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We study the effective Batalin-Vilkovisky quantization theory for chiral deformation of two dimensional conformal field theories. We establish an exact correspondence between renormalized quantum master equations for effective functionals…
Proposed is an alternative method for permutational sampling in quantum gases using the path integral formulation of statistical mechanics. It is shown that in principle we are able to use two operators which enable us to construct a Markov…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
Hamilton-Jacobi theory is a fundamental subject of classical mechanics and has also an important role in the development of quantum mechanics. Its conceptual framework results from the advantages of transformation theory and, for this…
We present a quantum description of photon creation via dynamical Casimir effect based on the standard Hamiltonian formulation. The particle representation is constructed in the expansion of field operators fixed with the initial modes. The…
The scope of the paper has been broadened to include a more complete discussion of the following topics: The derivation of composition laws in quantum cosmology. The connection between the existence of a composition law in the sum over…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
A careful treatment of the discretization errors in the path integral formulation of quantum mechanics leads to a unique prescription for the translation from the Hamiltonian to the action in the functional integral. An example is given by…
This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…
A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a…
The variational formulation for Lie-transform Hamiltonian perturbation theory is presented in terms of an action functional defined on a two-dimensional parameter space. A fundamental equation in Hamiltonian perturbation theory is shown to…
Starting from a solution to the classical Batalin-Vilkovisky master equation,an extended solution to an extended master equation is constructed by coupling all the observables, the anomaly candidates and the generators of global symmetries.…
The canonical structure of theories whose Lagrangian contains higher powers of time derivatives is often obscured by the nonlinear relationship between the velocities and momenta. We use the Dirac formalism and define a generalized Legendre…
We investigate the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lema\^{i}tre-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
Different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism. Firstly, the case of canonoid transformations is studied with great detail and…
We present an integral formalism for constructing scheme transformations in a quantum field theory. We apply this to generate several new useful scheme transformations. A comparative analysis is given of these scheme transformations in…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint…
We consider canonically conjugated generalized space and linear momentum operators $\hat{x}_q$ and $ \hat{p}_q$ in quantum mechanics, associated to a generalized translation operator which produces infinitesimal deformed displacements…
We present the quantum and classical mechanics formalisms for a particle with position-dependent mass in the context of a deformed algebraic structure (named $\kappa$-algebra), motivated by the Kappa-statistics. From this structure we…