The Experts below are selected from a list of 18228 Experts worldwide ranked by ideXlab platform
R. P. Malik - One of the best experts on this subject based on the ideXlab platform.
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superspace Unitary Operator in superfield approach to non abelian gauge theory with dirac fields
Advances in High Energy Physics, 2016Co-Authors: T. Bhanja, D Shukla, R. P. MalikAbstract: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
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universal superspace Unitary Operator for some interesting abelian models superfield approach
Advances in High Energy Physics, 2016Co-Authors: T. Bhanja, N. Srinivas, R. P. MalikAbstract: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
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Universal Superspace Unitary Operator and Nilpotent (Anti-)dual BRST Symmetries: Superfield Formalism
Advances in High Energy Physics, 2016Co-Authors: T. Bhanja, N. Srinivas, R. P. MalikAbstract: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.
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Superspace Unitary Operator for Some Interesting Abelian Models: Superfield Approach
arXiv: High Energy Physics - Theory, 2015Co-Authors: T. Bhanja, N. Srinivas, R. P. MalikAbstract:Within the framework of augmented version of superfield formalism, we choose 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 theory. 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 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 interacting Abelian 1-form gauge theories with Dirac and complex scalar fields which have been discussed earlier).
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universal superspace Unitary Operator for some interesting abelian models superfield approach
arXiv: High Energy Physics - Theory, 2015Co-Authors: T. Bhanja, N. Srinivas, R. P. MalikAbstract: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.
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superspace Unitary Operator in superfield approach to non abelian gauge theory with dirac fields
Advances in High Energy Physics, 2016Co-Authors: T. Bhanja, D Shukla, R. P. MalikAbstract: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
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universal superspace Unitary Operator for some interesting abelian models superfield approach
Advances in High Energy Physics, 2016Co-Authors: T. Bhanja, N. Srinivas, R. P. MalikAbstract: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
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Universal Superspace Unitary Operator and Nilpotent (Anti-)dual BRST Symmetries: Superfield Formalism
Advances in High Energy Physics, 2016Co-Authors: T. Bhanja, N. Srinivas, R. P. MalikAbstract: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.
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Superspace Unitary Operator for Some Interesting Abelian Models: Superfield Approach
arXiv: High Energy Physics - Theory, 2015Co-Authors: T. Bhanja, N. Srinivas, R. P. MalikAbstract:Within the framework of augmented version of superfield formalism, we choose 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 theory. 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 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 interacting Abelian 1-form gauge theories with Dirac and complex scalar fields which have been discussed earlier).
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universal superspace Unitary Operator for some interesting abelian models superfield approach
arXiv: High Energy Physics - Theory, 2015Co-Authors: T. Bhanja, N. Srinivas, R. P. MalikAbstract: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.
M Kibler - One of the best experts on this subject based on the ideXlab platform.
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an angular momentum approach to quadratic fourier transform hadamard matrices gauss sums mutually unbiased bases the Unitary group and the pauli group
Journal of Physics A, 2009Co-Authors: M KiblerAbstract:The construction of Unitary Operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained from a polar decomposition of SU(2) and is analyzed in terms of cyclic groups, quadratic Fourier transforms, Hadamard matrices and generalized Gauss sums. Weyl pairs, generalized Pauli Operators and their application to the Unitary group and the Pauli group naturally arise in this approach.
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An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, Unitary group and Pauli group
Journal of Physics A: Mathematical and Theoretical, 2009Co-Authors: M KiblerAbstract:The construction of Unitary Operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained from a polar decomposition of SU(2) and analysed in terms of cyclic groups, quadratic Fourier transforms, Hadamard matrices and generalized Gauss sums. Weyl pairs, generalized Pauli Operators and their application to the Unitary group and the Pauli group naturally arise in this approach.
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On the Wigner-Racah algebra of the group $SU_{2}$ in a non-standard basis
1998Co-Authors: M KiblerAbstract:The algebra su(2) is derived from two commuting quon algebras for which the parameter q is a root of unity. This leads to a polar decomposition of the shift Operators of the group SU(2). The Wigner-Racah algebra of SU(2) is developed in a new basis arising from the simultanenous diagonalization of two commuting Operators, viz., the Casimir of SU(2) and a Unitary Operator which takes its origin in the polar decomposition of the shift Operators of SU(2).
Suguru Tamaki - One of the best experts on this subject based on the ideXlab platform.
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quantum query complexity of Unitary Operator discrimination
Computing and Combinatorics Conference, 2017Co-Authors: Akinori Kawachi, Kenichi Kawano, Francois Le Gall, Suguru TamakiAbstract:Unitary Operator discrimination is a fundamental problem in quantum information theory. The basic version of this problem can be described as follows: given a black box implementing a quantum Operator U, and the promise that the black box implements either the Unitary Operator \(U_1\) or the Unitary Operator \(U_2\), the goal is to decide whether \(U=U_1\) or \(U=U_2\). In this paper, we consider the query complexity of this problem. We show that there exists a quantum algorithm that solves this problem with bounded-error probability using \(\left\lceil \frac{\pi }{3\theta _\mathrm{cover}} \right\rceil \) queries to the black-box, where \(\theta _\mathrm{cover}\) represents the “closeness” between \(U_1\) and \(U_2\) (this parameter is determined by the eigenvalues of the matrix \(U_1^\dag U_2\)). We also show that this upper bound is essentially tight: we prove that there exist Operators \(U_1\) and \(U_2\) such that any quantum algorithm solving this problem with bounded-error probability requires at least \(\left\lceil \frac{2}{3\theta _\mathrm{cover}} \right\rceil \) queries.
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COCOON - Quantum Query Complexity of Unitary Operator Discrimination
Lecture Notes in Computer Science, 2017Co-Authors: Akinori Kawachi, Kenichi Kawano, François Le Gall, Suguru TamakiAbstract:Unitary Operator discrimination is a fundamental problem in quantum information theory. The basic version of this problem can be described as follows: given a black box implementing a quantum Operator U, and the promise that the black box implements either the Unitary Operator \(U_1\) or the Unitary Operator \(U_2\), the goal is to decide whether \(U=U_1\) or \(U=U_2\). In this paper, we consider the query complexity of this problem. We show that there exists a quantum algorithm that solves this problem with bounded-error probability using \(\left\lceil \frac{\pi }{3\theta _\mathrm{cover}} \right\rceil \) queries to the black-box, where \(\theta _\mathrm{cover}\) represents the “closeness” between \(U_1\) and \(U_2\) (this parameter is determined by the eigenvalues of the matrix \(U_1^\dag U_2\)). We also show that this upper bound is essentially tight: we prove that there exist Operators \(U_1\) and \(U_2\) such that any quantum algorithm solving this problem with bounded-error probability requires at least \(\left\lceil \frac{2}{3\theta _\mathrm{cover}} \right\rceil \) queries.
Ameur Dhahri - One of the best experts on this subject based on the ideXlab platform.
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Repeated Quantum Interactions and Unitary Random Walks
Journal of Theoretical Probability, 2010Co-Authors: Stéphane Attal, Ameur DhahriAbstract:Among the discrete evolution equations describing a quantum system ℋ_ S undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by classical random variables in ℝ^ N . The characterization we obtain is entirely algebraical in terms of the Unitary Operator driving the elementary interaction. We show that the solutions of these equations are then random walks on the group U (ℋ_0) of Unitary Operators on ℋ_0.
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Repeated Quantum Interactions and Unitary Random Walks
Journal of Theoretical Probability, 2010Co-Authors: Stéphane Attal, Ameur DhahriAbstract:Among the discrete evolution equations describing a quantum system $\rH_S$ undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by classical random variables in $\RR^N$. The characterization we obtain is entirely algebraical in terms of the Unitary Operator driving the elementary interaction. We show that the solutions of these equations are then random walks on the group $U(\rH_0)$ of Unitary Operators on $\rH_0$.
