scholarly journals BFFT FORMALISM APPLIED TO THE MINIMAL CHIRAL SCHWINGER MODEL

2004 ◽  
Vol 19 (39) ◽  
pp. 2957-2969 ◽  
Author(s):  
C. P. NATIVIDADE ◽  
H. BOSCHI-FILHO ◽  
L. V. BELVEDERE
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Point Of View ◽  
Chiral Model ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Invariant Action ◽  
Invariant Formulation

We consider the minimal chiral Schwinger model, by embedding the gauge non-invariant formulation into a gauge theory following the Batalin–Fradkin–Fradkina–Tyutin point of view. Within the BFFT procedure, the second-class constraints are converted into strongly involutive first-class ones, leading to an extended gauge-invariant formulation. We also show that, like the standard chiral model, in the minimal chiral model the Wess–Zumino action can be obtained by performing a q-number gauge transformation into the effective gauge non-invariant action.

OPERATOR GAUGE TRANSFORMATION AND THE WESS–ZUMINO TERM

1995 ◽  
Vol 10 (03) ◽  
pp. 207-217 ◽  
Author(s):  
L. V. BELVEDERE ◽  
K. D. ROTHE
Keyword(s):  
Gauge Transformation ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Invariant Formulation

We discuss the generation of the Wess–Zumino term in the chiral Schwinger model via an operator-valued gauge transformation of its gauge noninvariant formulation. Furthermore, the completely fermionized version of the gauge-invariant formulation of this model for a general value of the JR parameter is shown to be equivalent to a generalized chiral Schwinger model including a Thirring interaction.

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 Duality and gauge invariance of non-commutative spacetime Podolsky electromagnetic theory

2017 ◽  
Vol 32 (03) ◽  
pp. 1750019 ◽  
Author(s):  
Everton M. C. Abreu ◽  
Rafael L. Fernandes ◽  
Albert C. R. Mendes ◽  
Jorge Ananias Neto ◽  
Mario Jr. Neves
Keyword(s):  
Gauge Transformation ◽  
Gauge Invariance ◽  
Electromagnetic Theory ◽  
Physical Models ◽  
Field Theories ◽  
Invariance Property ◽  
Gauge Invariant ◽  
Invariant Action ◽  
Original Action ◽  
Higher Derivative

The interest in higher derivative field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. In this paper, we have introduced the non-commutative (NC) version of the Podolsky theory and we investigated the effect of the non-commutativity over its original gauge invariance property. We have demonstrated precisely that the non-commutativity spoiled the primary gauge invariance of the original action under this primary gauge transformation. After that we have used the Noether dualization technique to obtain a dual and gauge invariant action. We have demonstrated that through the introduction of a Stueckelberg field in this NC model, we can also recover the primary gauge invariance. In this way, we have accomplished a comparison between both methods.

θ VACUUM IN THE CHIRAL SCHWINGER MODEL

1991 ◽  
Vol 06 (02) ◽  
pp. 243-261 ◽  
Author(s):  
M. CARENA ◽  
C.E.M. WAGNER
Keyword(s):  
Physical Properties ◽  
Vacuum State ◽  
Cluster Property ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Invariant Formulation ◽  
Dependent Parameter ◽  
Vector Theory ◽  
Θ Vacuum

The physical properties of the chiral Schwinger model are studied, for the particular value of the regularization-dependent parameter a=2. Within a gauge-invariant formulation, we prove that, apart from free physical chiral states, the chiral Schwinger model is equivalent to the vector Schwinger model. In particular, we show that, as in the vector theory, the cluster property is not fulfilled unless the vacuum state is properly defined.

scholarly journals Gauge invariant actions for the noncommutative phase-space relativistic particle

2017 ◽  
Vol 32 (38) ◽  
pp. 1750215 ◽  
Author(s):  
Everton M. C. Abreu ◽  
Cresus F. L. Godinho
Keyword(s):  
Gauge Theory ◽  
Phase Space ◽  
Relativistic Particle ◽  
Point Of View ◽  
Noncommutative Phase Space ◽  
Main Interest ◽  
Gauge Invariant ◽  
Class System ◽  
Original Action ◽  
Constraint Set

Our main interest here is to analyze the gauge invariance issue concerning the noncommutative relativistic particle. Since the analysis of the constraint set from Dirac’s point of view classifies it as a second-class system, it is not a gauge theory. Hence, the objective here is to obtain gauge invariant actions linked to the original one. However, we have two starting points, meaning that firstly we will begin directly from the original action and, using the Noether procedure, we have obtained a specific dual (gauge invariant) action. Following another path, we will act towards the constraints so that we have carried out the conversion of second to first-class constraints through the Batalin–Fradkin–Fradkina–Tyutin formalism, obtaining the second gauge invariant Lagrangian.

scholarly journals NEW GAUGE INVARIANT FORMULATION OF THE CHERN–SIMONS GAUGE THEORY: CLASSICAL AND QUANTAL ANALYSIS

2009 ◽  
Vol 24 (31) ◽  
pp. 5933-5975
Author(s):  
MU-IN PARK ◽  
YOUNG-JAI PARK
Keyword(s):  
Gauge Theory ◽  
Longitudinal Mode ◽  
Momentum Tensor ◽  
Simons Theory ◽  
Gauge Invariant ◽  
Invariant Formulation ◽  
Poincaré Algebra ◽  
Chern Simons ◽  
Schrödinger Picture ◽  
Chern Simons Theory

A recently proposed new gauge invariant formulation of the Chern–Simons gauge theory is considered in detail. This formulation is consistent with the gauge fixed formulation. Furthermore, it is found that the canonical (Noether) Poincaré generators are not gauge invariant even on the constraints surface and do not satisfy the Poincaré algebra contrast to usual case. It is the improved generators, constructed from the symmetric energy–momentum tensor, which are (manifestly) gauge invariant and obey the quantum as well as classical Poincaré algebra. The physical states are constructed and it is found in the Schrödinger picture that unusual gauge invariant longitudinal mode of the gauge field is crucial for constructing the physical wave-functional which is genuine to (pure) Chern–Simons theory. In matching to the gauge fixed formulation, we consider three typical gauges, Coulomb, axial and Weyl gauges as explicit examples. Furthermore, recent several confusions about the effect of Dirac's dressing function and the gauge fixings are clarified. The analysis according to old gauge independent formulation á la Dirac is summarized in an appendix.

scholarly journals Gauge invariant formulation and bosonisation of the Schwinger model

1998 ◽  
Vol 419 (1-4) ◽  
pp. 285-290 ◽  
Author(s):  
J. Kijowski ◽  
G. Rudolph ◽  
M. Rudolph
Keyword(s):  
Gauge Invariant ◽  
Schwinger Model ◽  
Invariant Formulation
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