On the quantization of supersymmetric particle

The modified action of Siegel for a point superparticle is quantized by using the BRS transformation. We also present another action for a superparticle. We discuss the second-quantization of a superparticle and then point out some difficulties in the covariant second quantization of superstring.     

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transformations of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was obtained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propagators were obtained. Supported by Knowledge Innovation Project of the Chinese Academy of Sciences (Grant Nos. KJCX2-SW-N02 and KJCX2-SW-N016), the National Natural Science Foundation of China (Grant Nos. 10435080 and 10575123), Beijing Natural Science Foundation (Grant No. 1072005) and the Science and Technology Development Foundation of Beijing Municipal Education Committee (Grant No. Km200310005018)     

BRST quantization of a scalar particle in a curved background

The BRST formalism is employed to quantize a scalar particle and interactions with an external scalar field (x ) and vector gauge fieldA (x ) in the background of an arbitrary gravitational field. The second-quantized actions are obtained.     

BRST quantization of the superparticle

We show that the quantization of the superparticle action is possible. This is done by shifts in the BRST operator and the resulting action has an infinite number of ghosts. The total BRST operator is given by an infinite sum and is shown to be nilpotent. We also obtain a BRST invariant kinetic operator that contains the dynamical, auxiliary and gauge pieces in it.     

Geometric quantization of the BRST charge

In the first half of this paper (Sects. 1–4) we generalise the standard geometric quantization procedure to symplectic supermanifolds. In the second half (Sects. 5, 6) we apply this to two examples that exhibit classical BRST symmetry, i.e., we quantize the BRST charge and the ghost number. More precisely, in the first example we consider the reduced symplectic manifold obtained by symplectic reduction from a free group action with Ad^*-equivariant moment map; in the second example we consider a foliated configuration space, whose cotangent bundle admits the construction of a BRST charge associated to this foliation. We show that the classical BRST symmetry can be described in terms of a hamiltonian supergroup action on the extended phase space, and that geometric quantization gives us a super-unitary representation of this supergroup. Finally we point out how these results are related to reduction at the quantum level, as compared with the reduction at the classical level.Research supported by the Dutch Organization for Scientific Research (NWO)     

Solving local constraint condition problem in slave particle theory with the BRST quantization

With the Becchi-Rouet-Stora-Tyutin(BRST) quantization of gauge theory,we solve the long-standing difficult problem of the local constraint conditions,i.e.the single occupation of a slave particle per site,in the slave particle theory.This difficulty is actually caused by inconsistently dealing with the local Lagrange multiplier λ_i which ensures the constraint:in the Hamiltonian formalism of the theory,λ_i is time-independent and commutes with the Hamiltonian while in the Lag...     

BRST quantization in the Siegel gauge

From a formal generalization to N copies of the free open string field theory BRST-quantized in the Siegel gauge we reproduce the BRST quantization of the free closed bosonic string field theory and obtain the one of massless higher spin field theories.     

Dirac propagator from path integral quantization of the pseudoclassical spinning particle

We show how the Dirac propagator can be reproduced by summing over the paths of a pseudoclassical spinning particle.     

BRST quantization of superstring field theory

We write the gauge fixed action which arises in the quantization of Witten's string field theory in a linear gauge, in a form which applies to both the superstring and the bosonic string. The corresponding BRST transformation is nilpotent only on-shell. We construct also an off-shell nilpotent BRST transformation which formally leaves invariant the quantum effective action. This BRST transformation has a geometrical interpretation which could allow to describe the gauge anomalies of the superstring field theory as the nontrivial cohomology of the BRST charge via the Wess-Zumino consistency condition.     

On the BRST quantization of chiral bosons

The Siegel action for two right-moving chiral bosons can be BRST quantized. In the case in which their kinetic terms have opposite signs the momenta in the left-moving sector must be constrained to be zero. In this case the two chiral bosons can be described also by a quadratic action. There is no analogous BRST quantization for a single chiral boson.     

Hamiltonian BRST quantization of the conformal string

We present a new formulation of the tensionless string (T = 0) where the space-time conformal symmetry is manifest. Using a Hamiltonian BRST scheme we quantize this Conformal String and find that it has critical dimension D = 2. This is in keeping with our classical result that the model describes massless particles in this dimension. It is also consistent with our previous results which indicate that quantized conformally symmetric tensionless strings describe a topological phase away from D = 2.

We reach our result by demanding nilpotency of the BRST charge and consistency with the Jacobi identities. The derivation is presented in two different ways: in operator language and using mode expansions.

Careful attention is paid to regularization, a crucial ingredient in our calculations.     

The algebraic structure of BRST quantization

It is shown that a system of first-class bosonic constraints obeying a Lie algebra has associated with it a natural superalgebra. BRST quantization arises as a non-linear representation of this superalgebra. Two distinct superalgebras are explicitly constructed and their associated BRST quantizations presented. The first BRST quantization is the canonical one with the BRST charge a grassmannian scalar. The second is new — the BRST charge is a grassmannian spinor transforming in the fundamental representation of the appropriate superalgebra. Generalizations are briefly discussed.