BRST OPERATOR METHOD—QUANTUM BRST COHOMOLOGY

2020 ◽  
pp. 296-332
Keyword(s):  
Operator Method ◽  
Brst Operator ◽  
Brst Cohomology

scholarly journals sℓ(2)−4 WZW MODEL AS AN (N=4)-SUPERSYMMETRIC BOSONIC STRING WITH c=−2 MATTER

1996 ◽  
Vol 11 (15) ◽  
pp. 2721-2748 ◽  
Author(s):  
A.M. SEMIKHATOV ◽  
I. YU. TIPUNIN
Keyword(s):  
Spectral Sequence ◽  
Current Algebra ◽  
Bosonic String ◽  
Singular Vectors ◽  
Brst Operator ◽  
Irreducible Modules ◽  
Brst Cohomology ◽  
Operator Construction

We consider the sℓ(2) current algebra at level k=−4 when the sℓ(2) BRST operator is nilpotent. We formulate a spectral sequence converging to the cohomology of this BRST operator. At the second term in the spectral sequence, we observe the existence of an N=4 algebra. This algebra is generated in a c=−2 bosonic string whose BRST operator [Formula: see text] represents the next term in the spectral sequence. We realize the cohomology of the irreducible modules as [Formula: see text] primitives of theN=4 singular vectors and relate the latter to the Lian–Zuckerman states of c=−2 matter. The relation between the sℓ(2)−4 WZW model and the c=−2 bosonic string is established both at the level of BRST cohomology and at the level of an explicit operator construction. The relation of the N=4 algebra to the known symmetries of matter+gravity systems is also investigated.

GENERALIZED CONNECTION FORMALISM AND BRST COHOMOLOGY STRUCTURE FOR BF THEORIES

1998 ◽  
Vol 13 (23) ◽  
pp. 1837-1844 ◽  
Author(s):  
A. ABDESSELAM ◽  
M. TAHIRI
Keyword(s):  
Brst Symmetry ◽  
Brst Operator ◽  
Exact Quantum ◽  
Brst Cohomology ◽  
Quantum Action ◽  
Arbitrary Dimensions

The non-Abelian BF theories in arbitrary dimensions are studied in a generalized connection formalism. This gives rise to the off-shell nilpotent BRST operator which permits construction of BRST exact quantum action. A set of operators satisfying the descent equations is derived from the generalized curvature; but it cannot lead to non-trivial observables. An off-shell superalgebra of Wess–Zumino type, containing the vector supersymmetry and the BRST symmetry, is also derived.

ON QUANTUM BRST COHOMOLOGY

2009 ◽  
Vol 06 (07) ◽  
pp. 1151-1160
Author(s):  
Z. BENTALHA ◽  
M. TAHIRI
Keyword(s):  
Brst Operator ◽  
Brst Cohomology

Within bicovariant differential calculi framework, the BRST operator Ω is constructed. We showed that Ω is nil-potent (Ω2=0).

scholarly journals (NON)TRIVIALITY OF PURE SPINORS AND EXACT PURE SPINOR–RNS MAP

2009 ◽  
Vol 24 (14) ◽  
pp. 2677-2687 ◽  
Author(s):  
DIMITRI POLYAKOV
Keyword(s):  
Hilbert Space ◽  
String Theory ◽  
Vertex Operator ◽  
Similarity Transformation ◽  
Pure Spinor ◽  
Brst Operator ◽  
Variable Λ ◽  
Brst Cohomology ◽  
Spinor Formalism ◽  
Pure Spinor Formalism

All the BRST-invariant operators in pure spinor formalism in d = 10 can be represented as BRST commutators, such as [Formula: see text] where λ+ is the U(5) component of the pure spinor transforming as [Formula: see text]. Therefore, in order to secure nontriviality of BRST cohomology in pure spinor string theory, one has to introduce "small Hilbert space" and "small operator algebra" for pure spinors, analogous to those existing in RNS formalism. As any invariant vertex operator in RNS string theory can also represented as a commutator V = {Q brst , LV} where L = -4c∂ξξe-2ϕ, we show that mapping [Formula: see text] to L leads to identification of the pure spinor variable λα in terms of RNS variables without any additional nonminimal fields. We construct the RNS operator satisfying all the properties of λα and show that the pure spinor BRST operator ∮λαdα is mapped (up to similarity transformation) to the BRST operator of RNS theory under such a construction.

scholarly journals A Dynamical Study of Fusion Hindrance with Nakajima-Zwanzig Projection Method

2021 ◽  
Author(s):  
Yasuhisa Abe ◽  
David Boilley ◽  
Quentin Hourdillé ◽  
Caiwan Shen
Keyword(s):  
Cross Sections ◽  
Degrees Of Freedom ◽  
Operator Method ◽  
Initial Distribution ◽  
Physical Parameters ◽  
Relaxation Processes ◽  
Fast Variable ◽  
Dynamical Study ◽  
Injection Point ◽  
Slow Variables

Abstract A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima-Zwanzig projection operator method is employed to eliminate fast variable and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a propagation of the given initial distribution. The term results in a slip to the initial values of the slow variables. We expect that gives a dynamical origin of the so-called “injection point s” introduced by Swiatecki et al in order to reproduce absolute values of measured cross sections for SHE. A formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation, and permits us to compare various incident channels.

A nonlocal operator method for finite deformation higher-order gradient elasticity

2021 ◽  
Vol 384 ◽  
pp. 113963
Author(s):  
Huilong Ren ◽  
Xiaoying Zhuang ◽  
Nguyen-Thoi Trung ◽  
Timon Rabczuk
Keyword(s):  
Finite Deformation ◽  
Gradient Elasticity ◽  
Operator Method ◽  
Higher Order ◽  
Nonlocal Operator
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