Related papers: Poincar\'e invariant quantum theory, J. Lab lectur…
We review the construction and applications of exactly Poincar\'e invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincar\'e group on few-particle Hilbert…
Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.
A survey of results on quantum Poincare groups and quantum Minkowski spaces is presented.
We present some reflections concerning two papers by H. Poincar\'e concerning the theory of quanta.
We discuss the role of spin in Poincar\'e invariant formulations of quantum mechanics.
It is by now well known that the Poincar\'e group acts on the Moyal plane with a twisted coproduct. Poincar\'e invariant classical field theories can be formulated for this twisted coproduct. In this paper we systematically study such a…
A new quantum gauge model is proposed. From this quantum gauge model we derive a quantum invariant of 3-manifolds. We show that this quantum invariant of 3-manifolds gives a classification of closed (orientable and connected) 3-manifolds.…
We present a bicovariant differential calculus on the quantum Poincare group in two dimensions. Gravity theories on quantum groups are discussed.
This is a series of lecture notes explaining topos theory and its application in physics.
A method is presented for constructing a class of Poincare invariant quantum mechanical models of systems of a finite number of degrees of freedom that satisfy cluster separability, the spectral condition, but do not conserve particle…
The Dirac approach to constrained systems can be adapted to construct relativistic invariant theories on a noncommutative (NC) space. As an example, we propose and discuss relativistic invariant NC particle coupled to electromagnetic field…
The concept of $Diff^4$ invariant Poincare transformations is a cornerstone of T(opological) G(eometro)D(ynamics). This concept makes it possible to understand the concept of subjective time and irreversibelity as well as nontriviality of…
Using the general theory of [10] ( hep-th 9412058 ), quantum Poincar\'e groups (without dilatations) are described and investigated. The description contains a set of numerical parameters which satisfy certain polynomial equations. For most…
The formula for the Poincare series of the algebra of invariant of $n$-ary form is found.
Lead by examples we introduce the notions of Hopf algebra and quantum group. We study their geometry and in particular their Lie algebra (of left invariant vectorfields). The examples of the quantum sl(2) Lie algebra and of the quantum…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
We investigate a formulation of Poincar\'e invariant quantum mechanics where the dynamical input is Euclidean invariant Green functions or their generating functional. We argue that within this framework it is possible to calculate…
I outline the construction of exactly Poincar\'e invariant quantum models that satisfy cluster separability but do not conserve particle number.
We study the variances of the coordinates of an event considered as quantum observables in a Poincare' covariant theory. The starting point is their description in terms of a covariant positive-operator-valued measure on the Minkowski…