scholarly journals WIGNER'S LITTLE GROUP AND BRST COHOMOLOGY FOR ONE-FORM ABELIAN GAUGE THEORY

2004 ◽  
Vol 19 (16) ◽  
pp. 2721-2737 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Decisive Role ◽  
Decomposition Theorem ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Brst Cohomology ◽  
The Relationship ◽  
Translation Subgroup

We discuss the (dual-)gauge transformations for the gauge-fixed Lagrangian density and establish their intimate connection with the translation subgroup T(2) of Wigner's little group for the free one-form Abelian gauge theory in four (3+1)-dimensions (4D) of space–time. Though the relationship between the usual gauge transformation for the Abelian massless gauge field and T(2) subgroup of the little group is quite well known, such a connection between the dual-gauge transformation and the little group is a new observation. The above connections are further elaborated and demonstrated in the framework of Becchi–Rouet–Stora–Tyutin (BRST) cohomology defined in the quantum Hilbert space of states where the Hodge decomposition theorem (HDT) plays a very decisive role.

scholarly journals TOPOLOGICAL FEATURES IN NON-ABELIAN GAUGE THEORY

1999 ◽  
Vol 14 (28) ◽  
pp. 1937-1949 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Decomposition Theorem ◽  
Laplacian Operator ◽  
Two Dimensional ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Topological Features ◽  
Brst Cohomology ◽  
Topological Field

We discuss the BRST cohomology and exhibit a connection between the Hodge decomposition theorem and the topological properties of a two-dimensional free non-Abelian gauge theory (having no interaction with matter fields). The topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. We obtain two sets of topological invariants with respect to BRST and co-BRST charges on the two-dimensional compact manifold and show that the Lagrangian density of the theory can be expressed as the sum of terms that are BRST and co-BRST invariants. Thus, this theory captures together some of the salient features of both Witten and Schwarz type of topological field theories.

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 COUPLINGS BETWEEN A COLLECTION OF BF MODELS AND A SET OF THREE-FORM GAUGE FIELDS

2006 ◽  
Vol 21 (31) ◽  
pp. 6477-6490 ◽  
Author(s):  
CONSTANTIN BIZDADEA ◽  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
Gauge Theory ◽  
Master Equation ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Free Theory ◽  
Lagrangian Action ◽  
Deformation Procedure

Consistent interactions that can be added to a free, Abelian gauge theory comprising a collection of BF models and a set of three-form gauge fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smooth, local, PT invariant, Lorentz covariant, and Poincaré invariant interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra.

CHIRALITY IN ELECTRODYNAMICS

1999 ◽  
Vol 14 (32) ◽  
pp. 5121-5135 ◽  
Author(s):  
G. C. MARQUES ◽  
D. SPEHLER
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Gauge Invariance ◽  
Spinor Field ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Left Right Asymmetry

We show that a not necessarily totally symmetric Bargman–Wigner second rank spinor field is able to accommodate a left–right symmetric U (1)L⊗ U (1)R Abelian gauge theory. We show that some features of the standard QED, such as vectorial gauge invariance, invariance under gauge transformation of the second kind, and the nonexistence of monopoles, follow from imposing left–right asymmetry on the level of self-interaction of the spinorial constituents.

scholarly journals TWO-DIMENSIONAL INTERACTIONS BETWEEN A BF-TYPE THEORY AND A COLLECTION OF VECTOR FIELDS

2004 ◽  
Vol 19 (24) ◽  
pp. 4101-4125 ◽  
Author(s):  
E. M. CIOROIANU ◽  
S. C. SĂRARU
Keyword(s):  
Gauge Theory ◽  
Type Theory ◽  
Special Class ◽  
Vector Fields ◽  
Two Dimensional ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Lagrangian Action ◽  
Deformation Procedure

Consistent interactions that can be added to a two-dimensional, free Abelian gauge theory comprising a special class of BF-type models and a collection of vector fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. The deformation procedure modifies the Lagrangian action, the gauge transformations, as well as the accompanying algebra of the interacting model.

scholarly journals GAUGE TRANSFORMATIONS, BRST COHOMOLOGY AND WIGNER'S LITTLE GROUP

2004 ◽  
Vol 19 (32) ◽  
pp. 5663-5692 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Internal Symmetry ◽  
Transformation Groups ◽  
Polarization Tensor ◽  
Gauge Transformations ◽  
Brst Cohomology ◽  
Lagrangian Densities ◽  
Translation Subgroup

We discuss the (dual-)gauge transformations and BRST cohomology for the two (1+1)-dimensional (2D) free Abelian one-form and four (3+1)-dimensional (4D) free Abelian two-form gauge theories by exploiting the (co-)BRST symmetries (and their corresponding generators) for the Lagrangian densities of these theories. For the 4D free two-form gauge theory, we show that the changes on the antisymmetric polarization tensor eμν(k) due to (i) the (dual-)gauge transformations corresponding to the internal symmetry group, and (ii) the translation subgroup T(2) of the Wigner's little group, are connected with each other for the specific relationships among the parameters of these transformation groups. In the language of BRST cohomology defined with respect to the conserved and nilpotent (co-)BRST charges, the (dual-)gauge transformed states turn out to be the sum of the original state and the (co-)BRST exact states. We comment on (i) the quasitopological nature of the 4D free two-form gauge theory from the degrees of freedom count on eμν(k), and (ii) the Wigner's little group and the BRST cohomology for the 2D one-form gauge theory vis-à-vis our analysis for the 4D two-form gauge theory.

scholarly journals BRST COHOMOLOGY AND HODGE DECOMPOSITION THEOREM IN ABELIAN GAUGE THEORY

2000 ◽  
Vol 15 (11) ◽  
pp. 1685-1705 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Single Photon ◽  
Equations Of Motion ◽  
Decomposition Theorem ◽  
Hodge Decomposition ◽  
Laplacian Operator ◽  
Two Dimensional ◽  
Abelian Gauge ◽  
Brst Charge ◽  
Brst Cohomology

We discuss the Becchi–Rouet–Stora–Tyutin (BRST) cohomology and Hodge decomposition theorem for the two-dimensional free U(1) gauge theory. In addition to the usual BRST charge, we derive a local, conserved and nilpotent co(dual)-BRST charge under which the gauge-fixing term remains invariant. We express the Hodge decomposition theorem in terms of these charges and the Laplacian operator. We take a single photon state in the quantum Hilbert space and demonstrate the notion of gauge invariance, no-(anti)ghost theorem, transversality of photon and establish the topological nature of this theory by exploiting the concepts of BRST cohomology and Hodge decomposition theorem. In fact, the topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. On the two-dimensional compact manifold, we derive two sets of topological invariants with respect to the conserved and nilpotent BRST- and co-BRST charges and express the Lagrangian density of the theory as the sum of terms that are BRST- and co-BRST invariants. Mathematically, this theory captures together some of the key features of both Witten- and Schwarz-type of topological field theories.

Regge behavior of spontaneously broken non-Abelian gauge theory

1978 ◽  
Vol 17 (2) ◽  
pp. 585-597 ◽  
Author(s):  
J. B. Bronzan ◽  
R. L. Sugar
Keyword(s):  
Gauge Theory ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Regge Behavior
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