Hermitian Conjugate

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R. P. Malik - One of the best experts on this subject based on the ideXlab platform.

  • Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields
    2020
    Co-Authors: T. Bhanja, D Shukla, R. P. Malik
    Abstract:

    The publication of this article was funded by SCOAP 3 . Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3 + 1)-dimensional (4D) interacting nonAbelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates (with = 0, 1, 2, 3) and a pair of Grassmannian variables ( , ) which satisfy the standard relationships: 2 = 2 = 0 and + = 0. Various consequences of the application of the above superspace (SUSP) unitary operator (and its Hermitian Conjugate) are discussed. In particular, we obtain the results of the application of horizontality condition (HC) and gauge-invariant restriction (GIR) in the language of the above SUSP operators. One of the novel results of our present investigation is the derivation of explicit expressions for the SUSP unitary operator (and its Hermitian Conjugate) without imposing any Hermitian conjugation condition from outside on the parameters and (super)fields of the supersymmetric version of our 4D interacting non-Abelian 1-form theory with Dirac fields

  • superspace unitary operator in superfield approach to non abelian gauge theory with dirac fields
    Advances in High Energy Physics, 2016
    Co-Authors: T. Bhanja, D Shukla, R. P. Malik
    Abstract:

    Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3

  • Universal Superspace Unitary Operator and Nilpotent (Anti-)dual BRST Symmetries: Superfield Formalism
    Advances in High Energy Physics, 2016
    Co-Authors: T. Bhanja, N. Srinivas, R. P. Malik
    Abstract:

    We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator and its Hermitian Conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one ( )-dimensional (1D) rigid rotor and modified versions of the two ( )-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian Conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of the dual unitary operators and corresponding (anti-)dual-BRST symmetries are completely novel results in our present investigation.

  • Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields
    Hindawi Limited, 2016
    Co-Authors: T. Bhanja, D Shukla, R. P. Malik
    Abstract:

    Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3 + 1)-dimensional (4D) interacting non-Abelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates xμ (with μ=0,1,2,3) and a pair of Grassmannian variables (θ,θ-) which satisfy the standard relationships: θ2=θ-2=0 and  θθ-+θ-θ=0. Various consequences of the application of the above superspace (SUSP) unitary operator (and its Hermitian Conjugate) are discussed. In particular, we obtain the results of the application of horizontality condition (HC) and gauge-invariant restriction (GIR) in the language of the above SUSP operators. One of the novel results of our present investigation is the derivation of explicit expressions for the SUSP unitary operator (and its Hermitian Conjugate) without imposing any Hermitian conjugation condition from outside on the parameters and (super)fields of the supersymmetric version of our 4D interacting non-Abelian 1-form theory with Dirac fields

  • universal superspace unitary operator for some interesting abelian models superfield approach
    arXiv: High Energy Physics - Theory, 2015
    Co-Authors: T. Bhanja, N. Srinivas, R. P. Malik
    Abstract:

    Within the framework of augmented version of superfield formalism, we derive the superspace unitary operator and show its usefulness in the derivation of Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a set of interesting models for the Abelian 1-form gauge theories. These models are (i) a one (0+1)-dimensional (1D) toy model of a rigid rotor, (ii) the two (1+1)-dimensional (2D) modified versions of the Proca and anomalous Abelian 1-form gauge theories, and (iii) the 2D self-dual bosonic gauge field theory. We provide, in some sense, the alternatives to the horizontality condition (HC) and the gauge invariant restrictions (GIRs) in the language of the above superspace (SUSP) unitary operator. One of the key observations of our present endeavor is the result that the SUSP unitary operator and its Hermitian Conjugate are found to be the same for all the Abelian models under consideration (including the 4D interacting Abelian 1-form gauge theories with Dirac and complex scalar fields which have been discussed earlier). Thus, we establish the universality of the SUSP operator for the above Abelian theories.

T. Bhanja - One of the best experts on this subject based on the ideXlab platform.

  • Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields
    2020
    Co-Authors: T. Bhanja, D Shukla, R. P. Malik
    Abstract:

    The publication of this article was funded by SCOAP 3 . Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3 + 1)-dimensional (4D) interacting nonAbelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates (with = 0, 1, 2, 3) and a pair of Grassmannian variables ( , ) which satisfy the standard relationships: 2 = 2 = 0 and + = 0. Various consequences of the application of the above superspace (SUSP) unitary operator (and its Hermitian Conjugate) are discussed. In particular, we obtain the results of the application of horizontality condition (HC) and gauge-invariant restriction (GIR) in the language of the above SUSP operators. One of the novel results of our present investigation is the derivation of explicit expressions for the SUSP unitary operator (and its Hermitian Conjugate) without imposing any Hermitian conjugation condition from outside on the parameters and (super)fields of the supersymmetric version of our 4D interacting non-Abelian 1-form theory with Dirac fields

  • superspace unitary operator in superfield approach to non abelian gauge theory with dirac fields
    Advances in High Energy Physics, 2016
    Co-Authors: T. Bhanja, D Shukla, R. P. Malik
    Abstract:

    Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3

  • Universal Superspace Unitary Operator and Nilpotent (Anti-)dual BRST Symmetries: Superfield Formalism
    Advances in High Energy Physics, 2016
    Co-Authors: T. Bhanja, N. Srinivas, R. P. Malik
    Abstract:

    We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator and its Hermitian Conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one ( )-dimensional (1D) rigid rotor and modified versions of the two ( )-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian Conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of the dual unitary operators and corresponding (anti-)dual-BRST symmetries are completely novel results in our present investigation.

  • Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields
    Hindawi Limited, 2016
    Co-Authors: T. Bhanja, D Shukla, R. P. Malik
    Abstract:

    Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3 + 1)-dimensional (4D) interacting non-Abelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates xμ (with μ=0,1,2,3) and a pair of Grassmannian variables (θ,θ-) which satisfy the standard relationships: θ2=θ-2=0 and  θθ-+θ-θ=0. Various consequences of the application of the above superspace (SUSP) unitary operator (and its Hermitian Conjugate) are discussed. In particular, we obtain the results of the application of horizontality condition (HC) and gauge-invariant restriction (GIR) in the language of the above SUSP operators. One of the novel results of our present investigation is the derivation of explicit expressions for the SUSP unitary operator (and its Hermitian Conjugate) without imposing any Hermitian conjugation condition from outside on the parameters and (super)fields of the supersymmetric version of our 4D interacting non-Abelian 1-form theory with Dirac fields

  • universal superspace unitary operator for some interesting abelian models superfield approach
    arXiv: High Energy Physics - Theory, 2015
    Co-Authors: T. Bhanja, N. Srinivas, R. P. Malik
    Abstract:

    Within the framework of augmented version of superfield formalism, we derive the superspace unitary operator and show its usefulness in the derivation of Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a set of interesting models for the Abelian 1-form gauge theories. These models are (i) a one (0+1)-dimensional (1D) toy model of a rigid rotor, (ii) the two (1+1)-dimensional (2D) modified versions of the Proca and anomalous Abelian 1-form gauge theories, and (iii) the 2D self-dual bosonic gauge field theory. We provide, in some sense, the alternatives to the horizontality condition (HC) and the gauge invariant restrictions (GIRs) in the language of the above superspace (SUSP) unitary operator. One of the key observations of our present endeavor is the result that the SUSP unitary operator and its Hermitian Conjugate are found to be the same for all the Abelian models under consideration (including the 4D interacting Abelian 1-form gauge theories with Dirac and complex scalar fields which have been discussed earlier). Thus, we establish the universality of the SUSP operator for the above Abelian theories.

D Shukla - One of the best experts on this subject based on the ideXlab platform.

  • Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields
    2020
    Co-Authors: T. Bhanja, D Shukla, R. P. Malik
    Abstract:

    The publication of this article was funded by SCOAP 3 . Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3 + 1)-dimensional (4D) interacting nonAbelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates (with = 0, 1, 2, 3) and a pair of Grassmannian variables ( , ) which satisfy the standard relationships: 2 = 2 = 0 and + = 0. Various consequences of the application of the above superspace (SUSP) unitary operator (and its Hermitian Conjugate) are discussed. In particular, we obtain the results of the application of horizontality condition (HC) and gauge-invariant restriction (GIR) in the language of the above SUSP operators. One of the novel results of our present investigation is the derivation of explicit expressions for the SUSP unitary operator (and its Hermitian Conjugate) without imposing any Hermitian conjugation condition from outside on the parameters and (super)fields of the supersymmetric version of our 4D interacting non-Abelian 1-form theory with Dirac fields

  • superspace unitary operator in superfield approach to non abelian gauge theory with dirac fields
    Advances in High Energy Physics, 2016
    Co-Authors: T. Bhanja, D Shukla, R. P. Malik
    Abstract:

    Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3

  • Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields
    Hindawi Limited, 2016
    Co-Authors: T. Bhanja, D Shukla, R. P. Malik
    Abstract:

    Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3 + 1)-dimensional (4D) interacting non-Abelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates xμ (with μ=0,1,2,3) and a pair of Grassmannian variables (θ,θ-) which satisfy the standard relationships: θ2=θ-2=0 and  θθ-+θ-θ=0. Various consequences of the application of the above superspace (SUSP) unitary operator (and its Hermitian Conjugate) are discussed. In particular, we obtain the results of the application of horizontality condition (HC) and gauge-invariant restriction (GIR) in the language of the above SUSP operators. One of the novel results of our present investigation is the derivation of explicit expressions for the SUSP unitary operator (and its Hermitian Conjugate) without imposing any Hermitian conjugation condition from outside on the parameters and (super)fields of the supersymmetric version of our 4D interacting non-Abelian 1-form theory with Dirac fields

  • superspace unitary operator in qed with dirac and complex scalar fields superfield approach
    EPL, 2015
    Co-Authors: D Shukla, T. Bhanja, R. P. Malik
    Abstract:

    We exploit the strength of the superspace (SUSP) unitary operator to obtain the results of the application of the horizontality condition (HC) within the framework of the augmented version of the superfield formalism that is applied to the interacting systems of Abelian 1-form gauge theories where the U(1) Abelian 1-form gauge field couples to the Dirac and complex scalar fields in the physical four (3 + 1)-dimensions of spacetime. These interacting theories are generalized onto a (4, 2)-dimensional supermanifold that is parametrized by the four -dimensional (4D) spacetime variables and a pair of Grassmannian variables. To derive the (anti-)BRST symmetries for the matter fields, we impose the gauge-invariant restrictions (GIRs) on the superfields defined on the (4, 2)-dimensional supermanifold. We discuss various outcomes that emerge out from our knowledge of the SUSP unitary operator and its Hermitian Conjugate. The latter operator is derived without imposing any operation of Hermitian conjugation on the parameters and fields of our theory from outside. This is an interesting observation in our present investigation.

  • superspace unitary operator in superfield approach to non abelian gauge theory with dirac fields
    arXiv: High Energy Physics - Theory, 2015
    Co-Authors: T. Bhanja, D Shukla, R. P. Malik
    Abstract:

    Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3 + 1)-dimensional (4D) interacting non-Abelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates x^\mu (with \mu = 0, 1, 2, 3) and a pair of Grassmannian variables (\theta, \bar\theta) which satisfy the standard relationships: \theta^2 = {\bar\theta}^2 = 0, \theta\,\bar\theta + \bar\theta\,\theta = 0. Various consequences of the application of the above superspace (SUSP) unitary operator (and its Hermitian Conjugate) are discussed. In particular, we obtain the results of the application of horizontality condition (HC) and gauge invariant restriction (GIR) in the language of the above SUSP operators. One of the novel results of our present investigation is the derivation of explicit expressions for the SUSP unitary operator (and its Hermitian Conjugate) without imposing any Hermitian conjugation condition from outside on the parameters and (super)fields of the supersymmetric version of our 4D interacting non-Abelian 1-form theory with Dirac fields.

Malik R. P. - One of the best experts on this subject based on the ideXlab platform.

  • Universal Superspace Unitary Operator and Nilpotent (Anti-)dual BRST Symmetries: Superfield Formalism
    'Hindawi Limited', 2017
    Co-Authors: Bhanja T., Srinivas N., Malik R. P.
    Abstract:

    We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator (and its Hermitian Conjugate) and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one (0+1)-dimensional (1D) rigid rotor, modified versions of the two (1+1)-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian Conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual-horizontality condition (DHC) and dual-gauge invariant restrictions (DGIRs) of the superfield formalism. The derivation of the dual unitary operators and corresponding (anti-)dual BRST symmetries are completely novel results in our present investigation.Comment: LaTeX file, 25 pages, journal reference is give

  • Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields
    'Hindawi Limited', 2016
    Co-Authors: Bhanja T., Shukla D., Malik R. P.
    Abstract:

    Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian Conjugate) in the context of four (3 + 1)-dimensional (4D) interacting non-Abelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates x^\mu (with \mu = 0, 1, 2, 3) and a pair of Grassmannian variables (\theta, \bar\theta) which satisfy the standard relationships: \theta^2 = {\bar\theta}^2 = 0, \theta\,\bar\theta + \bar\theta\,\theta = 0. Various consequences of the application of the above superspace (SUSP) unitary operator (and its Hermitian Conjugate) are discussed. In particular, we obtain the results of the application of horizontality condition (HC) and gauge invariant restriction (GIR) in the language of the above SUSP operators. One of the novel results of our present investigation is the derivation of explicit expressions for the SUSP unitary operator (and its Hermitian Conjugate) without imposing any Hermitian conjugation condition from outside on the parameters and (super)fields of the supersymmetric version of our 4D interacting non-Abelian 1-form theory with Dirac fields.Comment: LaTeX file, 16 pages, journal versio

  • Universal Superspace Unitary Operator for Some Interesting Abelian Models: Superfield Approach
    'Hindawi Limited', 2016
    Co-Authors: Bhanja T., Srinivas N., Malik R. P.
    Abstract:

    Within the framework of augmented version of superfield formalism, we derive the superspace unitary operator and show its usefulness in the derivation of Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a set of interesting models for the Abelian 1-form gauge theories. These models are (i) a one (0+1)-dimensional (1D) toy model of a rigid rotor, (ii) the two (1+1)-dimensional (2D) modified versions of the Proca and anomalous Abelian 1-form gauge theories, and (iii) the 2D self-dual bosonic gauge field theory. We provide, in some sense, the alternatives to the horizontality condition (HC) and the gauge invariant restrictions (GIRs) in the language of the above superspace (SUSP) unitary operator. One of the key observations of our present endeavor is the result that the SUSP unitary operator and its Hermitian Conjugate are found to be the same for all the Abelian models under consideration (including the 4D interacting Abelian 1-form gauge theories with Dirac and complex scalar fields which have been discussed earlier). Thus, we establish the universality of the SUSP operator for the above Abelian theories.Comment: LaTeX file, 16 pages, journal versio

  • Superspace Unitary Operator in QED with Dirac and Complex Scalar Fields: Superfield Approach
    'IOP Publishing', 2015
    Co-Authors: Shukla D., Bhanja T., Malik R. P.
    Abstract:

    We exploit the strength of the superspace (SUSP) unitary operator to obtain the results of the application of the horizontality condition (HC) within the framework of augmented version of superfield formalism that is applied to the interacting systems of Abelian 1-form gauge theories where the U(1) Abelian 1-form gauge field couples to the Dirac and complex scalar fields in the physical four (3 + 1)-dimensions of spacetime. These interacting theories are generalized onto a (4, 2)-dimensional supermanifold that is parametrized by the four (3 + 1)-dimensional (4D) spacetime variables and a pair of Grassmannian variables. To derive the (anti-)BRST symmetries for the matter fields, we impose the gauge invariant restrictions (GIRs) on the superfields defined on the (4, 2)-dimensional supermanifold. We discuss various outcomes that emerge out from our knowledge of the SUSP unitary operator and its Hermitian Conjugate. The latter operator is derived without imposing any operation of Hermitian conjugation on the parameters and fields of our theory from outside. This is an interesting observation in our present investigation.Comment: LaTeX file, 11 pages, journal versio

N. Srinivas - One of the best experts on this subject based on the ideXlab platform.

  • Universal Superspace Unitary Operator and Nilpotent (Anti-)dual BRST Symmetries: Superfield Formalism
    Advances in High Energy Physics, 2016
    Co-Authors: T. Bhanja, N. Srinivas, R. P. Malik
    Abstract:

    We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator and its Hermitian Conjugate and demonstrate their utility in the derivation of the nilpotent and absolutely anticommuting (anti-)dual-BRST symmetry transformations for a set of interesting models of the Abelian 1-form gauge theories. These models are the one ( )-dimensional (1D) rigid rotor and modified versions of the two ( )-dimensional (2D) Proca as well as anomalous gauge theories and 2D model of a self-dual bosonic field theory. We show the universality of the SUSP dual unitary operator and its Hermitian Conjugate in the cases of all the Abelian models under consideration. These SUSP dual unitary operators, besides maintaining the explicit group structure, provide the alternatives to the dual horizontality condition (DHC) and dual gauge invariant restrictions (DGIRs) of the superfield formalism. The derivations of the dual unitary operators and corresponding (anti-)dual-BRST symmetries are completely novel results in our present investigation.

  • universal superspace unitary operator for some interesting abelian models superfield approach
    arXiv: High Energy Physics - Theory, 2015
    Co-Authors: T. Bhanja, N. Srinivas, R. P. Malik
    Abstract:

    Within the framework of augmented version of superfield formalism, we derive the superspace unitary operator and show its usefulness in the derivation of Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a set of interesting models for the Abelian 1-form gauge theories. These models are (i) a one (0+1)-dimensional (1D) toy model of a rigid rotor, (ii) the two (1+1)-dimensional (2D) modified versions of the Proca and anomalous Abelian 1-form gauge theories, and (iii) the 2D self-dual bosonic gauge field theory. We provide, in some sense, the alternatives to the horizontality condition (HC) and the gauge invariant restrictions (GIRs) in the language of the above superspace (SUSP) unitary operator. One of the key observations of our present endeavor is the result that the SUSP unitary operator and its Hermitian Conjugate are found to be the same for all the Abelian models under consideration (including the 4D interacting Abelian 1-form gauge theories with Dirac and complex scalar fields which have been discussed earlier). Thus, we establish the universality of the SUSP operator for the above Abelian theories.

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