相关论文: On the Path Integral Representation for Spin Syste…

We derive a formalism to express the spin algebra $\mathfrak{su}(2)$ in a spin $s$ representation in terms of the algebra of $L$ fermionic operators that obey the Canonical Anti-commutation Relations. We also give the reverse direction of…

In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…

We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model…

A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of…

We derive the gauge-free Hamiltonian structure of an extended kinetic theory, for which the intrinsic spin of the particles is taken into account. Such a semi-classical theory can be of interest for describing, e.g., strongly magnetized…

Resonant behavior involving spin-orbit entangled states occurs for spin transport along a narrow channel defined in a two-dimensional electron gas, including an apparent rapid relaxation of the spin polarization for special values of the…

The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of non-trivial viable dynamic modes for the Poincar\'e gauge theory of gravity. Two modes with propagating spin-zero torsion are analyzed. The…

In this article, we study topological and noninertial effects on the motion of the two-dimensional Dirac oscillator in the presence of a uniform magnetic field and the Aharonov-Bohm potential. We obtain the Dirac equation that describes the…

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…

The role of dynamical chiral condensate in spin polarization is investigated in a kinetic theory framework. Transport equations for quark matter are derived in the mean-field approximation for the Nambu--Jona-Lasinio model. The dynamical…

In this Letter we propose two path integral approaches to describe the classical mechanics of spinning particles. We show how these formulations can be derived from the associated quantum ones via a sort of geometrical dequantization…

In a previous work we showed that spin can be envisioned as living in a phase space that is dual to the standard phase space of position and momentum. In this work we demonstrate that the second class constraints inherent in this "Dual…

A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins),…

The similarity renormalization group is used to transform Dirac Hamiltonian into a diagonal form, which the upper (lower) diagonal element becomes an operator describing Dirac (anti-)particle. The eigenvalues of the operator are verfied to…

We propose a simple model of two-dimensional N=2 superconformal mechanics with a spin-orbit interaction term and demonstrate that it inherits the Galilean symmetry of the initial free-particle system. We then propose a quaternionic…

We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin^c-complex under consideration is allowed to be further twisted by certain exterior power…

The Green function of the quark-antiquark system in the confining background field is analysed using the Feynman-Schwinger formalism. The Hamiltonian for the case of massive spinning quarks is obtained in the form containing essentially…

For the `classical' formulation of a massive spinning particle, the propagator is obtained along with the spin factor. We treat the system with two kinds of constraints that were recently shown to be concerned with the reparametrization…

Lattice formulation of a fermionic field theory defined on a randomly triangulated compact manifold is discussed, with emphasis on the topological problem of defining spin structures on the manifold. An explicit construction is presented…

We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…