Related papers: General Superfield Quantization Method. II. Genera…
The rules to construct Lagrangian formulation for $\theta$-superfield theory of fields ($\theta$-STF) are introduced and considered on the whole in the framework of new superfield quantization method for general gauge theories. Algebraic,…
The rules for superfield Lagrangian quantization method for general gauge theories on a basis of their generalization to special superfield models within a so-called $\theta$-superfield theory of fields ($\theta$-STF) are formulated. The…
The basic theorem of the Lagrangian formulation for general superfield theory of fields (GSTF) is proved. The gauge transformations of general type (GTGT) and gauge algebra of generators of GTGT (GGTGT) as the consequences of the above…
Extension procedure for supermanifold ${\cal M}_{cl}$ of superfields ${\cal A}^{\imath}(\theta)$, ghost number construction are considered. Classical and $\hbar$-deformed generating (master) equations, existence theorems for their solutions…
The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…
Reparametrization invariant Lagrangian theories with higher derivatives are considered. We investigate the geometric structures behind these theories and construct the Hamiltonian formalism in a geometric way. The Legendre transformation…
An action principle that applies uniformly to any number N of supercharges is proposed. We perform the reduction to the N=0 partition function by integrating out superpartner fields. As a new feature for theories of extended supersymmetry,…
The field equations of the generalized field theory (GFT) are derived from an action principle. A comparison between (GFT), M\o ller's tetrad theory of gravitation (MTT), and general relativity is carried out regarding the Lagrangian of…
A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…
Within a superfield approach, we formulate a simple quantum generating equation of the field - antifield formalism. Then, we derive the Schroedinger equation with the Hamiltonian whose $\Delta$ - exact part serves as a generator to the…
This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are…
Applied to field theory, the familiar symplectic technique leads to instantaneous Hamiltonian formalism on an infinite-dimensional phase space. A true Hamiltonian partner of first order Lagrangian theory on fibre bundles $Y\to X$ is…
The Hamiltonian and Lagrangian formalisms offer two perspectives on quantum field theory. This paper sets up a framework to compare these approaches for the supersymmetric sigma model. The goal is to use techniques from physics to construct…
Gauge invariant regularization of quantum field theory in the framework of Light-Front (LF) Hamiltonian formalism via introducing a lattice in transverse coordinates and imposing boundary conditions in LF coordinate $x^-$ for gauge fields…
The well-known geometric approach to field theory is based on description of classical fields as sections of fibred manifolds, e.g. bundles with a structure group in gauge theory. In this approach, Lagrangian and Hamiltonian formalisms…
A $\theta$-local formulation of superfield Lagrangian quantization in non-Abelian hypergauges is proposed on the basis of an extension of general reducible gauge theories to special superfield models with a Grassmann parameter $\theta$. We…
A superfield version on superspace $(x^\mu,\theta^a)$ is proposed for the $Sp(2)$-- covariant Lagrangian quantization of general gauge theories. The BRST- and antiBRST- transformations are realized on superfields as supertranslations in the…
A novel routine to investigate the scalar fields in a cosmological context is discussed in the framework of the Hamiltonian formalism. Starting from the Einstein-Hilbert action coupled to a Lagrangian density that contains two components -…
Field theoretical models with first order Lagrangean can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for…
The focus of the thesis is to obtain a universal formalism to evaluate the perturbations during inflation at all orders that can be applied to any theory of gravity and matter source in the early universe. We first look at the equivalence…