Related papers: Canonical Transformations in Quantum Mechanics
A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices…
A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit…
The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic…
Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that…
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the…
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…
The method of continuous canonical transformation is applied to the double exchange model with a purpose to eliminate the interaction term responsible for non conservation of magnon number. Set of differential equations for the effective…
The rigorous approach aimed at providing exact analytical results for hybrid classical-quantum models is elaborated on the grounds of generalized algebraic mapping transformations. This conceptually simple method allows one to obtain novel…
In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the method of differential equations has proven…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. That all quantum canonical transformations without an explicit $\hbar$ dependence are also…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
The celebrated quantum no-cloning theorem states that an arbitrary quantum state cannot be cloned perfectly. This raises questions about cloning of classical states, which have also attracted attention. Here, we present a physical approach…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
We discuss canonical transformations in Quantum Field Theory in the framework of the functional-integral approach. In contrast with ordinary Quantum Mechanics, canonical transformations in Quantum Field Theory are mathematically more subtle…
A preferred form for the path integral discretization is suggested that allows the implementation of canonical transformations in quantum theory.