Related papers: Classical and quantum Lagrangian field theories wi…
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first…
The correspondence between the BV-formalism and integration theory on supermanifolds is established. An explicit formula for the density on a Lagrangian surface in a superspace provided with an odd symplectic structure and a volume form is…
The connection between the Hamilton and the standard Lagrange formalism is established for a generic Quantum Field Theory with vanishing vacuum expectation values of the fundamental fields. The Effective Actions in both formalisms are the…
We investigate the role of external constraints in quantum field theory using the path integral formalism. We begin by reviewing the quantization of constrained systems and extend the analysis to cases where constraints are added to the…
Lately, to provide a solid ground for quantization of the open string theory with a constant B-field, it has been proposed to treat the boundary conditions as hamiltonian constraints. It seems that this proposal is quite general and should…
An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian…
We quantize the spontaneously broken abelian U(1) Higgs model by using the improved BFT and BFV formalisms. We have constructed the BFT physical fields, and obtain the first class observables including the Hamiltonian in terms of these…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
We introduce a version of the Hamiltonian formalism based on the Clairaut equation theory, which allows us a self-consistent description of systems with degenerate (or singular) Lagrangian. A generalization of the Legendre transform to the…
The purpose of this paper is to study in detail the constraint structure of the Hamiltonian and symplectic-Lagrangian descriptions for the scalar and electromagnetic fields in the presence of spatial boundaries. We carefully discuss the…
The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of…
Boundaries in gauge field theories are known to be the locus of a wealth of interesting phenomena, as illustrated for example by the holographic principle or by the AdS/CFT and bulk-boundary correspondences. In particular, it has been…
In fundamental theories that accounts for quantum gravitational effects, the spacetime causal structure is expected to be quantum uncertain. Previous studies of quantum causal structure focused on finite-dimensional systems. Here we present…
Despite the widely-held premise that initial boundary conditions (BCs) corresponding to measurements/interactions can fully specify a physical subsystem, a literal reading of Hamilton's principle would imply that both initial and final BCs…
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…
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive…
The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of…
Based on the most general principles of reality, gauge and reparametrization invariance, a problem of constructing the action describing dynamics of a classical color-charged particle interacting with background non-Abelian gauge and…
This paper has few different, but interrelated, goals. At first, we will propose a version of discretization of quantum field theory (Chapter 3). We will write down Lagrangians for sample bosonic fields (Section 3.1) and also attempt to…
We discuss a free scalar field subject to generalized Wentzell boundary conditions. On the classical level, we prove well-posedness of the Cauchy problem and in particular causality. Upon quantization, we obtain a field that may naturally…