Related papers: Relativistic Quantum Theory with Fractional Spin a…
I introduce spin in field theory by emphasizing the close connection between quantum field theory and quantum mechanics. First, I show that the spin-statistics connection can be derived in quantum mechanics without relativity or field…
The fractional quantum and statistical mechanics have been developed via new path integrals approach.
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical…
The majority of current understanding of the quantum correlations is in the field of non-relativistic quantum mechanics. To develop quantum information and computation tasks fully, one must inevitably take into account the relativistic…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…
In the free case, it is possible to define quantum fields which describe particles with integer or half-integer spin larger than one. It is shown that particles with integer spin must have Bose statistic and particles with half-integer-spin…
A realistic physical axiomatic approach of the relativistic quantum field theory is presented. Following the action principle of Schwinger, a covariant and general formulation is obtained. The correspondence principle is not invoked and the…
Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
The framework of locally covariant quantum field theory, an axiomatic approach to quantum field theory in curved spacetime, is reviewed. As a specific focus, the connection between spin and statistics is examined in this context. A new…
In two space dimensions the possibilities of fractional spin as well as fractional statistics exist. I examine the relation between fractional spin and statistics for Laughlin quasi-particles in a two-dimensional electron system with…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the L\'evy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems…
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum…
Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…
A Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales.…
We derive the representation theory of $SU(2)$ from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin $\frac{1}{2}$ particle are described from a…