Related papers: The Operator Manifold Formalism. I
The need to enforce fermionic antisymmetry in the nuclear many-body problem commonly requires use of single-particle coordinates, defined relative to some fixed origin. To obtain physical operators which nonetheless act on the nuclear…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
The worldline formalism is a useful scheme in Quantum Field Theory which has also become a powerful tool for numerical computations. It is based on the first quantisation of a point-particle whose transition amplitudes correspond to the…
A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration…
The BV formalism is a well-established method for analyzing symmetries and quantization of field theories. In this paper we use the BV formalism to derive partition functions of gauge invariant operators up to equations of motions and their…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
In a previous paper we built a modified Hamiltonian formalism to make possible explicit maps among manifolds. In this paper the modified formalism was generalized. As an application, we have built maps among spaces associated to spinors, as…
An operator formalism for bosonic $\beta-\gamma$ systems on arbitrary algebraic curves is introduced. The classical degrees of freedom are identified and their commutation relations are postulated. The explicit realization of the algebra…
A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter…
We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…
The third quantization formalism of quantum cosmology adds simplicity and conceptual insight into the quantum description of the multiverse. Within such a formalism, the existence of squeezed and entangled states raises the question of…
We describe an efficient scheme for evaluating higher order contributions to primordial cosmological perturbations using the "in-in" formalism, which is the basis of modern calculations of non-Gaussian and higher order contributions to the…
In this paper we try to prepare a framework for field quantization. To this end, we aim to replace the field of scalars R by self-adjoint elements of a commutative C-algebra, and reach an appropriate generalization of geometrical concepts…
We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
The in-out formalism is a systematic and powerful method for finding the effective actions in an electromagnetic field and a curved spacetime provided that the field equation has explicitly known solutions. The effective action becomes…
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
We show that various kinds of one-photon quantum states studied in the field of quantum optics admit ladder operator formalisms and have the generally deformed oscillator algebraic structure. The two-photon case is also considered. We…