Spinning Particle In Interaction Research Articles

Harmony of spinning conformal blocks

Conformal blocks for correlation functions of tensor operators play an increasingly important role for the conformal bootstrap programme. We develop a universal approach to such spinning blocks through the harmonic analysis of certain bundles over a coset of the conformal group. The resulting Casimir equations are given by a matrix version of the Calogero-Sutherland Hamiltonian that describes the scattering of interacting spinning particles in a 1-dimensional external potential. The approach is illustrated in several examples including fermionic seed blocks in 3D CFT where they take a very simple form.

Ponzano–Regge model revisited: I. Gauge fixing, observables and interacting spinning particles

We show how to properly gauge fix all the symmetries of the Ponzano–Regge model for 3D quantum gravity. This amounts to doing explicit finite computations for transition amplitudes. We give the construction of the transition amplitudes in the presence of interacting quantum spinning particles. We introduce a notion of operators whose expectation value gives rise to either gauge fixing, introduction of time, or insertion of particles, according to the choice. We give the link between the spin foam quantization and the Hamiltonian quantization. We finally show the link between the Ponzano–Regge model and the quantization of Chern–Simons theory based on the double quantum group of SU(2).

A neutral spinning particle in interaction with a magnetic field and Poschl–Teller potential

The problem of a neutral spinning particle in interaction with a linear increasing rotating magnetic field and a Poschl–Teller potential is considered via path integrals. The calculations are carried out explicitly using an external current source. The problem is then reduced to that of a spinning forced Poschl–Teller oscillator whose spin is coupled to external derivative current sources. The result of the propagator is given as a series. The relative propagator of this forced oscillator is converted to that of an angular momentum via an extension of the dimension. Next, the series is exactly summed by means of a Laplace transformation and the orthonormalization relation of the eigenfunctions of the angular momentum.

Exact Path Integral for Neutral Spinning Particle in Interaction with Helical Magnetic Field

In this paper we consider a neutral spinning particle in interaction with a helical magnetic field using the path integral formalism. The spin matrices are replaced by two fermionic oscillators via the Schwinger model. The calculations are done explicitly with the help of an identity over two auxiliary fields. The propagator is exactly evaluated and the energy spectrum and the corresponding wave functions are then deduced.

Spinning Particle in Interaction with Plane Wave Field Via Path Integral

An exact solution for a spinning particle in interaction with an electromagnetic plane wave field is obtained using classical equations of motion. The Green's function is found and the result agrees with those of the literature. Besides, the Polyakov spin factor has been explicitly deduced.

Path integral for a neutral spinning particle in interaction with a rotating magnetic field and a scalar potential

In this paper we consider a neutral spinning particle in interaction with a linear increasing rotating magnetic field and a scalar harmonic potential using the path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger’s model. The calculations are carried out explicitly using fermionic exterior current sources. The problem is then reduced to that of a spinning forced harmonic particle whose spin is coupled to exterior derivative current sources. The result of the propagator is given as a series which is exactly summed up by means of the Laplace transformation and the use of some recurrence formula of the oscillator wave functions. The energy spectrum and the corresponding wave functions are also deduced.

Path Integral for Dirac Particle in Plane Wave Field

The problem of a relativistic spinning particle in interaction with an electromagnetic plane wave field is treated via path integrals. The dynamics of the spin of the particle is described using the supersymmetric action proposed by Fradkin and Gitman. The problem has been solved by using two identities, one bosonic and the other fermionic, which are related directly to the classical equations of motion. The exact expression of the relative Green's function is given and the result agrees with those of the literature. Further, the suitably normalized wave functions are also extracted.

Relativistic Equations of Motion within Nambu's Formalism of Dynamics

The equations of motion for the relativistic particle in an external electromagnetic field are reformulated within the framework of the Nambu three-order phase space formalism. This formulation implies the mass of a relativistic particle as an integral of motion. The Lorentz-covariant four-vector of momentum is decomposed into two four-dimensional euclidean vectors forming the coordinates of the three-order phase space formalism. The new set of equations of motion describing the motion of a relativistic charged spinning particle in interaction with an external electromagnetic field is given in terms of quaternions. These equations give rise to Lorentz-force equations with no auxiliary conditions.

Path integral for spinning particle in magnetic field via bosonic coherent states

Using the coherent states representation and the Schwinger boson model, the propagator of a spinning particle in interaction with an arbitrary magnetic field is derived in the framework of the path integral formalism. To show the relevance of the formalism to some applications, the Green function of spinning particle s=1/2 in special configuration of magnetic field is calculated. The transition amplitude and Berry’s phase for an arbitrary spin and time dependent magnetic field are deduced. The case of half integer spin is also considered.

New procedure for introduction of lorentz covariant interactions into two-body dirac equations

In the past, Dirac's constraint mechanics and supersymmetries for two interacting spinning particles has yielded compatible two-body Dirac equations for particles interacting through worldscalar and vector potentials. Here, we extend the procedure to include pseudoscalar, pseudovector, and tensor interactions.