Gaupta-Bleuler triplet for massless spin-3/2 field in de Sitter space

Physicists have been interested in quantization of spinor and vector free fields in 4-dimensional de Sitter space-time,in ambient space notation.The Gupta-Bleuler formalism has been extensively applied to the quantization of gauge invariant theories.The field equation of the massless spin-3/2 fields is gauge invariant in de Sitter space.In this paper,we study the quantization of massless spin-3/2 gauge fields in de Sitter space-time by the Gupta-Bleuler formalism.This triplet carries an indecomposable representation of the de Sitter group.     

The Fokker-Planck equations in lattice gauge theories

The stochastic quantization in lattice gauge theories (LGT) is discussed by using Langevin equations and Fokker-Planck equations. It is shown that the evolution equations in the stochastic process reduce to the Schwinger-Dyson equation when the lattice system reaches equilibrium.     

Langevin equation in field theory

A new approach to quantum field theory is developed based on the Langevin equation (stochastic quantization). Applications to conventional and gauge theories are discussed, as well as various extensions; the Langevin difference equation, the complex Langevin equation in Minkowski space, etc.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 66–76, March, 1986.     

The equivalence theorem is subtle

We show that the equivalence theorem as is usually stated is valid only within the scheme of perturbation theory. New conditions have to be imposed on the theorem to make it valid in a nonperturbative context. Implications for a nonperturbative quantization of gravitation as also quantization of gauge theories in the unitary gauge are discussed.     

Quantization of gauge theories with global anomalies

Global anomalies, which obstruct the quantization of certain gauge theories in the temporal gauge, get bypassed in canonical quantization.     

Quantization of the Green-Schwarz superstring

The problem of quantization of superstrings is traced back to the nilpotency of gauge generators of the first-generation ghosts. The quantization of such theories is performed. The novel feature of this quantization is the freedom in choosing the number of ghost generations as well as gauge conditions. As an example, we perform the quantization of the heterotic string in a gauge that preserves spacetime supersymmetry. The equations of motion are those of a free theory.     

Soliton quantization in gauge theories

We present a simple quantization method for solitons in gauge theories based on a straight-forward application of pathintegral techniques. There is no zero mode problem and the intricacies of the canonical approach (the Dirac theory of constrained systems) are avoided.     

Stochastic quantization and regularization

In this paper the method of stochastic quantization introduced by Parisi and Wu is extended to field theories that include fermions and are supersymmetric. A new non-perturbative regulator based on stochastic quantization is introduced. This regulator preserves all the symmetries of the lagrangian, including gauge, chiral, and supersymmetries, at the expense of introducing non-locality.     

Fermions and gauge fields in the Einstein static universe

Exact solutions of the massive Dirac equation are obtained in an SU(2) gauge field background in the Einstein static universe. The static, finite-energy gauge field used as background is the one obtained by continuing the meron-antimeron solution to this base space. The regular spinor solutions lead to a quantization condition.     

On the structure of generalized monopole solutions in gauge theories

A method is presented for constructing generalized 't Hooft monopole solutions in a gauge theory with an arbitrary gauge group. We derive restriction arising from the condition of finite energy. The radial oscillation of the solution is discussed. Using our method we reproduce all the SU(3) solutions known in the literature. Finite energy monopoles possessing magnetic charge in the range g₀?kg₀?(N?1)g₀ are found in SU(N) gauge theories. Different charge quantization conditions are analyzed to understand the structure of our solutions.     

The Chern-Simons theory and knot polynomials

The Chern-Simons gauge theory is studied using a functional integral quantization. This leads to a differential equation for expectations of Wilson lines. The solution of this differential equation is shown to be simply related to the two-variable Jones polynomial of the corresponding link, in the case where the gauge group isSU(N). A similar equation has been used before to get the Jones polynomial from a braid representation of the link. The main novelty of our approach is that we get the Jones polynomial from a plat representation of the link.     

Equivalence of stochastic and canonical quantization in perturbation theory

It is shown that the stochastic quantization method introduced by Parisi and Wu reproduces, order by order, the ordinary perturbation expansion. The proof is valid for any field theory, including gauge theories, provided one considers gauge-invariant quantities.     

Becchi-Rouet-Stora-Tyutin quantization and Hamiltonian formalism

An introductory review of BRST hamiltonian formalism is presented. The method of quantization of gauge and string theories is discussed. A few simple examples are presented to illustrate the BRST techniques.     

Remarks on a New Possible Discretization Scheme for Gauge Theories

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.     

Gaussian quantization of the Klein-Gordon equation in variational derivatives and secondary quantization of a Boson string

A Klein-Gordon equation in variational derivatives is proposed for the quantum theory of a Boson string in a fixed gauge. By using this equation a secondary quantization is constructed for a Boson string in the functional space of string functionals that are square summable in a countable additive Gaussian measure.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 32–36, January, 1990.The author is grateful to V. S. Vladimirov and I. V. Volovich for useful discussions of the quantum and field theories of a boson string.     

Electric-charge quantization in gauge theories

The electric-charge quantization and fixing conditions of particles are found using a number of gauge theories, and it is shown that the presence of Higgs fields is a necessary condition for the electric-charge quantization in the considered models.     

超对称电动力学系统的Faddeev-Senjanovic量子化

用Faddeev-Senjanovic量子化方法对超对称电动力学系统在一般情况下进行了量子化, 得到了格林函数的生成泛函. 通过对一些约束作线性组合获得了另一个第一类约束, 构造出了该体系的规范生成元, 导出了该系统的规范不变的对称变. 由一个规范条件的自恰性导出了另一个规范条件, 发现超对称电动力学系统的次级第一类约束对应物理电荷守恒律, 从而使过去要算很多次级约束才能截断的约束自然截断, 因而使超对称电动力学系统在一般情况下的Faddeev-Senjanovic量子化被简化.     

Renormalization group equations and the continuum limit of some renormalizable quantum field theories

The renormalization group equations for asymptotically and non-asymptotically free theories are discussed by exploiting the general properties of their integral curves. Some constraints are derived on the existence of a consistent continuum limit for pure Yang-Mills theories in an infinite quantization volume. An analogy between the far infrared behaviour of non-abelian gauge theories and the deep ultraviolet one of asymptotically free theories is discussed.     

Gauge fixing procedure in the extended BRST theory. The example of the abelian 2‐forms

The paper proposes a general procedure to find the form of the gauge fixing term in the extended BRST quantization of the gauge theories, a difficult problem in the standard approach. Our proposal is based on the many level structure of the extended spaces and leads to a simple form of the gauge fixing term. The abelian 2‐form model is completely analyzed as an example.     

On Generalized Triplectic Quantization

The generalization of a triplectic quantization scheme of gauge theories is considered for the case where the reference space is an arbitrary super-Poisson one.