<i>BF</i>actions for the Husain-Kuchař model

Villaseñor, Eduardo J. S.

doi:10.1103/physrevd.63.084021

Cited by 17 publications

(30 citation statements)

References 22 publications

(2 reference statements)

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“…As (7) are only necessary conditions we know that every solution to the field Eqs. (4), (5) can be parametrized with the help of (10), (11), and (13) but (5) Though this last equation may look as complicated as the original field equations it is, in a sense that we make precise below, a simple algebraic equation that can be easily handled. Anyway some simplifications are already evident because the arbitrary objects Λ q and Θ p do not appear in it.…”

Section: Solutions Tomentioning

confidence: 99%

“…We hope that interesting theories may appear in this search hopefully leading to a new understanding of Yang-Mills and other theories such as general relativity. For example, as shown in [11], the HusainKuchař model can be described by coupling two BF Lagrangians with a quadratic part involving cross-terms with 1-and 2-forms. An open and interesting question is if one can find a quadratic action with consistent deformations that include the Husain-Kuchař model in its BF description.…”

Section: Conclusion and Commentsmentioning

confidence: 99%

See 1 more Smart Citation

Quadratic s-form field actions with semi-bounded energy

G¹,

Villaseñor²

2001

Nuclear Physics B

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We give in this paper a partial classification of the consistent quadratic gauge actions that can be written in terms of s-form fields. This provides a starting point to study the uniqueness of the YangMills action as a deformation of Maxwell-like theories. We also show that it is impossible to write kinetic 1-form terms that can be consistently added to other 1-form actions such as tetrad gravity in four space-time dimensions even in the presence of a Minkowskian metric background.  2001 Elsevier Science B.V. All rights reserved.

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Section: Solutions Tomentioning

confidence: 99%

Section: Conclusion and Commentsmentioning

confidence: 99%

Quadratic s-form field actions with semi-bounded energy

G¹,

Villaseñor²

2001

Nuclear Physics B

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“…Some interesting features follow from the gauge orbits. There exist a vector density, namely n" = n"/ê [32], where ê represents an auxiliary foliation defined by a scalar function t as ê = ñ"dat. The fiow lines of n" define a privileged reference frame through ñ" = ^e"'^'^''e/jft:e¿e¡^e^.…”

Section: A Escalante and J Berramentioning

confidence: 99%

A Pure Dirac's Method for Husain–kuchar Theory

Escalante

Berra

2013

Int. J. Geom. Methods Mod. Phys.

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A pure Dirac's canonical analysis, defined in the full phase space for the Husain-Kuchar (HK) model is discussed in detail. This approach allows us to determine the extended action, the extended Hamiltonian, the complete constraint algebra and the gauge transformations for all variables that occur in the action principle. The complete set of constraints defined on the full phase space allow us to calculate the Dirac algebra structure of the theory and a local weighted measure for the path integral quantization method. Finally, we discuss briefly the necessary mathematical structure to perform the canonical quantization program within the framework of the loop quantum gravity approach.

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“…Although this is a consistent picture for Abelian 2-form, it is problematic for its non-Abelian counterpart owing to the difficulties in defining surface-ordered exponentials, which appear when a 2-form is coupled to the world surface of a string [1]. Nevertheless, non-Abelian 2-forms have appeared in the context of nonlinear sigma model [3,4], in the loop space formulations of Yang-Mills theory [5,6] and gravity as a gauge theory [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…Just as 1-form (4-vector potential) couples to charged point particle, p-forms couple to higher-dimensional objects, such as strings, membranes, etc. A generalisation of the 1-form gauge theories to p-form gauge theories has been a long discussed problem in theoretical physics [1,2,3,4,5,6,7,8]. Since a 2-form couples to surface, it is natural to think of it as a gauge field for (open or closed) strings.…”

Section: Introductionmentioning

confidence: 99%

Superunitary operator and BRST transformations of a non-Abelian two-form

Shukla

Kumar

2017

EPL

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Using superspace unitary operator formalism, we derive various (anti-)BRST symmetry transformations explicitly for the non-Abelian 2-form gauge theories. We introduce a new Lagrangian with a coupling of matter fields not only with 1-from background field but also with a 2-form field. Moreover, the two gauge fields couple mutually as well. A new covariant derivative involving the 2-form gauge field is introduced. We also put forth a conjecture to generalise this idea to any p-form gauge theory.1 BRST is the abbreviation of the names of its founders, viz. Becchi, Rouet, Stora and Tyutin.1-form gauge and corresponding ghost and anti-ghost fields can be derived exploiting the so-called horizontality condition (HC). This condition is basically equating the supercurvature 2-form defined on (D + 2)-dimensional superspace to the ordinary curvature 2-form defined on the D-dimensional Minkowski spacetime. To include interacting systems where the gauge field couples to matter fields, this formalism has been consistently generalised to obtain the (anti-)BRST transformations for the matter fields as well, which is called the augmented superfield formalism [14,15,16,17], where, in addition to the horizontality condition, some gauge-invariant restrictions (GIRs) are also exploited. The mapping of ordinary fields on the Minkowski spacetime to the superfields on the superspace can also be carried out via a superspace unitary operator [9,10,11,18,19], or superunitary operator for short. The superunitary operator upgrades the fields and gauge connections to their superspace-counterparts in the same fashion as the unitary gauge operator maps the fields and gauge connections to their gauge-transformed counterparts. This superunitary operator is determined from the horizontality condition and gauge-invariant restrictions.Our goal in this paper is to deduce the (anti-)BRST transformation for the Kalb-Raymond B-field 2-form, following the superunitary operator approach. For that we consider the interacting theory where the matter fields interact with the 1-form as well as the 2-form gauge field. The two gauge fields, too, interact with each-other through the well known B ∧ F interaction term. Our focus would be to find out the (anti-)BRST symmetry transformations for the various fields and to obtain the corresponding covariant derivatives for both the gauge fields, i.e. for 1-form and 2-form gauge connections.We start with a brief review, in Sec. 2, of 1-form gauge theories, (anti-)BRST transformations and the idea of superfields and superunitary operator. Exploiting the horizontality condition and the gauge-invariant restrictions, the superunitary operator is obtained which upgrades the fields to their superspace-counterparts. The expansion of the superfields in terms of the ordinary fields yields the (anti-)BRST transformations of that field. We have incorporated the matter fields also and both the Abelian and non-Abelian cases are discussed. In Sec. 3, we extend the superunitary operator formalism to 2-form non-Abelian gauge theories...

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BFactions for the Husain-Kuchař model

Cited by 17 publications

References 22 publications

Quadratic s-form field actions with semi-bounded energy

Quadratic s-form field actions with semi-bounded energy

A Pure Dirac's Method for Husain–kuchar Theory

Superunitary operator and BRST transformations of a non-Abelian two-form

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