相关论文: The principle of symmetric bracket invariance as t…
Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…
Recently we showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p=\partial_q S_0 and exploits a basic GL(2,C)-symmetry which…
The symmetrized product for quantum mechanical observables is defined. It is seen as consisting of the ordinary multiplication and the application of the superoperator that orders the operators of coordinate and momentum. This superoperator…
The noncovariant duality symmetric action put forward by Schwarz-Sen is quantized by means of the Dirac bracket quantization procedure. The resulting quantum theory is shown to be, nevertheless, relativistically invariant.
It is shown that Schroedinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle…
The role of symmetries in formation of quantum dynamics is discussed. A quantum version of the d'Alambert's principle is proposed to take into account symmetry constrains for quantum case. It is noted that in this approach one can find, in…
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…
We demonstrate that the covariance of the algebra of quantum NC fields under quantum-deformed Poincare symmetries implies the appearence of braided algebra of fields and the notion of braided locality in NC QFT. We briefly recall the…
We give a review of brackets and interior products in bosonic string theory, in different representations, used in formulation of a theory and derived in a transformation of related mathematical structures. We consider the C-bracket,…
The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying physics. In this manuscript, it is shown that…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
It is made the attempt to explain why there exists a division between internal symmetries referring to quantum numbers and external symmetries referring to space-time within the description of relativistic quantum field theories. It is hold…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
We consider the double field formulation of the closed bosonic string theory, and calculate the Poisson bracket algebra of the symmetry generators governing both general coordinate and local gauge transformations. Parameters of both of…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
Two-dimensional quantum field theories are important in many problems in physics because they contain exact symmetries and are often completely integrable. We demonstrate the power of bosonization in elucidating the structure of a…
A hypothetical exclusion principle for quantum particles is introduced that generalizes the exclusion and inclusion principles for fermions and bosons, respectively: the correlated exclusion principle. The sum-free condition for Schur…
Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…
The Hamiltonian for a fractional supersymmetric oscillator is derived from three approaches. The first one is based on a decomposition in which a Q-uon gives rise to an ordinary boson and a k-fermion (a k-fermion being an object…