Related papers: Remarks on generalized uncertainty principle induc…
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
In this work, we point out an overlooked and subtle feature of the generalized uncertainty principle (GUP) approach to quantizing gravity: namely that different pairs of modified operators with the same modified commutator,…
The generalized uncertainty principle (GUP) is a modification of standard quantum mechanics due to Planck scale effects. The GUP has recently been used to improve the short distance behaviour of classical black hole spacetimes by invoking…
The authors previous derivation of a variational principle from the total work functional, as a generalization of the first variation of an action functional, is extended by deriving a corresponding generalization of the Hamiltonian…
This is a review of the constrained dynamical structure of Poincare gauge theory which concentrates on the basic canonical and gauge properties of the theory, including the identification of constraints, gauge symmetries and conservation…
We consider Uncertainty Principles which take into account the role of gravity and the possible existence of extra spatial dimensions. Explicit expressions for such Generalized Uncertainty Principles in 4+n dimensions are given and their…
It is shown that the Dirac approach to Hamiltonization of singular theories can be slightly modified in such a way that primary Dirac constraints do not appear in the process. According to the modified scheme, Hamiltonian formulation of…
Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of…
In this note we generalize the quantum uncertainty relation proposed by Vancea and Santos [7] in the entropic force law, by introducing Planck scale modifications. The latter is induced by the Generalized Uncertainty Principle. We show that…
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
A method to construct Hamiltonian theories for systems of both ordinary and partial differential equations is presented. The knowledge of a Lagrangian is not at all necessary to achieve the result. The only ingredients required for the…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…
As it is well-known, Poisson brackets play a fundamental role both in mechanics and in classical field theories. In this paper we develop a theory of extensions of graded Poisson brackets in graded Dirac manifolds. We then show how these…
A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the…
A carefully motivated symmetric variant of the Poisson bracket in ordinary (not Grassmann) phase space variables is shown to satisfy identities which are in algebraic correspondence with the anticommutation postulates for quantized Fermion…
We look at generalized complex structures from the point of view of Poisson and Dirac geometry and we remark that the puzzling equations underlying the notion of generalized complex structure have miraculously simple meaning when passing to…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
We investigate the transformation laws of coordinates in generalizations of special relativity with two observer-independent scales. The request of covariance leads to simple formulas if one assumes noncanonical Poisson brackets,…