Dirac particle with memory: Proper time non-locality

Non-locality in Particle-physics*

Proper Dirac Quantization of Free Particle on D-Dimensional Sphere

We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in D dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first class in Dirac’s classification scheme. The energy spectrum is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curv...

Stochasticity and Non-locality of Time

We present simple classical dynamical models to illustrate the idea of introducing a stochasticity with non-locality into the time variable. For stochasticity in time, these models include noise in the time variable but not in the “space” variable, which is opposite to the normal description of stochastic dynamics. Similarly with respect to nonlocality, we discuss delayed and predictive dynamic...

Generalized Schwinger proper time method for Dirac operator with dynamical chiral symmetry breaking

Schwinger proper time method is generalized for the calculation of real part of determinant and coincidence limit of inverse for Dirac operator with dynamical chiral symmetry breaking caused by momentum dependent fermion self energy Σ(k2). The obtained series generalizes the heat kernel expansion for hard fermion mass. PACS number(s): 03.65.Db, 11.10Ef, 11.30.Rd, 12.39.Fe

Can nonlocal Dirac operators be topologically proper ?

By examining the analyticity of a sequence of topologically-proper lattice Dirac operators, we show that they tend to a nonlocal Dirac operator. This implies that a nonlocal lattice Dirac operator can have exact zero modes satisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero topological charge. PACS numbers: 11.15.Ha, 11.30.Rd, 11.30.Fs It is well known that all fundame...