Nonlinear Operator Superalgebras and BFV-BRST Operators for Lagrangian Description of Mixed-symmetry HS Fields in AdS Spaces
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2008
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| author | Reshetnyak, A. A. |
| author_facet | Reshetnyak, A. A. |
| contents | We study the properties of nonlinear superalgebras $\mathcal{A}$ and algebras $\mathcal{A}_b$ arising from a one-to-one correspondence between the sets of relations that extract AdS-group irreducible representations $D(E_0,s_1,s_2)$ in AdS$_d$-spaces and the sets of operators that form $\mathcal{A}$ and $\mathcal{A}_b$, respectively, for fermionic, $s_i=n_i+{1/2}$, and bosonic, $s_i=n_i$, $n_i \in \mathbb{N}_0$, $i=1,2$, HS fields characterized by a Young tableaux with two rows. We consider a method of constructing the Verma modules $V_\mathcal{A}$, $V_{\mathcal{A}_b}$ for $\mathcal{A}$, $\mathcal{A}_b$ and establish a possibility of their Fock-space realizations in terms of formal power series in oscillator operators which serve to realize an additive conversion of the above (super)algebra ($\mathcal{A}$) $\mathcal{A}_b$, containing a set of 2nd-class constraints, into a converted (super)algebra $\mathcal{A}_{b{}c}$ = $\mathcal{A}_{b}$ + $\mathcal{A}'_b$ ($\mathcal{A}_c$ = $\mathcal{A}$ + $\mathcal{A}'$), containing a set of 1st-class constraints only. For the algebra $\mathcal{A}_{b{}c}$, we construct an exact nilpotent BFV--BRST operator $Q'$ having nonvanishing terms of 3rd degree in the powers of ghost coordinates and use $Q'$ to construct a gauge-invariant Lagrangian formulation (LF) for HS fields with a given mass $m$ (energy $E_0(m)$) and generalized spin $\mathbf{s}$=$(s_1,s_2)$. LFs with off-shell algebraic constraints are examined as well. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_0812_2329 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | Nonlinear Operator Superalgebras and BFV-BRST Operators for Lagrangian Description of Mixed-symmetry HS Fields in AdS Spaces Reshetnyak, A. A. High Energy Physics - Theory Mathematical Physics Operator Algebras Quantum Algebra 81T11 17A45 17B10 22E47 G.0; I.1.1 We study the properties of nonlinear superalgebras $\mathcal{A}$ and algebras $\mathcal{A}_b$ arising from a one-to-one correspondence between the sets of relations that extract AdS-group irreducible representations $D(E_0,s_1,s_2)$ in AdS$_d$-spaces and the sets of operators that form $\mathcal{A}$ and $\mathcal{A}_b$, respectively, for fermionic, $s_i=n_i+{1/2}$, and bosonic, $s_i=n_i$, $n_i \in \mathbb{N}_0$, $i=1,2$, HS fields characterized by a Young tableaux with two rows. We consider a method of constructing the Verma modules $V_\mathcal{A}$, $V_{\mathcal{A}_b}$ for $\mathcal{A}$, $\mathcal{A}_b$ and establish a possibility of their Fock-space realizations in terms of formal power series in oscillator operators which serve to realize an additive conversion of the above (super)algebra ($\mathcal{A}$) $\mathcal{A}_b$, containing a set of 2nd-class constraints, into a converted (super)algebra $\mathcal{A}_{b{}c}$ = $\mathcal{A}_{b}$ + $\mathcal{A}'_b$ ($\mathcal{A}_c$ = $\mathcal{A}$ + $\mathcal{A}'$), containing a set of 1st-class constraints only. For the algebra $\mathcal{A}_{b{}c}$, we construct an exact nilpotent BFV--BRST operator $Q'$ having nonvanishing terms of 3rd degree in the powers of ghost coordinates and use $Q'$ to construct a gauge-invariant Lagrangian formulation (LF) for HS fields with a given mass $m$ (energy $E_0(m)$) and generalized spin $\mathbf{s}$=$(s_1,s_2)$. LFs with off-shell algebraic constraints are examined as well. |
| title | Nonlinear Operator Superalgebras and BFV-BRST Operators for Lagrangian Description of Mixed-symmetry HS Fields in AdS Spaces |
| topic | High Energy Physics - Theory Mathematical Physics Operator Algebras Quantum Algebra 81T11 17A45 17B10 22E47 G.0; I.1.1 |
| url | https://arxiv.org/abs/0812.2329 |