Related papers: A Note on Non-commutativity
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=\omega^{ij}(x), and construct the complete algebra of…
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
A `covariant' field that transforms like a relativistic field operator is required to be a linear combination of `canonical' fields that transform like annihilation and creation operators and with invariant coefficients. The Invariant…
The approximations of classical mechanics resulting from quantum mechanics are richer than a correspondence of classical dynamical variables with self-adjoint Hilbert space operators. Assertion that classical dynamic variables correspond to…
Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the…
We derive the classical limit of quantum mechanics by describing the center of mass of a system constituted by a large number of particles. We will show that in that limit the commutator between the position and velocity of the center of…
At this paper, it is considered to find a way for defining non-commutative spaces by ordinary commutative ones and vice versa. A novel parameter which has not been considered so far is represented. This parameter describes equivalent…
The electromagnetic vacuum is known to have energy. It has been recently argued that the quantum vacuum can possess momentum, that adds up to the momentum of matter. This ``Casimir momentum'' is closely related to the Casimir effect, in…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
Since Einstein's equations $G_{ij} = 8\pi \, G \, T_{ij} \, / c^4 $ relate the metric $g_{ij}$ of spacetime to the energy-momentum tensor $T_{ij}$ which is a quantum field, the metric $g_{ij}$ must be a quantum field. And since the metric…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…
There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which…
Noncommutative phase space of an arbitrary dimension is considered. The both of operators coordinates and momenta in noncommutative phase space may be noncommutative. In this paper, we introduce momentum-momentum noncommutativity in…
Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical…
Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…