauge Fixing ◽  
Vector Gauge ◽  
Covariant Gauge ◽  
Brst Invariance

The constraints of CSDR are solved for vector gauge fields over a coset space IOSp (1/2, R)/ OSp (1/2, R) including supertranslations (extended BRST transformations) and ordinary translations (rotations on the circle). The gauge-fixing action incorporates standard ghost and multiplier fields (and their modes) but is nonpolynomial in an additional scalar field ϕ and its modes. There is a new "ϕ-BRST" invariance with respect to ϕ dependent gauge transformations, a bosonic counterpart of the usual "ghost-BRST" invariance. In the Abelian case, ϕ can be integrated out, leading to a formalism equivalent to ordinary covariant gauge-fixing.

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